Hello Peers, Today we are going to share** all week’s assessment and quizzes answers** of the **Digital Signal Processing 1: Basic Concepts and Algorithms **course launched by **Coursera **totally **free of cost**✅✅✅. This is a** certification course** for every interested student.

In case you didn’t find this course for free, then you can** apply for financial ads** to get this course for totally free.

*Check out this article – “How to Apply for Financial Ads?”*

**About The Coursera**

**Coursera**, **India’s biggest learning platform** launched millions of free courses for students daily. These courses are from various recognized universities, where industry experts and professors teach in a very well manner and in a more understandable way.

Here, you will find ** Digital Signal Processing 1: Basic Concepts and AlgorithmsExam Answers** in

**Bold Color**which are given below.

These answers are updated recently and are **100% correct✅** answers of all week, assessment, and final exam answers of **Digital Signal Processing 1: Basic Concepts and Algorithms** from **Coursera Free Certification Course.**

Use “Ctrl+F” To Find Any Questions Answer. & For Mobile User, You Just Need To Click On Three dots In Your Browser & You Will Get A “Find” Option There. Use These Option to Get Any Random Questions Answer.

**About Digital Signal Processing 1: Basic Concepts and Algorithms** **Course**

The subfield of engineering known as digital signal processing is responsible for the extraordinary levels of interpersonal communication and on-demand entertainment that have been made possible in the space of just a few decades. DSP, or digital signal processing, is at the core of the digital revolution that gave rise to CDs, DVDs, MP3 players, mobile phones, and countless other gadgets. It does this by rearranging the fundamental concepts of electronics, telecommunication, and computer science into a unifying paradigm.

You will start from nothing and work your way up to mastering the principles of digital signal processing with this four-part course series. Building a DSP toolkit that is comprehensive enough to analyze a real-world communication system in minute detail will require us to begin with the definition of a discrete-time signal at its most fundamental level. From there, we will move on to topics such as Fourier analysis, filter design, sampling, interpolation, and quantization. In order to bridge the gap that exists between theory and practice, we will routinely make use of hands-on examples and demonstrations.

You will be given several programming examples in the form of Python notebooks, but you are free to use any programming language you like to test the algorithms described in the course. It is recommended that you are proficient in basic calculus and linear algebra in order to get the most out of this class.

**WHAT YOU WILL LEARN**

- The nature of discrete-time signals
- Discrete-time signals are vectors in a vector space
- Discrete-time signals can be analyzed in the frequency domain via the Fourier transform

**Course Apply Link – Digital Signal Processing 1: Basic Concepts and Algorithms**

**Digital Signal Processing 1: Basic Concepts and Algorithms** **Quiz Answers**

### Week 1 Quiz Answers

#### Quiz 1: Homework for Module 1.1 Quiz Answers

Q1. (Difficulty: \star⋆) What are the advantages of using digital signals over analog ones? Choose the correct answer(s).

- Digital signals are more robust to noise.
- Processing of digital signals can be easily implemented in modern computers.
- Digital signals can be easily stored.
- Digital signals contains more information than analog ones.

Q2. (Difficulty: \star⋆) Amongst the signals listed below, select those that are in digital format.

- Music recorded on a CD.
- Music recorded on a vinyl record.
- A handwritten book manuscript.
- JPEG image on a website.

Q3. (Difficulty: \star⋆ \star⋆) Consider the following finite support signal:

x[n]={(−1)nn0for n=1,2,3otherwise

Consider also its periodic repetition

y[n] = \sum_{k=-\infty}^{\infty} x[n + 7k]y[n]=∑

k=−∞

∞

x[n+7k].

Compute the energy of x[n]x[n].

For a guide to entering numerical results, see here; infinity is written as oo, i.e. a double lowercase letter ‘o’.

Enter answer here

Q4. (Difficulty: \star⋆ \star⋆) Consider the same signals as the previous question. Compute the power of x[n]x[n].

For a guide to entering numerical results, see here; infinity is written as oo, i.e. a double lowercase letter ‘o’.

Enter answer here

Q5. (Difficulty: \star⋆ \star⋆) Consider the same signals as the previous question. Compute the energy of y[n]y[n].

For a guide to entering numerical results, see here; infinity is written as oo, i.e. a double lowercase letter ‘o’.

Enter answer here

Q6. (Difficulty: \star⋆ \star⋆) Consider the same signals as the previous question. Compute the power of y[n]y[n].

Enter answer here

- CSS Cheatsheet 2022 | CSS Cheatsheet For Interview | CSS Interview Questions
- The Ultimate HTML Cheatsheet for Beginners | HTML Cheatsheet for Web Developers [Latest Update‼️]
- Best Python Cheatsheet: The Ultimate Guide to Learning Python (Updated 2022) | For Beginners and Experts Alike
- Learn C++ Programming Basic To Advanced | C++ Cheatsheet 2022

Q7. (Difficulty: \star⋆ \star⋆) Consider the signal

x[n] = \delta[n] + 2\delta[n − 1] + 3\delta[n − 2].x[n]=δ[n]+2δ[n−1]+3δ[n−2].

Consider now its moving average, i.e. the signal

- y[n]=\frac{1}{2}(x[n]+x[n-1])y[n]=
- (x[n]+x[n−1])

Select the correct expressions from the options below.

y[n]=0.5\delta[n] + 1.5\delta[n − 1] + 2.5\delta[n − 2]+1.5\delta[n-3]y[n]=0.5δ[n]+1.5δ[n−1]+2.5δ[n−2]+1.5δ[n−3].

The output for n\ge 0n≥0 is always zero.

Q8. (Difficulty: \star⋆) A music song recorded in a studio is stored as a digital sequence on a CD. The analog signal representing the music is 2 minutes long and is sampled at a frequency f_s=44100\;s^{-1}f

s

=44100s

−1

. How many samples should be stored on the CD? Write the number of samples without commas or dots. Assume that the audio file is mono, or in other words, single channel.

Enter answer here

Q9. (Difficulty: \star \star \star⋆⋆⋆) Given the following filter

What is the input-output relationship?

- y[n]=b(ax[n]+x[n-1])-(c+1)x[n-3]y[n]=b(ax[n]+x[n−1])−(c+1)x[n−3].
- y[n]=abx[n]+bx[n-1]+cx[n-3]-x[n-4]y[n]=abx[n]+bx[n−1]+cx[n−3]−x[n−4].
- y[n]=(bax[n]+x[n-1])+(cx[n-3]+x[n-4])y[n]=(bax[n]+x[n−1])+(cx[n−3]+x[n−4]).
- y[n]=b(ax[n]+x[n-1])-(cx[n-3]+x[n-4])y[n]=b(ax[n]+x[n−1])−(cx[n−3]+x[n−4]).

Q10. (Difficulty: \star \star⋆⋆) What is the minimum period PP (in samples) of the signal e^{j(M/N)2\pi n}e

j(M/N)2πn

for M=1,N=3M=1,N=3.

Enter answer here

Q11. (Difficulty: \star \star⋆⋆) What is the minimum period PP (in samples) of the signal e^{j(M/N)2\pi n}e

j(M/N)2πn

for M=5, N=7M=5,N=7.

- Best Operating System Notes in 2022 | Last Minute Notes | Operating System Overview
- Best Python Cheatsheet: The Ultimate Guide to Learning Python (Updated 2022) | For Beginners and Experts Alike
- CSS Cheatsheet 2022 | CSS Cheatsheet For Interview | CSS Interview Questions

Enter answer here

Q12. (Difficulty: \star \star⋆⋆) What is the minimum period PP (in samples) of the signal e^{j(M/N)2\pi n}e

j(M/N)2πn

for M=35, N=15M=35,N=15.

Enter answer here

### Week 2 Quiz Answers

#### Quiz 1: Homework for Module 1.2 Quiz Answers

Q1. (Difficulty: \star⋆) Write the value for the inner product \langle \mathbf{v}^{(0)}, \mathbf{v}^{(1)}\rangle⟨v

(0)

,v

(1)

⟩ where

\mathbf{v}^{(0)}=

⎡⎣⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢12121212⎤⎦⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

and \mathbf{v}^{(1)}=

⎡⎣⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢1212−12−12⎤⎦⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

,

Enter answer here

Q2. (Difficulty: \star⋆\star⋆) Consider the following vectors in \mathbb R^4R

4

\mathbf{v}^{(0)}=

⎡⎣⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢12121212⎤⎦⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

, \mathbf{v}^{(1)}=

⎡⎣⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢1212−12−12⎤⎦⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

and \mathbf{v}^{(2)}=

⎡⎣⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢12−1212−12⎤⎦⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

You can verify that the vectors are mutually orthogonal and have unit norm.

Microsoft Internship For Fresh Graduates 2022 | Free Internship | Especially For College Students

How many different vectors \mathbf{v}^{(3)}v

(3)

could we find such that {\mathbf{v}^{(0)},\ \mathbf{v}^{(1)},\ \mathbf{v}^{(2)},\ \mathbf{v}^{(3)}}{v

(0)

, v

(1)

, v

(2)

, v

(3)

} is a full orthogonal basis in \mathbb R^4R

4

?

0

1

2

3

3

Q3. Let \mathbf{y}=

⎡⎣⎢⎢−0.50.50.51.5⎤⎦⎥⎥

,

what are the expansion coefficients of \mathbf{y}y in the basis {\mathbf{v}^{(0)}, \mathbf{v}^{(1)}, \mathbf{v}^{(2)}, \mathbf{v}^{(3)}}{v

where

\mathbf{v}^{(0)}=

⎡⎣⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢12121212⎤⎦⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

#AnyoneCanCode: Python Essentials 1 | Cisco Free Course With Certificate | Programming Essentials Using Python

, \mathbf{v}^{(1)}=

⎡⎣⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢1212−12−12⎤⎦⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

, \mathbf{v}^{(2)}=

⎡⎣⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢12−1212−12⎤⎦⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

, \mathbf{v}^{(3)}=

⎡⎣⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢12−12−1212⎤⎦⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

Important: Enter your answer as space separated floating point decimal numbers, e.g. the vector \mathbf{y}y would be entered as :

-0.5 0.5 0.5 1.5

Enter answer here

Q4. Which of the following sets form a basis of \mathbb R^4R?

- {\mathbf{y},\mathbf{v}_0,\mathbf{v}_1,\mathbf{v}_2}{y,v
- {\mathbf{y},\mathbf{v}_0,\mathbf{v}_2,\mathbf{v}_3}{y,v
- {\mathbf{y},\mathbf{v}_1+\mathbf{v}_2,\mathbf{v}_2,\mathbf{v}_3}{y,v
- {\mathbf{y},\mathbf{v}_0,\mathbf{v}_1,\mathbf{v}_3}{y,v

Q5. (Difficulty: \star⋆) If we represent finite-length signals as vectors in Euclidean space, many operations on signals can be encoded as a matrix-vector multiplication. Consider for example a circular shift in \mathbb{C}

: a delay by one (i.e. a right shift) transforms the signal \mathbf{x} = [x_0 \, x_1 \, x_2]^Tx=[x

into \mathbf{x}’ = [x_2 \, x_0 \, x_1]^Tx

and it can be described by the matrix

D= ⎡⎣010001100⎤⎦

so that \mathbf{x}’ = D\mathbf{x}x

′

=Dx.

Determine the matrix FF that implements the one-step-difference operator in {C}

i.e. the operator that transforms a signal \mathbf{x}x into [(x_0-x_2) \,\, (x_1-x_0) \,\, (x_2-x_1)]^T[(x

Write the 9 integer matrix coefficients one after the other, row by row and separated by spaces.

Enter answer here

Q6. (Difficulty \star⋆) Given the matrix

A= ⎡⎣⎢⎢0100001000011000⎤⎦⎥⎥

compute the matrix A^4A

(i.e. the fourth power of AA).

(Hint: there is a simple way to do that and, if you’ve solved the previous question, it should be obvious).

Write the 16 integer matrix coefficients one after the other, row by row and separated by spaces.

Enter answer here

### Week 3 Quiz Answers

#### Quiz 1: Homework for Module 1.3 Quiz Answers

Q1. (Difficulty: \star⋆) Write out the phase of the complex numbers a_1=1-\mathrm{j}a

1

=1−j and a_2=-1-\mathrm{j}a

2

=−1−j.

Express the phase in degrees and separate the two phases by a single white space. Each phase should be a number in the range [-180,180][−180,180].

Enter answer here

Q2. (Difficulty: \star⋆) Let W_N^k=e^{-\mathrm{j}\frac{2\pi}{N}k}W

N

k

=e

−j

N

2π

k

and N>1N>1. Then W^{N/2}_NW

N

N/2

is equal to…

-1

1

-\mathrm{j}−j

e^{-\mathrm{j}(2\pi/N)+N}e

−j(2π/N)+N

Q3. (Difficulty: \star⋆) Which of the following signals (continuous- and discrete-time) are periodic signals?

Note that t\in\mathbb{R}t∈R and n\in\mathbb{Z}n∈Z.

1 point

x[n]=1x[n]=1.

x(t)=\cos(2\pi f_0 t+\phi)x(t)=cos(2πf

0

t+ϕ) with f_0\in\mathbb{R}f

0

∈R.

x(t)=t-\operatorname{floor}(t)x(t)=t−floor(t).

x[n]=e^{-\mathrm{j} f_0 n}+e^{+\mathrm{j} f_0 n}x[n]=e

−jf

0

n

+e

+jf

0

n

, where f_0 = \sqrt{2}f

0

=

2

.

x[n] = \sin(n)x[n]=sin(n).

Q4. (Difficulty: \star\star\star⋆⋆⋆) Choose the correct statements from the choices below.

Consider the length-NN signal x[n]=(-1)^nx[n]=(−1)

n

with NN even. Then X[k]=0X[k]=0 for all kk except k=N/2k=N/2

If we apply the DFT twice to a signal x[n]x[n], we obtain the signal itself scaled by NN, i.e. Nx[n]Nx[n].

Consider the length-NN signal x[n]=\cos(\frac{2\pi}{N}Ln+\phi),x[n]=cos(

N

2π

Ln+ϕ), where NN is even and L = N/2L=N/2. Then X[k]=

⎧⎩⎨N2ejϕ0 for k=L otherwise

.X[k]={

2

N

e

jϕ

0

for k=L

otherwise

.

Q5. (Difficulty: \star⋆) Consider the Fourier basis {\mathbf{w}^k}_{k=0,\ldots,N-1}{w

k

}

k=0,…,N−1

, where \mathbf{w}^k[n]=e^{-j \frac{2\pi}{N}nk}w

k

[n]=e

−j

N

2π

nk

for 0\le n\le N-10≤n≤N−1.

Select the correct statement below.

The elements of the basis are orthonormal:

\langle \mathbf{w}^i,\mathbf{w}^j\rangle=

{1 for i=j0 otherwise.

\quad⟨w

i

,w

j

⟩={

1 for i=j

0 otherwise.

The orthogonality of the vectors depends on the length NN of the elements of the basis.

The elements of the basis are orthogonal:

\langle \mathbf{w}^i,\mathbf{w}^j\rangle=

{N for i=j0 otherwise.

\quad⟨w

i

,w

j

⟩={

N for i=j

0 otherwise.

Q6. (Difficulty: \star\star⋆⋆) Consider the three sinusoids of length N=64N=64 as illustrated in the above figure; note that the signal values are shown from n=0n=0 to n=63n=63.

Call y_1[n]y

1

[n] the blue signal, y_2[n]y

2

[n] the green and y_3[n]y

3

[n] the red. Further, define x[n] = y_1[n] + y_2[n] + y_3[n]x[n]=y

1

[n]+y

2

[n]+y

3

[n].

Choose the correct statements from the list below. Note that the capital letters indicate the DFT vectors.

Y_2[k]=

⎧⎩⎨16j16j0 for k=8 for k=56 otherwise

Y

2

[k]=

⎩

⎪

⎪

⎨

⎪

⎪

⎧

16j

16j

0

for k=8

for k=56

otherwise

Y_1[k]=

{N0 for k=4,60 otherwise

Y

1

[k]={

N

0

for k=4,60

otherwise

Y_3[k]=

⎧⎩⎨32320 for k=0 for k=64 otherwise

Y

3

[k]=

⎩

⎪

⎪

⎨

⎪

⎪

⎧

32

32

0

for k=0

for k=64

otherwise

|x|_2^2=|X|_2^2=12800∥x∥

2

2

=∥X∥

2

2

=12800

Q7. (Difficulty: \star\star\star⋆⋆⋆) Consider the length-NN signal

x[n]=\cos\left(2\pi\frac{L}{M}n\right)x[n]=cos(2π

M

L

n)

where MM and LL are integer parameter with 0 \lt L \le N-10<L≤N−1, 0 \lt M \le N0<M≤N.

Choose the correct statements among the choices below.

If N=MN=M and N\neq 2LN

=2L, it is easier to compute the norm of the signal |\mathbf{x}|_2∥x∥

2

in the Fourier domain, using Parseval’s Identity.

Consider the circularly shifted signal y[n]=x[(n-D)\mod N].y[n]=x[(n−D)modN]. In the Fourier domain, since the DFT operator is shift invariant, it is Y[k]=X[k]Y[k]=X[k].

The signal has always exactly LL periods 0 \le n \lt N0≤n<N

The DFT X[k]X[k] has two elements different from zero if N=MN=M and N\neq 2lN

=2l.

Q8. (Difficulty: \star⋆) Consider an orthogonal basis {\phi_i}_{i=0,\dots,N-1}{ϕ

i

}

i=0,…,N−1

for \mathbb{R}^NR

N

. Select the statements that hold for any vector \mathbf{x} \in \mathbb{R}^Nx∈R

N

.

\displaystyle \Vert \mathbf{x}\Vert_2^2 = \frac{1}{P}\sum_{i=0}^{N-1} \vert \langle x , \phi_i \rangle \vert^2∥x∥

2

2

=

P

1

i=0

∑

N−1

∣⟨x,ϕ

i

⟩∣

2

if and only if |\phi_i|_2^2=P∥ϕ

i

∥

2

2

=P \forall i∀i.

\displaystyle \Vert \mathbf{x}\Vert_2^2 = \frac{1}{P}\sum_{i=0}^{N-1} \vert \langle x , \phi_i \rangle \vert^2∥x∥

2

2

=

P

1

i=0

∑

N−1

∣⟨x,ϕ

i

⟩∣

2

if and only if |\phi_i|_2=P∥ϕ

i

∥

2

=P \forall i∀i.

\displaystyle \Vert \mathbf{x}\Vert_2^2 = \sum_{i=0}^{N-1} \vert \langle x , \phi_i \rangle \vert^2 . ∥x∥

2

2

=

i=0

∑

N−1

∣⟨x,ϕ

i

⟩∣

2

.

\displaystyle \Vert \mathbf{x}\Vert_2^2 = \sum_{i=0}^{N-1} \vert \langle x , \phi_i \rangle \vert^2∥x∥

2

2

=

i=0

∑

N−1

∣⟨x,ϕ

i

⟩∣

2

if and only if |\phi_i|_2=1∥ϕ

i

∥

2

=1 \forall i∀i.

Q9. (Difficulty: \star\star⋆⋆) Pick the correct sentence(s) among the following ones regarding the DFT \mathbf{X}X of a signal \mathbf{x}x of length NN, where NN is odd.

Remember the following definitions for an arbitrary signal (asterisk denotes conjugation):

hermitian-symmetry: x[0]x[0] real and x[n]=x[N-n]^*x[n]=x[N−n]

∗

for n=1,\dots,N-1n=1,…,N−1.

hermitian-antisymmetry: x[0]=0x[0]=0 and x[n]=-x[N-n]^*x[n]=−x[N−n]

∗

for n=1,\dots,N-1n=1,…,N−1.

- If the signal \mathbf{x}x is hermitian antisymmetric, then its DFT \mathbf{X}X is purely imaginary.
- If the signal \mathbf{x}x is hermitian-symmetric, then the DFT \mathbf{X}X is also hermitian-symmetric.
- If the signal \mathbf{x}x is purely real, then the DFT \mathbf{X}X is purely imaginary.
- If the signal \mathbf{x}x is hermitian-symmetric, then its DFT is real.

### Week 4 Quiz Answers

#### Quiz 1: Homework for Module 1.4 Quiz Answers

Q1. (Difficulty: \star⋆) Consider the magnitude DTFTs |X(e^{j\omega})|∣X(e

jω

)∣ and |Y(e^{j\omega})|∣Y(e

jω

)∣ shown below, where vertical lines represent Dirac deltas:

Both underlying signals x[n]x[n] and y[n]y[n] are periodic. Find their periods and write them below, separated by a space. Please write the smallest period, i.e. a 5-periodic signal is also obviously 15-periodic but we’re interested in 5.

Enter the period of x[n]x[n] and y[n]y[n] with a unique white space in between.

Enter answer here

Q2. (Difficulty: \star⋆) We will see in later lectures that communication systems must fulfill what is called the “bandwidth constraint”, that is, the energy of the signals that they transmit must strictly fit into pre-defined frequency bands. In this problem we will look at the bandwidth constraint in the discrete-time domain.

The signal x[n]x[n] is real-valued and its spectrum is nonzero only over the [-\pi/8,\ \pi/8][−π/8, π/8] interval. Due to the bandwidth constraint we need to “fit” the signal over the bands indicated in green in the following figure

To this aim, we need to design a processing block \mathcal{H}H in order to convert x[n]x[n] into a sequence s[n]s[n] satisfying the following requirements:

The support of the DTFT of s[n] must be limited to [−3π/4, −π/2]∪[π/2, 3π/4]

The sequence s[n] must be real-valued (x[n] is real-valued)

Which of the following input/output relationships for \mathcal{H}H meet both requirements? (check all correct answers) :

s[n]=\sin(\frac{21\pi}{8}n)\cdot x[n]s[n]=sin(

8

21π

n)⋅x[n]

s[n] = e^{j\frac{5\pi}{8}n}\cdot x[n] s[n]=e

j

8

5π

n

⋅x[n]

s[n]=\cos(\frac{5\pi}{8}n)\cdot x[n]s[n]=cos(

8

5π

n)⋅x[n]

s[n]=\mathrm{IDTFT}{X(e^{j(\omega-5\pi/8)})}s[n]=IDTFT{X(e

j(ω−5π/8)

)}

Q3. (Difficulty: \star⋆) Consider the length-LL signal

x[n]=

{100≤n≤M−1M≤n≤L−1

\; ,x[n]={

1

0

0≤n≤M−1

M≤n≤L−1

,

Write out the closed-form analytical expression for its DFT coefficients X[k]X[k].

Be careful with your typing since the regular-expression parser can be a bit picky. Check Coursera help to enter math expression. In particular, remember that in the Coursera platform the symbols are different:

II (capital i) is used for the imaginary unit instead of jj

Euler’s number is EE instead of ee

you can also use the exponential function \exp(\cdot)exp(⋅)

\piπ is defined as pipi

The only other symbols you’ll need for the answer are the case-sensitive variables k, M, Lk,M,L.

Finally, do not forget to validate your syntax by clicking “Preview” before submitting your answer.

For instance, the expression e^{j(\pi L + 3\pi)}/(k + M)e

j(πL+3π)

/(k+M) should be entered as

E^(I*(pi*L + 3 * pi))/(k + M)

Preview will appear here…

Enter math expression here

Q4. The real and imaginary parts of X(e^{j\omega})X(e

jω

) are:

After examining the plots, check all the correct statements below.

x[n]x[n] is Hermitian-symmetric x[n]=x^\ast[-n]x[n]=x

∗

[−n].

x[n]x[n] is 0-mean, i.e. \sum_{n\in\mathbb Z} x[n]=0∑

n∈Z

x[n]=0.

x[n]x[n] is real valued.

Q5. (Difficulty: \star \star⋆⋆) Consider a signal x[n]x[n] and its DTFT X(e^{j\omega})X(e

jω

). Assume X(e^{j\omega})X(e

jω

) is differentiable. Compute the inverse DTFT of

j\frac{d}{d\omega}X(e^{j\omega})j

dω

d

X(e

jω

).

You should write your answer in terms of x[n]x[n] and elementary functions and constants, for example \frac{\pi}{2}x[n]

2

π

x[n] would be written :

pi/2*x[n]

Enter answer here

Q6. (Difficulty: \star⋆) Which property of the DTFT allows you to easily compute the inverse DTFT of 4X(e^{j\omega})/\pi -24X(e

jω

)/π−2 once you know x[n]x[n]? Just type the name of the property.

Enter answer here

Q7. (Difficulty: \star⋆) Take a length-NN signal x[n]x[n] and its DFT X[k]X[k], with 0 \le n,k, \le N-10≤n,k,≤N−1. Next, consider its periodized version \tilde x[n]=x[n\ \mathrm{mod}\ N]

x

~

[n]=x[n mod N] with its DFS \tilde X[k]

X

~

[k] where now n,k \in \mathbb{Z}n,k∈Z.

Which of the following statements are true?

\tilde X[l] = X[l\ \mathrm{mod}\ N]

X

~

[l]=X[l mod N], for all l\in\mathbb Zl∈Z

\tilde X[-2] = X[2]

X

~

[−2]=X[2] for all x[n]x[n] and N>2N>2

\tilde X[k+lN] = X[k]

X

~

[k+lN]=X[k], for all l\in\mathbb Zl∈Z and k=0,…,N-1k=0,…,N−1.

Q8. (Difficulty: ⋆) In the class, we learned how the modulation theorem can help us tune a musical instrument. Martin showed us an example with a bass but of course the same works with a classical guitar. Listen carefully to these two samples (with earphones, if possible); each audio clip is the recording of two notes played together:

Audio clip A

Audio Clip B

Select the correct options below.

- The notes are in tune in audio clip A and out of tune in audio clip B
- The notes are in tune in audio clip B and out of tune in audio clip A
- The notes are out of tune in both audio clips
- The notes are in tune in both audio clips

Q9. (Difficulty: \star\star⋆⋆) A ringback tone is the sound you hear in your landline telephone when the remote phone you are trying to call is ringing.

In most European countries, the ringback tone is a single sinusoid turned on and off periodically while in the USA, the ringbback tone is the sum of 2 sinusoids with relatively close frequencies turned on and off periodically.

Here are two audio clips:

Sample A

Sample B

Just by listening to the clips, you should be able to identify the US ringback tone. Explain in the box below what helped you identify the US tone. Use the wording and concepts that appear in the lecture slides. No credit, without a proper explanation, e.g., “I live there” is not an answer.

(use only lowercase letters in your answer)

Enter answer here

Q10. (Difficulty: \star⋆) As explained in previous question, the European and US ringback tones are composed of one or two sinusoids respectively, multiplied by a square wave switching between 00 and 11. This multiplication by a square wave periodically mutes the sinusoid(s).

Look at the following magnitude DTFT plots (each plot shows the interval [-\pi\ \pi][−π π]) :

Select the correct statement amongst the choices below.

Spectrum (a) corresponds to the European ringback tone.

Spectrum (b) corresponds to the US ringback tone.

Spectrum (a) corresponds to the US ringback tone.

Spectrum (b) corresponds to the European ringback tone.

Q11. (Difficulty: \star⋆) Consider the sequences

x_1[n]=\cos(2\pi n\cdot\sqrt{2}/30)x

1

[n]=cos(2πn⋅

2

/30)

x_2[n]=\cos(2\pi n\cdot 1.41421356/30)x

2

[n]=cos(2πn⋅1.41421356/30)

with n\in\mathbb Zn∈Z

Select the correct statements below.

There exists N\in\mathbb NN∈N for which x_2[n]x

2

[n] has a DFS of size NN

There exists N\in\mathbb NN∈N for which x_1[n]x

1

[n] has a DFS of size NN

Q12. (Difficulty: \star\star⋆⋆) Consider a signal x[n]x[n]; the only thing we know about the signal is that its DTFT is strictly bandlimited between -\frac{\pi}{10}−

10

π

and \frac{\pi}{10}

10

π

. We now modulate the signal to obtain y[n] = x[n]\cos(\omega_c n)y[n]=x[n]cos(ω

c

n).

Among the possibilities below, select all the values for \omega_cω

c

that allow us to perfectly demodulate y[n]y[n].

\frac{11\pi}{12}

12

11π

\frac{9\pi}{10}

10

9π

\frac{\pi}{3}

3

π

\frac{\pi}{20}

20

π

**Conclusion**

Hopefully, this article will be useful for you to find all the **Week, final assessment, and Peer Graded Assessment Answers of Digital Signal Processing 1: Basic Concepts and Algorithms** **Quiz of Coursera** and grab some premium knowledge with less effort. If this article really helped you in any way then make sure to share it with your friends on social media and let them also know about this amazing training. You can also check out our other course Answers. So, be with us guys we will share a lot more free courses and their exam/quiz solutions also, and follow our Techno-RJ **Blog** for more updates.

Great remarkable things here. I am very glad to peer your article. Thanks a lot and i am taking a look ahead to touch you. Will you kindly drop me a e-mail?

I really enjoy reading on this internet site, it has excellent content. “Never fight an inanimate object.” by P. J. O’Rourke.

Thanks a lot for sharing this with all of us you actually know what you’re talking about! Bookmarked. Kindly also visit my web site =). We could have a link exchange contract between us!

This blog is definitely rather handy since I’m at the moment creating an internet floral website – although I am only starting out therefore it’s really fairly small, nothing like this site. Can link to a few of the posts here as they are quite. Thanks much. Zoey Olsen

Great beat ! I would like to apprentice while you amend your website, how could i subscribe for a blog website? The account aided me a acceptable deal. I had been tiny bit acquainted of this your broadcast provided bright clear concept

Very well written post. It will be supportive to anyone who utilizes it, as well as me. Keep doing what you are doing – i will definitely read more posts.

An impressive share, I just given this onto a colleague who was doing a little analysis on this. And he in fact bought me breakfast because I found it for him.. smile. So let me reword that: Thnx for the treat! But yeah Thnkx for spending the time to discuss this, I feel strongly about it and love reading more on this topic. If possible, as you become expertise, would you mind updating your blog with more details? It is highly helpful for me. Big thumb up for this blog post!

I really appreciate this post. I have been looking everywhere for this! Thank goodness I found it on Bing. You have made my day! Thanks again

Howdy! I know this is kinda off topic but I was wondering which blog platform are you using for this website? I’m getting tired of WordPress because I’ve had issues with hackers and I’m looking at options for another platform. I would be great if you could point me in the direction of a good platform.

Great wordpress blog here.. It’s hard to find quality writing like yours these days. I really appreciate people like you! take care

Howdy! I simply want to give a huge thumbs up for the good data you’ve here on this post. I shall be coming again to your weblog for extra soon.

Some really nice and useful information on this internet site, also I think the design contains good features.

I view something truly special in this internet site.

Its like you read my mind! You seem to know a lot about this, like you wrote the book in it or something. I think that you could do with a few pics to drive the message home a little bit, but other than that, this is fantastic blog. An excellent read. I will definitely be back.

Yay google is my queen aided me to find this great site! .

I’m not that much of a online reader to be honest but your sites really nice, keep it up! I’ll go ahead and bookmark your site to come back later. All the best

I consider something really special in this web site.

Thanks a bunch for sharing this with all of us you actually know what you are talking about! Bookmarked. Please also visit my site =). We could have a link exchange agreement between us!

Hmm it seems like your site ate my first comment (it was super long) so I guess I’ll just sum it up what I wrote and say, I’m thoroughly enjoying your blog. I too am an aspiring blog writer but I’m still new to everything. Do you have any tips for newbie blog writers? I’d definitely appreciate it.

As a Newbie, I am constantly searching online for articles that can aid me. Thank you

buy cialis 5mg cialis super active best otc ed pills

Nice post. I learn something more challenging on different blogs everyday. It will always be stimulating to read content from other writers and practice a little something from their store. I’d prefer to use some with the content on my blog whether you don’t mind. Natually I’ll give you a link on your web blog. Thanks for sharing.

Thanks for sharing. I read many of your blog posts, cool, your blog is very good. https://accounts.binance.com/ro/register-person?ref=GJY4VW8W

order cefadroxil 500mg generic order combivir for sale propecia 1mg generic

diflucan 100mg over the counter order diflucan 100mg online ciprofloxacin 500mg uk

order estradiol 1mg pills estrace 1mg for sale prazosin 2mg uk

order vermox tadalis 20mg drug buy generic tadalis 20mg

clindamycin tablet buy erectile dysfunction medications order sildenafil 50mg pill

brand avanafil 100mg brand tadacip 10mg buy diclofenac 50mg online

order indocin online order indocin 50mg without prescription buy cheap generic cefixime

buy trimox paypal oral amoxicillin clarithromycin 250mg over the counter

bimatoprost pills buy cheap generic bimatoprost buy generic trazodone for sale

buy clonidine 0.1 mg online buy tiotropium bromide 9 mcg pill tiotropium bromide 9 mcg drug

order suhagra 100mg generic sildenafil 100 mg order sildalis generic

order minomycin buy minocycline 100mg sale buy actos generic

buy isotretinoin online cheap order amoxicillin pills cheap zithromax

order generic arava 20mg sildenafil pills 25mg order azulfidine 500mg online

generic cialis 10mg buy viagra 50mg without prescription real cialis fast shipping

buy azipro without a prescription buy gabapentin generic buy neurontin paypal

stromectol for lice brand prednisone 20mg deltasone 40mg drug

generic furosemide albuterol 2mg pill buy ventolin online cheap

order levitra 10mg without prescription order hydroxychloroquine 400mg without prescription buy hydroxychloroquine paypal

order levitra 10mg sale zanaflex where to buy order plaquenil online cheap

buy mesalamine without prescription azelastine online buy buy avapro 300mg pills

buy temovate for sale buy generic temovate order amiodarone 200mg pill

clobetasol order temovate price order amiodarone 200mg without prescription

carvedilol pill buy cenforce paypal buy aralen pills

buy acetazolamide online cheap buy isosorbide 40mg sale imuran tablet

buy digoxin 250mg without prescription buy molnupiravir 200 mg pill generic molnunat

naproxen 250mg pill order naproxen 250mg without prescription order lansoprazole 15mg online

order proventil 100mcg for sale protonix where to buy brand pyridium

baricitinib 2mg drug metformin 1000mg price buy atorvastatin 10mg without prescription

singulair canada buy montelukast cheap buy avlosulfon 100mg pill

brand nifedipine 30mg order adalat for sale buy fexofenadine 120mg for sale

order norvasc pill cheap omeprazole 10mg order generic omeprazole 10mg

I genuinely value your work, Great post.

priligy price buy dapoxetine online cheap cost xenical

lopressor 100mg drug atenolol pills buy methylprednisolone 4 mg

diltiazem price brand allopurinol order zyloprim 300mg pill

aristocort 4mg usa buy claritin online loratadine 10mg canada

generic rosuvastatin order domperidone generic motilium sale

purchase tetracycline generic tetracycline ca ozobax order online

sulfamethoxazole uk cost sulfamethoxazole clindamycin pill

order toradol 10mg for sale buy colchicine 0.5mg online purchase inderal pill

buy plavix no prescription generic clopidogrel 75mg how to get coumadin without a prescription

erythromycin 500mg us sildenafil 100mg tablet buy nolvadex pills for sale

buy reglan generic esomeprazole 40mg pills buy generic nexium online

topiramate 200mg pill order topamax 200mg online cheap buy levaquin 250mg online

buy methocarbamol 500mg robaxin for sale online suhagra 50mg canada

dutasteride order online order ranitidine 150mg without prescription buy generic mobic

aurogra 50mg without prescription sildenafil overnight estrace 2mg price

order generic celecoxib 100mg buy flomax online cheap zofran 8mg generic

lamotrigine 50mg canada minipress 1mg cost minipress online buy

buy aldactone 25mg generic valacyclovir oral valtrex over the counter

order generic tretinoin retin cream cheap buy avanafil 100mg

order finasteride generic buy propecia generic buy viagra 100mg generic

order cialis 40mg without prescription buy cialis without prescription viagra order

tadacip 10mg without prescription purchase diclofenac pill purchase indomethacin without prescription

order tadalafil 10mg ed pills that work ed pills that really work

oral lamisil 250mg suprax pills order amoxicillin 250mg

cheap azulfidine olmesartan 10mg for sale buy verapamil tablets

purchase arimidex anastrozole drug catapres online buy

where can i buy divalproex acetazolamide cheap where can i buy imdur

order meclizine 25mg online cheap order minocycline 50mg sale buy generic minocin

azathioprine online order digoxin 250mg without prescription buy micardis 20mg pill

buy molnupiravir tablets purchase movfor for sale order cefdinir 300 mg sale

otc ed pills that work buy viagra 100mg without prescription order sildenafil without prescription

lansoprazole 15mg cheap buy prevacid without a prescription buy pantoprazole paypal

cost phenazopyridine 200mg purchase singulair sale buy amantadine 100mg sale

medicine for erectile cialis 5mg oral tadalafil pills

avlosulfon 100 mg oral dapsone 100mg brand buy generic aceon 8mg

fexofenadine 120mg over the counter buy allegra 120mg pill purchase glimepiride pill

hytrin sale buy actos 30mg cost tadalafil

etoricoxib 60mg uk cost arcoxia 60mg order azelastine sprayers

where to buy avapro without a prescription buspar 5mg pill buspirone 5mg oral

amiodarone 100mg oral buy cheap generic cordarone order phenytoin 100mg pill

cost albendazole abilify 20mg canada buy provera 5mg for sale

purchase furadantin sale buy pamelor 25mg without prescription buy nortriptyline 25 mg for sale

buy fluvoxamine 100mg online cheap buy duloxetine no prescription duloxetine for sale online

oral glipizide buy betamethasone 20gm sale buy betnovate generic

anacin 500 mg for sale order paroxetine 10mg pills order famotidine 40mg for sale

anafranil without prescription buy sporanox 100mg pills prometrium 200mg over the counter

order prograf generic cheap tacrolimus 1mg buy generic ropinirole 2mg

buy generic tindamax 300mg nebivolol price how to buy bystolic

rocaltrol uk generic labetalol buy fenofibrate 200mg pills

buy decadron 0,5 mg for sale buy nateglinide medication nateglinide ca

order trileptal 300mg generic where can i buy trileptal urso 300mg over the counter

I don’t think the title of your article matches the content lol. Just kidding, mainly because I had some doubts after reading the article. https://accounts.binance.com/zh-TC/register?ref=YY80CKRN

bupropion pills cetirizine 5mg without prescription strattera order online

order capoten 25 mg online buy carbamazepine pills for sale carbamazepine 400mg canada

order generic ciprofloxacin 500 mg cefadroxil ca duricef buy online

buy seroquel no prescription buy seroquel 50mg pill buy escitalopram 20mg online cheap

purchase lamivudine pills pill zidovudine 300 mg cost accupril 10mg

fluoxetine for sale online letrozole 2.5mg uk buy femara 2.5 mg pills

order frumil 5 mg generic order clindamycin without prescription order generic zovirax

buy zebeta pills buy oxytetracycline online buy oxytetracycline 250mg generic

buy valaciclovir tablets order ofloxacin 200mg pill ofloxacin 200mg cost

cefpodoxime 100mg over the counter order cefaclor 250mg capsules purchase flixotide generic

levetiracetam 1000mg oral order tobra 10mg generic sildenafil next day delivery

cheap tadalafil pill viagra generic usa viagra sales

zaditor 1mg generic zaditor 1 mg tablet tofranil online buy

purchase minoxytop online cheap cialis sales buy ed pills for sale

where can i buy acarbose buy acarbose pills for sale buy griseofulvin 250 mg for sale

Wow! Thank you! I always wanted to write on my website something like that. Can I include a fragment of your post to my blog?

What i do not realize is in fact how you are not really a lot more neatly-appreciated than you might be now. You’re very intelligent. You understand therefore significantly when it comes to this subject, made me individually imagine it from so many varied angles. Its like men and women aren’t interested unless it is something to accomplish with Woman gaga! Your own stuffs great. All the time deal with it up!

aspirin canada buy generic aspirin imiquad drug

buy dipyridamole 25mg for sale lopid 300mg ca pravachol 10mg tablet

meloset 3mg without prescription order danazol generic cost danocrine 100 mg

dydrogesterone 10mg brand dydrogesterone 10mg ca jardiance 25mg without prescription

Thank you for the good writeup. It in reality was

once a enjoyment account it. Look complicated to far introduced agreeable from you!

By the way, how could we keep in touch?

order fludrocortisone online dulcolax 5 mg without prescription imodium for sale online

prasugrel 10mg generic thorazine 100mg uk tolterodine 2mg for sale

Exceptional post however , I was wanting to know if you could write a litte more on this topic?

I’d be very grateful if you could elaborate a little bit more.

Kudos!

order ferrous sulfate 100 mg purchase ferrous pills cost sotalol 40mg

Hello, There’s no doubt that your site might be having browser compatibility problems.

When I take a look at your web site in Safari, it looks fine but

when opening in IE, it’s got some overlapping issues. I merely wanted to give you a quick heads up!

Apart from that, fantastic website!

pyridostigmine 60 mg price buy maxalt cheap maxalt price

pill enalapril 5mg doxazosin 1mg for sale buy lactulose bottless

buy xalatan medication buy xeloda 500mg exelon 6mg for sale

buy premarin without prescription order premarin for sale order viagra 50mg

order prilosec 10mg sale buy omeprazole 10mg generic metoprolol 100mg price

telmisartan 80mg brand molnunat price molnupiravir 200 mg brand

order tadalafil 10mg online cheap cialis 20mg pills cost viagra 100mg

buy cenforce pills for sale cenforce 100mg pill cost chloroquine

provigil 100mg brand deltasone 5mg tablet order prednisone 10mg pill

order cefdinir 300 mg sale order generic cefdinir 300mg brand lansoprazole 15mg

buy isotretinoin 20mg online cheap buy amoxil 1000mg pill order zithromax 250mg online

azithromycin 250mg over the counter buy neurontin tablets gabapentin 100mg us

atorvastatin generic oral albuterol 100mcg buy norvasc pills

hollywood casino online real money buy furosemide without prescription diuretic generic furosemide 100mg

buy pantoprazole protonix uk pyridium 200 mg generic

free online roulette order acticlate pill antihistamine pills over the counter

casino slot free slots casino ivermectina 6mg

casino slots generic levoxyl cheap levoxyl online

I am really impressed with your writing talents as neatly as with the layout in your weblog.

Is this a paid subject matter or did you modify it yourself?

Anyway keep up the nice quality writing, it’s

rare to see a great blog like this one these days..

buy clomiphene 50mg buy imuran generic imuran 25mg pill

buy cheap methylprednisolone cost triamcinolone buy triamcinolone 10mg online cheap

levitra for sale tizanidine pill order tizanidine 2mg for sale

aceon buy online buy generic fexofenadine online fexofenadine 120mg canada

buy dilantin sale order oxybutynin pills generic ditropan 5mg

order baclofen for sale buy generic ketorolac over the counter ketorolac cost

buy claritin sale order loratadine generic dapoxetine without prescription

purchase lioresal for sale lioresal us ketorolac for sale

fosamax 70mg generic where to buy colchicine without a prescription purchase furadantin sale

buy inderal online order clopidogrel 150mg for sale order plavix sale

buy glimepiride generic amaryl 1mg usa etoricoxib 120mg cheap

buy pamelor tablets how to buy panadol acetaminophen ca

order generic xenical 60mg order orlistat 120mg sale diltiazem 180mg uk

warfarin 2mg drug order paxil 10mg sale cost metoclopramide 20mg

order famotidine 40mg generic brand tacrolimus 5mg buy prograf 5mg generic

astelin buy online buy irbesartan without prescription oral irbesartan 150mg

esomeprazole online order brand topamax 100mg order topiramate without prescription

buy zyloprim 100mg online cheap purchase rosuvastatin for sale

sumatriptan 50mg price order avodart sale oral dutasteride

buspirone online buy buy cheap generic amiodarone order cordarone 100mg

buy generic zantac 150mg purchase zantac generic buy celecoxib medication

domperidone 10mg oral purchase tetracycline online cheap tetracycline over the counter

tamsulosin 0.2mg tablet order zofran 8mg sale zocor where to buy

spironolactone over the counter brand finasteride 1mg proscar for sale online

pay for assignment buy essay service where can i buy a research paper

buy fluconazole 200mg online ciprofloxacin 1000mg cheap baycip without prescription

buy sildenafil 50mg generic buy sildenafil 100mg online cheap estradiol online buy

order metronidazole generic purchase flagyl generic oral keflex 125mg

buy lamictal pills for sale buy minipress 2mg generic order nemazole pill

cleocin for sale online order fildena 50mg pills sildenafil canada

buy retin tablets buy avanafil generic avana tablet

buy generic nolvadex 10mg order betahistine 16 mg pills rhinocort online order

tadacip 20mg us buy generic tadacip 20mg indocin 50mg pills

buy cefuroxime online lumigan for sale purchase robaxin online cheap

buy desyrel generic trazodone price clindamycin cheap

buy aspirin for sale free online slots no download no registration online casinos real money

essay for you purchase suprax online cheap buy cefixime tablets

buy essays for college help writing papers roulette games

buy trimox for sale order trimox 250mg pill biaxin 500mg cheap

buy generic catapres tiotropium bromide 9 mcg pill tiotropium bromide buy online

prescription strength acne treatment how to get rid of body acne fast buy trileptal 300mg online

minomycin oral order minocin 100mg pill order generic requip 2mg

uroxatral medication best allergy over the counter over the counter stomach relief

femara 2.5 mg oral buy albendazole pills abilify ca

sleeping prescription sleeping pills online top 10 strongest sleeping pills online weight loss medication clinic

buy cheap medroxyprogesterone buy hydrochlorothiazide order microzide 25 mg pills

best online herpes medication diabetic pills names list of oral antidiabetic drugs

Hello! I understand this is sort of off-topic but I needed to ask.

Does running a well-established website like yours

take a lot of work? I am brand new to operating a blog but I do

write in my journal everyday. I’d like to start a blog so I can easily share my experience and feelings online.

Please let me know if you have any ideas or tips for new

aspiring blog owners. Appreciate it!

fungus clear now fungus clear does it work high blood pills side effects

order cymbalta 40mg online provigil order order provigil 100mg online

strong medication for ulcers atrial fibrillation first line treatment over the counter urinary tract infection meds

This information is priceless. When can I find out more?

purchase promethazine pill stromectol pill ivermectina 6 mg

buy real estrogen pills antibiotics for nonbacterial prostatitis lifelong premature ejaculation treatment

deltasone 10mg brand buy cheap amoxil amoxicillin for sale online

Utterly composed content material, thankyou for entropy.

I think the admin of this website is truly working hard in favor of his web site, because here every material is quality

based data.

best over the counter ppi top five acid reflux prescription chocolate fart pills

order azithromycin 250mg generic neurontin online buy order gabapentin 100mg pills

oral urso 300mg order actigall 150mg generic order cetirizine without prescription

how to get atomoxetine without a prescription oral quetiapine zoloft price

buy lasix without prescription purchase albuterol generic ventolin 4mg uk

escitalopram pill buy sarafem 40mg pill order naltrexone 50 mg without prescription

generic augmentin augmentin 625mg ca clomid price

buy cheap generic combivent combivent 100mcg over the counter buy linezolid online

starlix usa brand candesartan order atacand 16mg

vardenafil 20mg us brand levitra 20mg order hydroxychloroquine 400mg online cheap

cenforce 100mg uk aralen brand buy glycomet 1000mg generic

Very good blog! Do you have any suggestions for aspiring writers? I’m hoping to start my own site soon but I’m a little lost on everything. Would you advise starting with a free platform like WordPress or go for a paid option? There are so many options out there that I’m totally overwhelmed .. Any recommendations? Kudos!

order lipitor 80mg generic order norvasc 10mg generic cheap lisinopril 5mg

buy cefadroxil generic lamivudine drug how to get combivir without a prescription

I know this if off topic but I’m looking into starting my own weblog and was wondering what all is required to get setup? I’m assuming having a blog like yours would cost a pretty penny? I’m not very internet savvy so I’m not 100 positive. Any tips or advice would be greatly appreciated. Many thanks

cabergoline 0.25mg drug loratadine tablet purchase priligy generic

buy medrol us methylprednisolone 8mg without prescription order clarinex 5mg online

cytotec price misoprostol 200mcg us diltiazem price

nootropil pill buy anafranil generic oral anafranil

zovirax 800mg usa acyclovir 400mg generic buy generic rosuvastatin 10mg

buy itraconazole 100mg without prescription prometrium 100mg uk buy tinidazole online cheap

buy zetia for sale order tetracycline 500mg online tetracycline 250mg price

GlucoTrust is a revolutionary blood sugar support solution that eliminates the underlying causes of type 2 diabetes and associated health risks.

zyprexa 10mg brand zyprexa pill buy diovan no prescription

generic flexeril 15mg buy generic baclofen cheap toradol 10mg

Hmm is anyone else experiencing problems with the pictures on this blog loading?

I’m trying to figure out if its a problem on my end or if it’s

the blog. Any suggestions would be greatly appreciated.

aid for ukraine

buy colcrys 0.5mg online cheap methotrexate 10mg cost methotrexate 10mg price

acne treatment for teenagers purchase cleocin for sale topical acne medication prescription list

Boostaro increases blood flow to the reproductive organs, leading to stronger and more vibrant erections. It provides a powerful boost that can make you feel like you’ve unlocked the secret to firm erections

Neotonics is an essential probiotic supplement that works to support the microbiome in the gut and also works as an anti-aging formula. The formula targets the cause of the aging of the skin.

Be The Ruthless Man In Bed That She Craves For. Be The Master Of Lovemaking Activity Just In A Month And Perform Like The Actor You See In

The Quietum Plus supplement promotes healthy ears, enables clearer hearing, and combats tinnitus by utilizing only the purest natural ingredients. Supplements are widely used for various reasons, including boosting energy, lowering blood pressure, and boosting metabolism.

Kerassentials are natural skin care products with ingredients such as vitamins and plants that help support good health and prevent the appearance of aging skin. They’re also 100% natural and safe to use. The manufacturer states that the product has no negative side effects and is safe to take on a daily basis. Kerassentials is a convenient, easy-to-use formula.

ProDentim is a nutritional dental health supplement that is formulated to reverse serious dental issues and to help maintain good dental health.

InchaGrow is an advanced male enhancement supplement. Discover the natural way to boost your sexual health. Increase desire, improve erections, and experience more intense orgasms.

Herpagreens is a dietary supplement formulated to combat symptoms of herpes by providing the body with high levels of super antioxidants, vitamins

GlucoFlush™ is an all-natural supplement that uses potent ingredients to control your blood sugar.

best allergy medications over the counter theophylline medication how long do antihistamines take to work

heartburn relief without calcium nsaid with least stomach problems

Sight Care is a daily supplement proven in clinical trials and conclusive science to improve vision by nourishing the body from within. The Sight Care formula claims to reverse issues in eyesight, and every ingredient is completely natural.

fantastic publish, very informative. I’m wondering why the other experts of this sector do not notice this. You must proceed your writing. I’m confident, you’ve a huge readers’ base already!

get ambien prescription online where to buy melatonin without a prescription

prednisone 5mg cheap order prednisone sale

Ini benar-benar mengesankan. Anda memiliki bakat yang hebat.

over the counter medication that causes nausea order roxithromycin online

Any updates from the author on the blog lately? We could use more insights on this topic!

I enjoyed your article! The content is well-presented, and I’m wondering if you plan to add more images in your upcoming pieces. It could make the content even more captivating for readers.

Brilliant work! 💪 The article is well-organized, and I’m wondering if you plan to include more images in your upcoming pieces. It could add a visually appealing touch. 🌠

acne treatment for teenage girl order aczone best pimple medication for teenagers

Well-crafted article! The information is valuable, and I believe incorporating more images in your next articles could be beneficial. Have you thought about that?

generic allergy medication list theo-24 Cr 400 mg cheap antihistamine generic names

acid reflux medications prescription list buy avapro cheap

oral isotretinoin 10mg order accutane 10mg pills cost accutane

buy sleeping pills uk online virtual visit online physician insomnia

order amoxicillin 1000mg pills order amoxicillin 1000mg generic amoxil tablets

order azithromycin 250mg without prescription azithromycin pill cost zithromax 250mg

neurontin order online gabapentin 800mg canada

But wanna comment that you have a very nice website , I like the pattern it actually stands out.

buy azithromycin 500mg azipro sale azithromycin 250mg cheap

buy lasix 100mg generic buy furosemide medication

brand prednisolone 40mg order prednisolone 20mg buy omnacortil 5mg online cheap

cheap amoxil purchase amoxicillin generic amoxicillin 250mg cost

vibra-tabs uk buy doxycycline 200mg generic

purchase ventolin pill purchase ventolin pills how to buy albuterol

Hi would you mind stating which blog platform you’re

using? I’m looking to start my own blog in the near future but I’m having a

difficult time deciding between BlogEngine/Wordpress/B2evolution and Drupal.

The reason I ask is because your layout seems different

then most blogs and I’m looking for something completely

unique. P.S My apologies for being off-topic but I had

to ask!

clavulanate ca amoxiclav order

buy generic synthroid for sale purchase levoxyl sale buy cheap generic levothyroxine

buy vardenafil 10mg generic levitra 20mg drug

where can i buy clomid clomid 100mg sale clomiphene 100mg cheap

buy semaglutide generic order semaglutide 14mg generic buy cheap generic rybelsus

Your writing style is so relatable and authentic It’s a breath of fresh air in a world filled with superficiality and pretense

socialmediatric.com

피곤하고 마비 된 호랑이는 쉬고 있습니다. 모두 일찍 쉬어야합니다. 잘 자요!

Aluminium recycling raw material sourcing Aluminium scrap ingot production Aluminium alloy recycling

I learned something new today, thanks to your post!

rivipaolo.com

Fang Jifan은 눈살을 찌푸리며 “그런데 왜 치료를 받아야합니까? “라고 말했습니다.

Your post today was exactly what I needed to read. Thank you for the timely insights!

rybelsus 14mg us order semaglutide 14mg without prescription semaglutide 14 mg brand

This blog is like a safe haven for me, where I can escape the chaos of the world and indulge in positivity and inspiration

agonaga.com

지금 당장, 모두에게 이번 달 안에 살아남는 방법.

You’ve built a blog that’s both informative and a pleasure to read.

The variety and richness of your blog content is impressive.

Your blog provides a unique blend of insights and practical advice.

Your blog provides a unique blend of insights and practical advice.

You manage to make even the most technical topics accessible and interesting.

Your commitment to quality and depth in your writing is clear.

Each article is a testament to your commitment to excellence.

Your writing is a wonderful mix of informative and compelling.

You have a knack for uncovering and sharing hidden gems of knowledge.

The creativity in your topics and presentation is inspiring.

For the reason that the admin of this site is working, no uncertainty very quickly it will be renowned, due to its quality contents.

The personal touch you add to each post makes your blog stand out.

Your writing is a wonderful mix of informative and compelling.

The consistency and quality of your blog content are remarkable.

What makes Sumatra Slim Belly Tonic even more unique is its inspiration from the beautiful Indonesian island of Sumatra. This supplement incorporates ingredients that are indigenous to this stunning island, including the exotic blue spirulina. How amazing is that? By harnessing the power of these rare and natural ingredients, Sumatra Slim Belly Tonic provides you with a weight loss solution that is both effective and enchanting.

netovideo.com

그래서 까이가 무섭고 무서워보였지만 사실은..

Scrap metal reusability Aluminium waste treatment Aluminium alloy recycling process

Metal salvage yard services, Scrap metal prices for aluminum cable, Metal waste reusability

Scrap metal reclamation and reutilization services Scrap aluminium waste audit Aluminum recycling strategies

Metal scrapping, Recycling facilities for aluminum cables, Metal recycling procurement

agonaga.com

“아직 확실하지 않다.” Fang Jifan은 “운에 달려있다”고 말했다.

Scrap metal retrieval Aluminium scrap environmental benefits Scrap aluminium disposal

Metal waste recycling technology, Best practices for aluminum cable recycling, Scrap metal traceability

💫 Wow, this blog is like a rocket blasting off into the galaxy of endless possibilities! 🎢 The captivating content here is a captivating for the mind, sparking excitement at every turn. 🎢 Whether it’s inspiration, this blog is a source of inspiring insights! #InfinitePossibilities Dive into this exciting adventure of discovery and let your imagination soar! 🚀 Don’t just read, immerse yourself in the thrill! #BeyondTheOrdinary Your brain will be grateful for this exciting journey through the dimensions of endless wonder! 🚀

Prostadine is a natural supplement that helps keep the prostate healthy and lowers the chances of it getting bigger. It’s not like medicines with bad effects – it’s made from natural things.

Metal reclaiming Yard Aluminium waste utilization Aluminium scrap consultation services

Scrap metal shredding, Recycling aluminum cable for cash, Scrap metal recycling yard

💫 Wow, this blog is like a fantastic adventure blasting off into the universe of wonder! 💫 The mind-blowing content here is a rollercoaster ride for the mind, sparking awe at every turn. 🌟 Whether it’s technology, this blog is a goldmine of exciting insights! 🌟 Embark into this thrilling experience of imagination and let your mind fly! 🚀 Don’t just read, immerse yourself in the thrill! #BeyondTheOrdinary Your brain will thank you for this exciting journey through the worlds of awe! ✨

saungsantoso.com

게시물에서 Zhen Guo 경은 모든 사람을 Xishan New City로 초대했습니다.

baseballoutsider.com

Zhou Yi는 잠시 침묵했고 서둘러 돌아 왔다고 말할 수 없어서 고개를 끄덕였습니다.

It means so much to receive positive feedback and know that my content is appreciated. I strive to bring new ideas and insights to my readers.

Sugar Defender’s prowess in managing blood sugar is deeply rooted in its exceptional blend of natural ingredients, each playing a distinct role that contributes to the overall success of the supplement. Here are some noteworthy positive impacts of the Sugar Defender Ingredients blend:

I have been struggling with this issue for a while and your post has provided me with much-needed guidance and clarity Thank you so much

chasemusik.com

Fang Jifan은 편리하게 말했습니다. “Wen 씨는 결과를 얻었습니다. 저에게 전화하는 것을 잊지 마십시오.”

Your posts always provide me with a new perspective and encourage me to look at things differently Thank you for broadening my horizons

Introducing Alpilean, a revolutionary weight loss solution dedicated to assisting you in shedding those unwanted pounds through a safe and organic approach. This exceptional supplement is meticulously crafted to synchronize with your body’s innate metabolism, elevating fat-burning capabilities while effectively curbing your appetite. The cornerstone of Alpilean’s success lies in its potent component, alpha-lipoic acid, a remarkable antioxidant renowned for its ability to foster weight loss by enhancing insulin sensitivity and decreasing glucose absorption within the body. Embrace Alpilean and embark on a transformative journey towards a healthier and more vibrant you.

Red Boost is an all-natural dietary supplement that boosts the body’s hormonal levels, blood flow, and supply of oxygen and nutrients.

10yenharwichport.com

Fang Jifan은 “구출 될 수 있다고 생각합니다. “라고 고개를 저었습니다.

kinoboomhd.com

Fang Jifan이 다시 냄새를 맡았습니다. 냄새 나는 젓갈 냄새는 정말 …

Metal recycling center Scrap metal recycling economics Iron and steel waste management

Ferrous material sorting, Iron material repurposing, Scrap metal transport

This Is One Of The Most Comprehensive Articles I’ve Read On This Topic. Kudos!

This Blog Is A Treasure Trove Of Knowledge. Thank You For Your Contributions!

This Is A Brilliant Piece Of Writing. You’ve Nailed It Perfectly!

buy desloratadine medication desloratadine ca clarinex usa

Your articles always make me think and reflect on my own life Thank you for prompting me to be introspective and make positive changes

homefronttoheartland.com

Xishan의 12 명이 아니었다면 아마도 그는 목록에 올랐을 것입니다.

Sugar Defender orchestrates a reduction in blood sugar levels through multifaceted pathways. Its initial impact revolves around enhancing insulin sensitivity, optimizing the body’s efficient use of insulin, ultimately leading to a decrease in blood sugar levels. This proactive strategy works to prevent the storage of glucose as fat, mitigating the risk of developing type 2 diabetes.

Your blog consistently provides valuable insights. We’re thrilled to be avid readers from Asheville!

Your blog is a shining example of excellence in the online sphere. We’re proud supporters from Asheville!

Thank you for sharing such insightful content! In Asheville, we love your blog and can’t wait to come back for more.

Your blog is a true gift to the world. We’re big fans from Asheville!

Your writing has a way of touching hearts and minds. We’re proud supporters of your blog from Asheville!

Hello guys, my name is Katterina! I live in Ukraine!

Thank you for enriching our lives with your wonderful blog. Asheville is blessed to have you!

Your posts always leave me feeling enlightened and inspired. Thank you for sharing your knowledge with us. Asheville sends its love!

Sugar Defender’s prowess in managing blood sugar is deeply rooted in its exceptional blend of natural ingredients, each playing a distinct role that contributes to the overall success of the supplement. Here are some noteworthy positive impacts of the Sugar Defender Ingredients blend:

yangsfitness.com

Liu An의 마음은 약간 피곤했고 신장이 과도하게 당겨진 것 같았습니다.

Thank you for enriching our lives with your wonderful blog. Asheville is blessed to have you!

strelkaproject.com

따라서 산에서의 삶은 소박하고 지루합니다.

Metanail Total Cleanse is a nutritional supplement that complements the effects of Metanail Serum Pro in addressing toenail fungus problems. It is designed to work from the inside out, supporting immunity and aiding in the body’s natural detoxification processes. By taking two capsules daily, you can benefit from its deep action formula.

Your blog is a true masterpiece, crafted with care and passion. We’re proud supporters from Asheville!

Thank you for sharing your expertise with the world through your blog. Asheville residents are grateful for your contributions.

Your blog is a true reflection of your passion and expertise. Asheville is lucky to have you!

Thank you for sharing your expertise with the world through your blog. Asheville residents are grateful for your contributions.

We’re a group of volunteers and starting a new

scheme in our community. Your web site offered us with valuable information to work on. You’ve done an impressive job and our entire

community will be grateful to you.

Your blog is a sanctuary of wisdom and inspiration. We’re grateful readers from Asheville!

lfchungary.com

그는 비틀거리며 말을 하려고 했으나 누가 알겠는가, 상대방의 길을 가로막았다.

sm-online-game.com

새로운 학교는 수도에서 번성했고 대부분의 오래된 학교는 해고되거나 보류되었습니다.

Your words have the power to uplift and inspire. Thank you for sharing your gift with us. Asheville loves your blog!

dota2answers.com

외쳐라: “폐하는 천 살이요, 왕의 전하는 천 살입니다.”

brand prilosec 20mg brand omeprazole 20mg omeprazole over the counter

lfchungary.com

아니나 다를까 많은 사람들이 Liu의 집에 왔고 문 앞에서는 차와 말 소리가 들렸다.류씨 일가의 갑작스러운 행동은 큰일임에 틀림없다.

sm-slot.com

아들이 보낸 편지의 내용이 드디어 확인되었습니다.

lfchungary.com

수많은 사람들이 케이블을 따라 능숙하게 큰 배에서 내리고 삼판을 탔습니다.

Excellent site. A lot of useful information here. I am sending it to some friends ans also sharing in delicious. And obviously, thanks for your sweat!

pragmatic-ko.com

Liu 부인은 상냥하게 웃으며 어쩔 수 없이 말했습니다. “스승님, 빨리 분해하고 알아보십시오.”

sm-slot.com

솔직히 말해서 Fang Jifan은 상당히 외로웠습니다.

andrejpos.com

Fang Jifan은 옆에 서서 귀찮게 움직이지 않고 어깨를 으쓱했습니다. “오.”

lfchungary.com

Fang Jifan은 잠시 생각했지만 진지해졌습니다. “아직도 독특한 비기가 있습니다.”

It means so much to receive positive feedback and know that my content is appreciated. I strive to bring new ideas and insights to my readers.

lfchungary.com

뜻밖에도 폐하께서는 통계의 마법 같은 효과를 한눈에 볼 수 있을 정도로 지혜로우십니다.

Scrap metal reclamation and utilization services Ferrous waste refinement Iron scrap recovery facilities

Ferrous metal recovery and reclaiming, Iron reuse, Scrap metal waste reduction

Keep up the fantastic work!

mega-slot66.com

전하, 얼굴 좀 보여주세요. 여기 오실 때 말씀하신 게 아닙니다.

apksuccess.com

“즉시… 선생님을 위해 책을 편집하고, 서둘러!” Jiang Chen의 흥분된 목소리가 떨리고 있었습니다.

Metal waste smelting Ferrous material bulk handling Iron scrap processing plant

Ferrous material value-added processes, Iron scrap reprocessing plants, Metal reclamation management

mega-slot1.com

“이건…” Fang Jifan과 달리 Zhu Houzhao의 혀는 너무 날카롭지 않습니다.

Metal waste recovery and repurposing Ferrous material baling Iron scrap export procedures

Ferrous metal packaging, Iron waste reusing, Scrap metal remolding

This is such an informative and well-written post! I learned a lot from reading it and will definitely be implementing some of these tips in my own life

chutneyb.com

그는 나가려고 했지만 이른 아침에도 서재에 촛불이 타고 있는 것을 보았습니다.

yangsfitness.com

“예, 예, 부인.” 내시는 병아리를 쫓는 독수리처럼 숨을 헐떡였다.

sm-online-game.com

나 Shen Wen은 좋은 부모라고 할 수 있고 딸도 잘 가르칠 수 있습니다.

sm-casino1.com

전문적인 조정 없이는 이 혼란스러운 장면을 통제할 수 없습니다.

Hello, I think your website might be having browser compatibility issues. When I look at your blog site in Ie, it looks fine but when opening in Internet Explorer, it has some overlapping. I just wanted to give you a quick heads up! Other then that, fantastic blog!

ttbslot.com

잠시 생각에 잠긴 팡지판은 크게 웃었다. “하하하하…”

I feel this is one of the such a lot significant information for me. And i’m glad reading your article. However want to statement on few general things, The site taste is great, the articles is in point of fact nice : D. Good task, cheers

ttbslot.com

폐하는 소파에 앉아 있었고 그의 눈은 유백색이었고 보는 것이 매우 무서웠습니다.

I’m not that much of a internet reader to be honest but your blogs really nice, keep it up! I’ll go ahead and bookmark your website to come back later. All the best

sandyterrace.com

하지만 분명히 … Xiao Jing은 너무 침착해서 침착하게 걸었을 것입니다.

I have been absent for some time, but now I remember why I used to love this site. Thank you, I’ll try and check back more frequently. How frequently you update your web site?

exprimegranada.com

読む価値のある素晴らしい記事でした。

animehangover.com

Wang Jinyuan은 놀라움으로 가득 차서 도울 수 없었지만 말했습니다. “삼촌, 이것은 …”

Regards for helping out, wonderful info. “I have witnessed the softening of the hardest of hearts by a simple smile.” by Goldie Hawn.

I was very pleased to find this web-site.I wanted to thanks for your time for this wonderful read!! I definitely enjoying every little bit of it and I have you bookmarked to check out new stuff you blog post.

Thanks for finally talking about > Digital Signal Processing 1:

Basic Concepts and Algorithms Coursera Quiz Answers 2022 | All Weeks Assessment Answers [💯Correct Answer] – Techno-RJ < Loved it!

What Is Sugar Defender? Sugar Defender is made of natural plant-based ingredients and minerals that support healthy blood sugar levels.

Do you mind if I quote a couple of your posts as long as I provide credit and sources back to your weblog? My blog site is in the very same area of interest as yours and my visitors would definitely benefit from a lot of the information you present here. Please let me know if this okay with you. Appreciate it!

You have mentioned very interesting points! ps decent site.

You actually make it seem so easy with your presentation but I find this topic to be actually something that I think I would never understand. It seems too complex and very broad for me. I’m looking forward for your next post, I will try to get the hang of it!

Would you be interested in exchanging hyperlinks?

Glad to be one of several visitors on this amazing site : D.

You should take part in a contest for one of the best blogs on the web. I will recommend this site!

I will immediately grab your rss as I can not in finding your email subscription hyperlink or e-newsletter service. Do you have any? Kindly let me know in order that I may subscribe. Thanks.

werankcities.com

이때 누군가가 오스만 대사관에 신속하게 소식을 보냈습니다.

thebuzzerpodcast.com

“왕 재무, 좋지 않아 또 떨어졌다 또 떨어졌다 …”

usareallservice.com

このブログはいつも実用的で価値ある情報を提供してくれます。

I know this if off topic but I’m looking into starting my own blog and was wondering what all is needed to get setup? I’m assuming having a blog like yours would cost a pretty penny? I’m not very internet savvy so I’m not 100 certain. Any recommendations or advice would be greatly appreciated. Thanks

tintucnamdinh24h.com

이러한 직관적인 수치는 거버넌스를 위한 마법의 무기일 뿐입니다.

I have read a few excellent stuff here. Certainly value bookmarking for revisiting. I wonder how much attempt you place to create any such wonderful informative web site.

I like what you guys are up also. Such clever work and reporting! Keep up the excellent works guys I’ve incorporated you guys to my blogroll. I think it will improve the value of my site 🙂

Thankyou for this marvellous post, I am glad I detected this web site on yahoo.

toasterovensplus.com

読む価値のある、実用的な内容でした。非常に勉強になります。

mikaspa.com

그런데 왜… 새가 알을 낳지 않는 곳으로…

As a Newbie, I am permanently exploring online for articles that can help me. Thank you

I’m really enjoying the design and layout of your site. It’s a very easy on the eyes which makes it much more pleasant for me to come here and visit more often. Did you hire out a developer to create your theme? Great work!

Thanks for the blog post, is there any way I can receive an update sent in an email whenever you make a new article?

I really like your writing style, great information, thanks for putting up : D.

toasterovensplus.com

素晴らしい情報源です。これからもフォローします。

Thankyou for this fantastic post, I am glad I noticed this site on yahoo.

I think that is one of the most vital information for me. And i’m satisfied reading your article. However wanna statement on few basic things, The web site taste is perfect, the articles is in reality great : D. Just right job, cheers

nikontinoll.com

그러나 폐하가 그들을 동정한다고 해도 그들이 궁궐에서 하룻밤을 지내는 것은 불가능하다.

toasterovensplus.com

素敵な記事でした。いつも明るい気持ちにさせてくれます。

thebuzzerpodcast.com

Hongzhi 황제는 눈살을 찌푸 렸습니다. “Xiao Banban, 무슨 일이야?”

exprimegranada.com

この記事は実用性が高くて、本当に助かります！

tvlore.com

그는 나가려고 했지만 이른 아침에도 서재에 촛불이 타고 있는 것을 보았습니다.

SightCare formula aims to maintain 20/20 vision without the need for any surgical process. This supplement is a perfect solution for people facing issues as they grow older. https://sightcare-web.com/

k8 カジノ 安全性

この記事はとても心に響きました。素晴らしい内容です。

nikontinoll.com

슐레이만 황제는 고개를 끄덕였고 그의 얼굴에 미소가 조금 더 짙어졌다.

Nagano Lean Body Tonic is a groundbreaking powdered supplement crafted to support your weight loss journey effortlessly. https://naganotonic-try.com/

Serolean, a revolutionary weight loss supplement, zeroes in on serotonin—the key neurotransmitter governing mood, appetite, and fat storage. https://serolean-web.com/

NanoDefense Pro utilizes a potent blend of meticulously chosen components aimed at enhancing the wellness of both your nails and skin. https://nanodefense-web.com/

ONLINE EXCLUSIVE OFFER! Only Available for purchase on the official website. Secure Your Package while stocks last https://prodentim-web.com

FlowForce Max is an innovative, natural and effective way to address your prostate problems, while addressing your energy, libido, and vitality. https://flowforcemax-web.com/

CLINICALLY PROVEN* To Increase Semen Volume And Intensity https://semenax-try.com/

DuoTrim is an innovative weight loss supplement that utilizes the power of natural plants and nutrients to create CSM bacteria https://duotrim-us.com/

Dentitox Pro is a liquid dietary solution created as a serum to support healthy gums and teeth. Dentitox Pro formula is made in the best natural way with unique, powerful botanical ingredients that can support healthy teeth. https://dentitox-us.com/

GlucoFlush is an advanced formula specially designed for pancreas support that will let you promote healthy weight by effectively maintaining the blood sugar level and cleansing and strengthening your gut. https://glucoflush-us.com/

Alpha Tonic is a powder-based supplement that uses multiple natural herbs and essential vitamins and minerals to help optimize your body’s natural testosterone levels. https://alphatonic-web.com

Nervogen Pro is an effective dietary supplement designed to help patients with neuropathic pain. When you combine exotic herbs, spices, and other organic substances, your immune system will be strengthened. https://nervogenpro-web.com/

Progenifi