mugup | revision rigorously

Question 1

Marks : +2 | -2

Pass Ratio : 100%

What is the Fourier transform of the signal x(n)=u(n)?

\\(\\frac{1}{2sinâ¡(Ï‰/2)} e^{j(Ï‰+Ï€)}\\)

\\(\\frac{1}{2sinâ¡(Ï‰/2)} e^{j(Ï‰-Ï€)}\\)

\\(\\frac{1}{2sinâ¡(Ï‰/2)} e^{j(Ï‰+Ï€)/2}\\)

\\(\\frac{1}{2sinâ¡(Ï‰/2)} e^{j(Ï‰-Ï€)/2}\\)

Explanation:

Given x(n)=u(n)

Question 2

Marks : +2 | -2

Pass Ratio : 100%

Which of the following condition is to be satisfied for the Fourier transform of a sequence to be equal as the Z-transform of the same sequence?

|z|=1

|z|<1

|z|>1

Can never be equal

Explanation:

Let us consider the signal to be x(n)

Question 3

Marks : +2 | -2

Pass Ratio : 100%

What is the period of the Fourier transform X(Ï‰) of the signal x(n)?

Ï€

1

Non-periodic

2Ï€

Explanation:

Let X(Ï‰) be the Fourier transform of a discrete time signal x(n) which is given as

Question 4

Marks : +2 | -2

Pass Ratio : 100%

If x(n) is a stable sequence so that X(z) converges on to a unit circle, then the complex cepstrum signal is defined as ____________

X(ln X(z))

ln X(z)

X-1(ln X(z))

None of the mentioned

Explanation:

Let us consider a sequence x(n) having a z-transform X(z). We assume that x(n) is a stable sequence so that X(z) converges on to the unit circle. The complex cepstrum of the signal x(n) is defined as the sequence cx(n), which is the inverse z-transform of Cx(z), where Cx(z)=ln X(z)

Question 5

Marks : +2 | -2

Pass Ratio : 100%

What is the Fourier transform X(Ï‰) of a finite energy discrete time signal x(n)?

\\(\\sum_{n=-âˆž}^âˆžx(n)e^{-jÏ‰n}\\)

\\(\\sum_{n=0}^âˆžx(n)e^{-jÏ‰n}\\)

\\(\\sum_{n=0}^{N-1}x(n)e^{-jÏ‰n}\\)

None of the mentioned

Explanation:

If we consider a signal x(n) which is discrete in nature and has finite energy, then the Fourier transform of that signal is given as

Question 6

Marks : +2 | -2

Pass Ratio : 100%

Which of the following relation is true if the signal x(n) is real?

X*(Ï‰)=X(Ï‰)

X*(Ï‰)=X(-Ï‰)

X*(Ï‰)=-X(Ï‰)

None of the mentioned

Explanation:

We know that,

Question 7

Marks : +2 | -2

Pass Ratio : 100%

What are the Fourier series coefficients for the signal x(n)=cosÏ€n/3?

c1=c2=c3=c4=0,c1=c5=1/2

c0=c1=c2=c3=c4=c5=0

c0=c1=c2=c3=c4=c5=1/2

none of the mentioned

Explanation:

In this case, f0=1/6 and hence x(n) is periodic with fundamental period N=6.

Question 8

Marks : +2 | -2

Pass Ratio : 100%

Which of the following represents the phase associated with the frequency component of discrete-time Fourier series(DTFS)?

ej2Ï€kn/N

e-j2Ï€kn/N

ej2Ï€knN

none of the mentioned

Explanation:

We know that,

Question 9

Marks : +2 | -2

Pass Ratio : 100%

What is the expression for Fourier series coefficient ck in terms of the discrete signal x(n)?

\\(\\frac{1}{N} \\sum_{n=0}^{N-1}x(n)e^{j2Ï€kn/N}\\)

\\(N\\sum_{n=0}^{N-1}x(n)e^{-j2Ï€kn/N}\\)

\\(\\frac{1}{N} \\sum_{n=0}^{N+1}x(n)e^{-j2Ï€kn/N}\\)

\\(\\frac{1}{N} \\sum_{n=0}^{N-1}x(n)e^{-j2Ï€kn/N}\\)

Explanation:

We know that, the Fourier series representation of a discrete signal x(n) is given as

Question 10

Marks : +2 | -2

Pass Ratio : 100%

What is the energy density spectrum Sxx(Ï‰) of the signal x(n)=anu(n), |a|<1?

\\(\\frac{1}{1+2acosÏ‰+a^2}\\)

\\(\\frac{1}{1+2asinÏ‰+a^2}\\)

\\(\\frac{1}{1-2asinÏ‰+a^2}\\)

\\(\\frac{1}{1-2acosÏ‰+a^2}\\)

Explanation:

Since |a|<1, the sequence x(n) is absolutely summable, as can be verified by applying the geometric summation formula.

Digital Signal Processing

Frequency Analysis of Discrete Time Signal

CBSE

Exams

Company