Question Paper: Discrete Time Signal Processing : Question Paper May 2015 - Electronics & Telecomm. (Semester 7) | Mumbai University (MU)
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## Discrete Time Signal Processing - May 2015

### Electronics & Telecomm. (Semester 7)

TOTAL MARKS: 100
TOTAL TIME: 3 HOURS
(1) Question 1 is compulsory.
(2) Attempt any four from the remaining questions.
(3) Assume data wherever required.
(4) Figures to the right indicate full marks.
1 (a) One of zeros of a causal linear phase FIR filter is at 0.5 e-ix/s. Show the locations of the zeros and hence find the transfer function and impulse response of the filter.(5 marks) 1 (b) Determine Zeros of the following FIR system and indicate when the system is minimum phase maximum phase and mixed phase.
1. H(z)=6+Z-1+Z-1
2. H[z]=1-Z-1-6Z-2
(5 marks)
1 (c) Find the number of complex multiplication and complex additions required to find DFT for 32 point sequence. Compare them with number of computation required if FFT algorithm is used.(5 marks) 1 (d) What is linear phase filters. Define group delay and phase delay.(5 marks) 2 (a) Derive Radix-2 Decimation in Time Fast Fourier-Transform and draw its signal flow graph.(10 marks) 2 (b) X[k]={36, -4+ j 9.656, -4 + j4, -4 +j1.656, -4, -4+j1.656, -4-4j4, -4 - j9.656} Find x[n] using IFFT algorithm (use DD IFFT).(10 marks) 3 (a) An 8 point sequence x[n]={1,2,3,4,5,6,7,8}
i) Find X[k] using DIF-FFT algorithm
ii) Let x1[n]={5,6,7,8,1,2,3,4} using appropriate DFT property and result of part (i) determine X1[k].
(10 marks)
4 (a) Design a Chetryshev I bandstop digital filter with the following specifications:
Passband range: 0 to 275 Hz and 2KHz to ?
Stopband range: 550 to 1000 Hz
Sampling frequency: 8KHz
Passband attenuation: 1dB
Stopping attenuation: 15dB Use BLT and assume T=1sec.
(10 marks)
4 (b) Design a Butterworth filter satisfying the following constraints: \begin {align*} 0.75 \le &|H(w)| \le 1 & for \ 0 \le w \le \pi /2 \ \ \\ & |H(w)|\le 0.2 & for \ 3 \pi /4 \le w \le \pi \end{align*} Use Bilinear Transformation Method.(10 marks) 5 (a) Design FIR digital highpass filter with a frequency response \begin {align*} H(w)&=1 &\pi /4 \le |w|\le \pi \\ &=0 &|w| \le \pi /4 \ \ \ \ \ \ \ \ \end{align*} Use Hamming window: N=7(10 marks) 5 (b) With a neat diagram describe frequency sampling realization of FIR filters.(10 marks) 6 (a) An FIR filter is given by the difference equation $$y[n] = 2x[n] + \dfrac {4}{5} x [ n-1] + \dfrac {3}{2} x [ n-2] + \dfrac {2}{3} x [n-3]$$ Determine the lattice form.(10 marks) 6 (b) Using linear convolution find y[n] for the sequence x[n]={1,2,-1,2,3,-2,-3,-1,1,2,-1} and h[n]={1,2}. Compare the result by solving the problem using overlap save method.(10 marks)

### Write Short Notes On:

7 (a) Digital Resonator.(5 marks) 7 (b) Parseval's Energy theorem and its significance.(5 marks) 7 (c) Goertzel Algorithm.(5 marks) 7 (d) Application of signal processing in RADAR(5 marks)

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