Question Paper: Discrete Time Signal Processing : Question Paper Dec 2015 - Electronics & Telecomm. (Semester 6) | Mumbai University (MU)
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## Discrete Time Signal Processing - Dec 2015

### Electronics & Telecomm. (Semester 6)

TOTAL MARKS: 80
TOTAL TIME: 3 HOURS
(1) Question 1 is compulsory.
(2) Attempt any three from the remaining questions.
(3) Assume data if required.
(4) Figures to the right indicate full marks.
1 (a) The first five points of eight point DFT of real valued signal are {0.25, 0.125 -j0.3018, 0, 0.125 -j0.0150, 0}. Determine the remaining three points.(5 marks) 1 (b) Sketch the frequency response and identify the following filters based on their passband. $$i) \ h(n) = \left \{1, - \dfrac {1}{2} \right \} \\ ii) \ H(z) = \dfrac {z^{-1}-a}{1-az^{-1}}$$(5 marks) 1 (c) What is multirate DSP? State its applications.(5 marks) 1 (d) An analog filter has transfer function $H(s)= \dfrac {S+0.1}{(S+0.1)^1 + 16}$
Determine transfer function of digital filter using bilinear transformation. The digital filter should have a specification of Ω, = π/2.
(5 marks)
2 (a) Compute DFT of sequence r(n)={1, 2, 2, 2, 1, 0, 0, 0} using DIT-FFT algorithm.(10 marks) 2 (b) Explain the effects coefficients quantization in FIR filters.(10 marks) 3 (a) Implement a two stage decimator for the following specification:
Sampling rate of the input signal = 20,000Hz,
Decimating factor M=100,
Passband=0 to 40Hz,
Passband ripple = 0.01,
Transition band = 40 to 50Hz.
Stop band ripple = 0.002.
(10 marks)
3 (b) If x(n)={1+2j, 3+4j, 5+6j, 7+8j}. Find DFT X(k) using DIF-FFT algorithm.(10 marks) 4 (a) Explain upsampling process in detail and derive for input-output relationship in time domain and frequency domain.(10 marks) 4 (b) Obtain cascade and parallel realization structures for the system described by y(n)= -0.1y(n-1) + 0.72y(n-2) + 0.7x(n) - 0.252 x(n-1).(10 marks) 5 (a) Design a FIR digital filter using windo method for following specifications \begin {align*} H(e^{j\omega}) &= e^{-j3\omega} & 0\le |\omega | \le \dfrac {3\pi}{4} \\ &=0 & \text{otherwise } \ \ \ \end{align*} Use Hamming window of length 7.(10 marks) 5 (b) Design a digital low pass IIR Butterworth filter for the following specification

 Passband ripple : ≤1 dB Passband edge : 4 KHz Stopband attenuation : 40 dB Stop edge : 8 KHz Sampling Rate : 24 KHz

Use bilinear transformation.(10 marks)

### Write a short note on.

6 (a) (i) Dual tone multi frequency signal detection.(5 marks) 6 (a) (ii) Different methods for digital signal synthesis.(5 marks) 6 (b) Determine the zeros of the following FIR systems and indicate whether the system is minimum phase, maximum phase or mixed phase, $$i) \ H_1 (z)= 6+z^{-1}- 6z^{-2} \\ ii) \ H_2 (z)= 1-z^{-1} - 6z^{-2} \\ iii) \ H_3 (z) = 1-\dfrac {5}{2}z^{-1} - \dfrac {3}{2}z^{-2}\\ iv) \ H_4 (z) = 1-\dfrac {5}{2}z^{-1} - \dfrac {2}{3}z^{-2}$$ Comment on stability of minimum and maximum phase system.(10 marks)

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