Digital Signal Processing

Frequency Analysis of Discrete Time Signal

Question 1
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 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%
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 4
Marks : +2 | -2
Pass Ratio : 100%
For a signal x(n) to exhibit even symmetry, it should satisfy the condition |X(-ω)|=| X(ω)|.
True
False
Explanation:
We know that, if a signal x(n) is real, then
Question 5
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 6
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 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 is the energy density spectrum Sxx(ω) of the signal x(n)=anu(n), |a|<1?
\\(\\frac{1}{1+2acosω+a^2}\\)
\\(\\frac{1}{1+2asinω+a^2}\\)
\\(\\frac{1}{1-2asinω+a^2}\\)
\\(\\frac{1}{1-2acosω+a^2}\\)
Explanation:
Since |a|<1, the sequence x(n) is absolutely summable, as can be verified by applying the geometric summation formula.
Question 9
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 10
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,