Digital Signal Processing

Frequency Analysis of Discrete Time Signal

Question 1
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 2
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 3
Marks : +2 | -2
Pass Ratio : 100%
What is the Fourier transform X(ω) of a finite energy discrete time signal x(n)?
\\(\\sum_{n=-∞}^∞x(n)e^{-jωn}\\)
\\(\\sum_{n=0}^∞x(n)e^{-jωn}\\)
\\(\\sum_{n=0}^{N-1}x(n)e^{-jωn}\\)
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 4
Marks : +2 | -2
Pass Ratio : 100%
Which of the following relation is true if the signal x(n) is real?
X*(ω)=X(ω)
X*(ω)=X(-ω)
X*(ω)=-X(ω)
None of the mentioned
Explanation:
We know that,
Question 5
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 6
Marks : +2 | -2
Pass Ratio : 100%
What is the Fourier transform of the signal x(n)=u(n)?
\\(\\frac{1}{2sin⁡(ω/2)} e^{j(ω+π)}\\)
\\(\\frac{1}{2sin⁡(ω/2)} e^{j(ω-π)}\\)
\\(\\frac{1}{2sin⁡(ω/2)} e^{j(ω+π)/2}\\)
\\(\\frac{1}{2sin⁡(ω/2)} e^{j(ω-π)/2}\\)
Explanation:
Given x(n)=u(n)
Question 7
Marks : +2 | -2
Pass Ratio : 100%
The sequence x(n)=\\(\\frac{sin⁡ ω_c n}{πn}\\) 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 8
Marks : +2 | -2
Pass Ratio : 100%
What is the period of the Fourier transform X(ω) of the signal x(n)?
Ï€
1
Non-periodic
2Ï€
Explanation:
Let X(ω) be the Fourier transform of a discrete time signal x(n) which is given as
Question 9
Marks : +2 | -2
Pass Ratio : 100%
The Fourier series for the signal x(n)=cos√2πn exists.
True
False
Explanation:
For ω0=√2π, we have f0=1/√2. Since f0 is not a rational number, the signal is not periodic. Consequently, this signal cannot be expanded in a Fourier series.
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.