mugup | revision rigorously

Question 1

Marks : +2 | -2

Pass Ratio : 100%

What is the Fourier series representation of a signal x(n) whose period is N?

\\(\\sum_{k=0}^{N+1}c_k e^{j2Ï€kn/N}\\)

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

\\(\\sum_{k=0}^Nc_k e^{j2Ï€kn/N}\\)

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

Explanation:

Here, the frequency F0 of a continuous time signal is divided into 2Ï€/N intervals.

Question 2

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 3

Marks : +2 | -2

Pass Ratio : 100%

The sequence x(n)=\\(\\frac{sinâ¡ Ï‰_c n}{Ï€n}\\) does not have both z-transform and Fourier transform.

True

False

Explanation:

The given x(n) do not have Z-transform. But the sequence have finite energy. So, the given sequence x(n) has a Fourier transform.

Question 4

Marks : +2 | -2

Pass Ratio : 100%

For a signal x(n) to exhibit even symmetry, it should satisfy the condition |X(-Ï‰)|=| X(Ï‰)|.

True

False

Explanation:

We know that, if a signal x(n) is real, then

Question 5

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 6

Marks : +2 | -2

Pass Ratio : 100%

What is the Fourier series representation of a signal x(n) whose period is N?

\\(\\sum_{k=0}^{\\infty}|c_k|^2\\)

\\(\\sum_{k=-\\infty}^{\\infty}|c_k|\\)

\\(\\sum_{k=-\\infty}^0|c_k|^2\\)

\\(\\sum_{k=-\\infty}^{\\infty}|c_k|^2\\)

Explanation:

The average power of a periodic signal x(t) is given as \\(\\frac{1}{T_p}\\int_{t_0}^{t_0+T_p}|x(t)|^2 dt\\)

Question 7

Marks : +2 | -2

Pass Ratio : 100%

What is the equation for average power of discrete time periodic signal x(n) with period N in terms of Fourier series coefficient ck?

\\(\\sum_{k=0}^{N-1}|c_k|\\)

\\(\\sum_{k=0}^{N-1}|c_k|^2\\)

\\(\\sum_{k=0}^N|c_k|^2\\)

\\(\\sum_{k=0}^N|c_k|\\)

Explanation:

We know that Px=\\(\\frac{1}{N} \\sum_{n=0}^{N-1}|x(n)|^2\\)

Question 8

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 9

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 10

Marks : +2 | -2

Pass Ratio : 100%

What is the average power of the discrete time periodic signal x(n) with period N?

\\(\\frac{1}{N} \\sum_{n=0}^{N}|x(n)|\\)

\\(\\frac{1}{N} \\sum_{n=0}^{N-1}|x(n)|\\)

\\(\\frac{1}{N} \\sum_{n=0}^{N}|x(n)|^2\\)

\\(\\frac{1}{N} \\sum_{n=0}^{N-1}|x(n)|^2 \\)

Explanation:

Let us consider a discrete time periodic signal x(n) with period N.

Digital Signal Processing

Frequency Analysis of Discrete Time Signal

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