STUPIDSID
1(a)
Define DFT and IDFT of signal. Establish relation between DFT and Z-transform.
6 M
1(b)
Find the IDFT of x(k)= (24, -2j, 0, +2j)
6 M
1(c)
Find the 8-point DFT of the sequence x(n) = {1, 1, 1, 0}
8 M
2(a)
State and prove the circular i) Time-shift
ii) Frequency-shift properties of an N-point sequence.
ii) Frequency-shift properties of an N-point sequence.
6 M
2(b)
Find the 4-point circular convolution of the sequences
x1(n) = (1, 2,3, 1) and x2(n) = (4, 3, 2, 2).
x1(n) = (1, 2,3, 1) and x2(n) = (4, 3, 2, 2).
6 M
2(c)
Let x(k) be a 14-point DFT of length - 14 real sequence x(n). The first 8-samples of x(k) are given by x(0) = 12,
x(1) = -1+3j,
x(2) = 3+4j,
x(3) = 1-5j,
x(5) = 6+3j,
x(6) = -2-3j,
x(7) =10. Find the remaining samples of x(k). Also evaluate the following:
i) x(0)
ii) x(7)
\( iii) \sum ^{13}_{n=0} x(n) \ \ iv) \sum ^{13}_{n=0}|x(n)|^2\)/
x(1) = -1+3j,
x(2) = 3+4j,
x(3) = 1-5j,
x(5) = 6+3j,
x(6) = -2-3j,
x(7) =10. Find the remaining samples of x(k). Also evaluate the following:
i) x(0)
ii) x(7)
\( iii) \sum ^{13}_{n=0} x(n) \ \ iv) \sum ^{13}_{n=0}|x(n)|^2\)/
10 M
3(a)
In the direct computation of N-point DFT of x(n), how many
i) Complex additions
ii) Complex multiplications
iii) Real multiplication
iv) Real additions and v) Trigonometric functions, evaluations are required?
i) Complex additions
ii) Complex multiplications
iii) Real multiplication
iv) Real additions and v) Trigonometric functions, evaluations are required?
10 M
3(b)
Find the output y(n) of a filter whose impulse response h(n) = {1, 2, 3, 4} and the input signal to the filter is x(n) = {1, 2, 1, -1, 3, 0, 5, 6, 2, -2, -5, -6, 7, 1, 2, 0, 1} using overlap add method with 6-point circular convolution.
10 M
4(a)
What is chirp-z-transform? Mention its applications.
4 M
4(b)
Given x(n) = {1,
0,
1,
0}, find x(2) using Goertzel algorithm.
0,
1,
0}, find x(2) using Goertzel algorithm.
6 M
4(c)
Determine 8-point DFT of a signl x(n) using, Radix -2 DIF-FFT algorithm, draw the signal flow graph. x(n) = {0,0.707,1,0.707, 0,-0.707, -1, -0.707}
10 M
5(a)
For Analog Butterworth filter, derive an expression for order. Cut off frequency for design of low pass filter.
10 M
5(b)
Design Butterworth filter for following specification:
0.8≤Ha(s)&le1 for 0≤1KHz and |Ha(s)|≤0.2 fo F≥5KHz
0.8≤Ha(s)&le1 for 0≤1KHz and |Ha(s)|≤0.2 fo F≥5KHz
10 M
6(a)
Realize an FIR filter given by \( h(n)=\left ( \frac{1}{2} \right )^{n}\left [ u(n)-u(n-4) \right ] \)/ using direct from -I.
6 M
6(b)
Obtain the direct from -I, direct from - II, cascade and parallel from realization for the following system. Y(n)=0.75 y(n-1) - 0.125y (n-2) + 6x(n) + 7x(n-1) + (n-2).
14 M
7(a)
Write equations of any four different windows used in design of FIR filters.
8 M
7(b)
Design the symmetric FIR. Low pass filter whose desired frequency response is given as, \( H _d (w) = \left\{\begin{matrix}
e^{-jwt}, & for |w|\leq w_c \\
0,& otherwise
\end{matrix}\right. \)/ The length of the filter should be 7 and wc =1 radian /sample. Use rectangular window.
12 M
8(a)
Explain how analog filter is mapped on to a digital filter using impulse invariant method.
8 M
8(b)
Design a digital low pass filter to satisfy the following pass band ripple 1≤H(jΩ)≤0, for 0≤Ω≤1404π rad/sec and stop band attenuation |H(Ω)| >60dB for Ω≥8268π rad/sec. Sampling interval \( T_s = \frac{1}{10^{-4}} \)/ sec. Use BLT for designing.
12 M
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