Digital Signal Processing

Frequency Analysis of Discrete Time Signal

Question 1
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 2
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.
Question 3
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 4
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 5
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 6
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 7
Marks : +2 | -2
Pass Ratio : 100%
If a power signal has its power density spectrum concentrated about zero frequency, the signal is known as ______________
Low frequency signal
Middle frequency signal
High frequency signal
None of the mentioned
Explanation:
We know that, for a low frequency signal, the power signal has its power density spectrum concentrated about zero frequency.
Question 8
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 9
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 10
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