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) which is defined as shown in the graph below?
Ae-j(ω/2)(L)\\(\\frac{sin⁡(\\frac{ωL}{2})}{sin⁡(\\frac{ω}{2})}\\)
Aej(ω/2)(L-1)\\(\\frac{sin⁡(\\frac{ωL}{2})}{sin⁡(\\frac{ω}{2})}\\)
Ae-j(ω/2)(L-1)\\(\\frac{sin⁡(\\frac{ωL}{2})}{sin⁡(\\frac{ω}{2})}\\)
None of the mentioned
Explanation:
The Fourier transform of this signal is
Question 2
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 3
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 4
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 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%
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 7
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 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%
What are the Fourier series coefficients for the signal x(n)=cosπn/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 10
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,