STUPIDSID
1 (a)
Define N-point DFT and IDFT of a sequence.
3 M
1 (b)
Find the 8-point DFT of the sequence x(n)= {1, 1, 1, 1, 1, 1, 0, 0}.
8 M
1 (c)
Find the IDFT of X(K) = {4, -2j, 0, 2j}.
6 M
1 (d)
Obtain the relation between DFT and Z-transform.
3 M
2 (a)
State and prove circular convolution property.
6 M
2 (b)
For x(n) = {7, 0, 8, 0}, find y(n), if Y(K)= X((K-2)).
6 M
2 (c)
Let x(n) = {1, 2, 0, 3, -2, 4, 7, 5}. Evaluate the following: \[ i) \ X(0) \\ ii) X(4) \\ iii) \sum_{K=0} X(K) \\ \sum_{K=0}|X(K)|^2 \]
8 M
3 (a)
In the direct computation of N-point DFT of x(n), how many
i) Complex multiplications,
ii) Complex additions
iii) Real multiplications
iv) Real additions and
v) Trigonometric function evaluations are required.
i) Complex multiplications,
ii) Complex additions
iii) Real multiplications
iv) Real additions and
v) Trigonometric function evaluations are required.
10 M
3 (b)
Find the output y(n) of a filter whose impulse response h(n)={1, 2} and input signal x(n)= {1, 2, -1, 2, 3, -2, -3, -1, 1, 1, 2, -1} using overlap save method.
10 M
4 (a)
Develop 8-point DIF-FFT radix-2 algorithm and draw the signal flow graph.
10 M
4 (b)
Find 8-point DFT of a sequence x(n)= {1, 1, 1, 1, 0, 0, 0, 0} using DIT-FFT radix-2 algorithm. Use butterfly diagram.
10 M
5 (a)
Given \( |H_a(j\Omega)|^2 = \dfrac {1}{(1+4\Omega^2)}, \) determine the analog filter system function Ha(s).
8 M
5 (b)
Let \( H(s) = \dfrac {1}{(s^2 + \sqrt{2s}+1)} \) respect transfer function of a low pass filter with a pass band 1 rad/sec. Use frequency transformation to find the transfer function of the analog filters.
i) A LPF with pass band of 10 rad/sec.
ii) A HPF with cut-off frequency of 5 rad/sec.
i) A LPF with pass band of 10 rad/sec.
ii) A HPF with cut-off frequency of 5 rad/sec.
8 M
5 (c)
Compare Butterworth and Chebyshev filters.
4 M
6 (a)
Realize the FIR filter \( H(z)= \dfrac {1}{2}+ \dfrac {1}{3}z^{-1}+ z^{-2}+ \dfrac {1}{4}z^{-3}+ z^{-4}+ \dfrac {1}{3}z^{-5} + \dfrac {1}{2}z^{-6} \) in direct form.
4 M
6 (b)
Obtain direct form-I, direct form-II, cascade and parallel form realization for the following systems: y(n)=0.75 y(n-1)-0.125y(n-2)+6x(n)+7x(n-1)+x(n-2).
16 M
7 (a)
A LPF is to be designed with frequency response. \[ H_d(e^{j\omega}) = H_d(\omega) = \left\{\begin{matrix}
e^{-j2\omega}& |\omega| < \frac {\pi}{4} \ \ \ \ \ \ \\0, & \frac {\pi}{4} <|\omega|<\pi
\end{matrix}\right. \] Determine hd(n) and h(n) if ω(n) is rectangular window, \[ \omega_R(n)= \left\{\begin{matrix}
1 &0\le n \le 4 \\0
& \text {Otherwise}
\end{matrix}\right. \] Also, find the frequency response. H(ω) of the resulting FIR filter.
10 M
7 (b)
Explain the design of linear phase FIR filter using frequency sampling technique.
10 M
8 (a)
Explain the design of IIR filter by using Impulse Invariance Method (IIM) technique also explain mapping of analog to digital filter by IIM.
10 M
8 (b)
Convert the analog filter with system function, \( H_a(s)= \dfrac {s+0.1}{(s+0.1)^2+16} \) into a digital IIR filter by means of bilinear transformation (BJT). The digital filter is to have a resonant frequency of \( \omega_r = \dfrac {\pi}{2} \).
10 M
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