STUPIDSID
1 (a)
What is zero padding? What are its uses?
3 M
1 (b)
Find the DFT of a sequence x(n)={1,1,0,0} and the IDFT of y(k)={1,0,1,0}.
6 M
1 (c)
Find the DFT of a sequence \[ \begin {align*}x(n)&=1 & for \ n \le n \le 1 \\
&=0 & Otherwise \ \ \ \ \ \ \end{align*} \] \[ for \ N=4 \ plot \ |x(k)| \ and \ \lfloor x(k) \]
8 M
2 (a)
State and prove time shifting property of DFT.
5 M
2 (b)
Find the output y(n) of a filter whose impulse response is h(n)={1,1,1} and the input signal x(n)= {3, -1, 0, 1, 3, 2, 0, 1, 2, 1} using overlap save method.
8 M
2 (c)
Obtain the 8-point circular of the following sequences:
x1(n)={2,3,6,8,2,1,7,5}
x2(n)={0,0,0,0,0,1,0,0}.
x1(n)={2,3,6,8,2,1,7,5}
x2(n)={0,0,0,0,0,1,0,0}.
7 M
3 (a)
Find the DFT of a sequence x(n)={1,2,3,4,4,3,2,1} using DIT-FFT algorithm.
10 M
3 (b)
Compute the IDFT of the sequence
x(k)={7, 0.707 - j0.707, -j, 0.707 - j0.707, 1, 0.707 + j0, 707, j, -0.707 + j0.707} using DIF-FFT algorithm.
x(k)={7, 0.707 - j0.707, -j, 0.707 - j0.707, 1, 0.707 + j0, 707, j, -0.707 + j0.707} using DIF-FFT algorithm.
10 M
4 (a)
Discuss Chirp Z-transformation algorithm.
6 M
4 (b)
Explain the following properties of twiddle factor WN.
i) Symmetric property
ii) Periodicity property
i) Symmetric property
ii) Periodicity property
4 M
4 (c)
Find x(k) for the input sequence x(n)=n+1 and N=8 using DIF-FFT algorithm.
10 M
5 (a)
Design an analog Chebyshev filter for which the squared magnitude response |Ha(jΩ)|2| satisfies the condition \[ 20 \log_{10} |H_a (j\Omega)|_{\Omega=0.2 n} \ge -1; \ \ 20\log_{10} |H_a (j\Omega)|_{\Omega=0.3 n} \le -15 \]
8 M
5 (b)
Distinguish between Butterworth and Chebyshev filters.
4 M
5 (c)
\[ Let \ H(s) = \dfrac {1}{s^2 + \sqrt{2s+1}} \] represent the transfer function of a lowpass filter with a passband of 1 rad/sec. Use frequency transformation to find the transfer functions the following analog filters:
i) A lowpass filter with passband of 10 rad/sec.
ii) A highpass filter with cut off frequency of 10 rad/sec.
i) A lowpass filter with passband of 10 rad/sec.
ii) A highpass filter with cut off frequency of 10 rad/sec.
8 M
6 (a)
What is a rectangular window function? Obtain its frequency domain characteristics.
5 M
6 (b)
Design FIR low pass filter using Hamming window (M=7) and also obtain frequency response for \[ \begin {align*}
H_d (e^{j\omega })&=e^{-3\omega }& 3\pi 4 < \omega < 3\pi /4 \\ &=0; & 3\pi/4 < |\omega| \le \pi \ \ \end{align*} \]
12 M
6 (c)
Explain Gibb's phenomenon.
3 M
7 (a)
What is bilinear transformation? Obtain the transformation formula for bilinear transformation.
10 M
7 (b)
Convert the following transfer function. \[ H(s)=\dfrac {s+a}{(s+a)^2 + b^2} \] into a digital filter with infinite impulse response by the use of impulse invariance mapping technique.
10 M
8 (a)
i) Obtain the cascade realization of the system function
H(z)=(1+2z-1-z-2)(1+z-1-z-2).
ii) Determine the direct from realization of the system function
H(z)=1+2z-1-3z-2-4z-3+5z-4
H(z)=(1+2z-1-z-2)(1+z-1-z-2).
ii) Determine the direct from realization of the system function
H(z)=1+2z-1-3z-2-4z-3+5z-4
6 M
8 (b)
Find the impulse response of an FIR lattice filter with coefficient k1=0.65, k2=0.34, k3=0.8.
9 M
8 (c)
Obtain the direct form-I and direct form-II structure for the filters given by system function \[ H(z) = \dfrac {1+0.4z^{-1}}{1-0.5z^{-1}+0.06z^{-2}} \]
5 M
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