Digital Signal Processing

Frequency Analysis of Discrete Time Signal

Question 1
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 2
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 3
Marks : +2 | -2
Pass Ratio : 100%
If cx(n) is the complex cepstrum sequence obtained from the inverse Fourier transform of ln X(ω), then what is the expression for cθ(n)?
\\(\\frac{1}{2π} \\int_0^π \\theta(ω) e^{jωn} dω\\)
\\(\\frac{1}{2π} \\int_{-π}^π \\theta(ω) e^{-jωn} dω\\)
\\(\\frac{1}{2π} \\int_0^π \\theta(ω) e^{jωn} dω\\)
\\(\\frac{1}{2π} \\int_{-π}^π \\theta(ω) e^{jωn} dω\\)
Explanation:
We know that,
Question 4
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 5
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 6
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 7
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 8
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 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}^{\\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 10
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)