Question Paper: Discrete Time Signal Processing : Question Paper May 2013 - Electronics & Telecomm. (Semester 7) | Mumbai University (MU)

Discrete Time Signal Processing - May 2013

Electronics & Telecomm. (Semester 7)

(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) Assume that a complex multiplier takes 1 micro sec to perform one multiplication and that the amount of time to compute a DFT is determined by the amount of time to perform all the multiplications.
(i) How much time does it take to compute a 1024 point DFT directly?
(ii) How much time is required is FFT is used?
(5 marks)
1 (b) Let h[n] be the unit impulse response of a Low Pass filter with a cutoff frequency ωc, what type of filter has a unit sample response g[n]= (-1)n h[n]. (5 marks) 1 (c) A two pole low pass filter has the system function $$H\left(z\right)=\frac{b_0}{{\left(1-pz^{-1}\right)}^z}$$ Determine the values of b0 and P(5 marks) 1 (d) Consider filter with transfer function. Identify the type of filter and justify it.
$$ H\left(z\right)=\frac{z^{-1}-a}{1-az^{-1}}$$
(5 marks)
2 (a) The unit sample response of a system is h(n)={3,2,1} use overlap-add method of linear filtering to determine output sequence for the repeating input sequence x[n]= {2,0,-2,0,2,1,0,-2,-1,0}(10 marks) 2 (b) For a given sequence x(n)= {2,0,0,1}, perform following operation :
(i) Find out the 4 point DFT of x(n)
(ii) Plot x(n), its periodic extension xp(n) and xp(n-3)
(iii) Find out 4 point DFT of xp(n-3)
(iv) Add phase angel in (i) with factor - $$-\ \ [\frac{2\pi{}rk}{N}]$$ where N=4, r=3, k=0,1,2,3
(v) Comment on the result you had in point (i) and (ii)
(10 marks)
3 (a) The transfer function of discrete time causal system is given below :
(i) Find the difference equation
(ii) Draw cascade and parallel realization
(iii) Show pole-zero diagram and then find magnitude at ω = 0 and ω= π
(iv) Calculate the impulse response of the system.
(10 marks)
3 (b) Obtain the lattice realization for the system :
(10 marks)
4 (a) What is a linear phase filter? What conditions are to be satisfied by the impulse response of an FIR system in order to have a linear phase? Plot and justify compulsory zero locations for symmetric even antisymmetric even and antisymmetric odd FIR filters. (10 marks) 4 (b) Determine the zero of be following FIR system and indicate whether the system is minimum phase, maximum phase, or mixed phase
Comment on the stability of the minimum and maximum phase system
(10 marks)
5 (a) A digital low pass filter is required to meet the following specification:
Pass band ripple : ≤1dB
Pass band edge : 4KHz
Stop band attenuation : ≥ 40dB
Stop band edge : 8KHz
Sampling rate : 24KHz
Find order, cutoff frequency and pole locations for Butterworth filter using bilinear transformation.
(10 marks)
5 (b) Design an FIR digital filter to approximate an ideal low pass filter with passband gain of unity, cut-off frequency of 950Hz and working at a sampling frequency of Fs=5000 Hz. The length of the impulse response should be 5. Use a rectangular window. (10 marks) 6 (a) Explain the need of a low pass filter with a decimator and mathematically prove that ωy = ωxD.(10 marks) 6 (b) Why is the direct form FIR structure for a multirate system inefficient? Explain with neat diagrams how this inefficiency is overdone in implementing a decimator and an interpolator.(10 marks)

Write short notes (any four ) :

7 (a) DTMF detection using Geortzel algorithm (5 marks) 7 (b) Filter bank (5 marks) 7 (c) Comparison of FIR and IIR filters (5 marks) 7 (d) Split radix FFT (5 marks) 7 (e) Optimum Equiripple Linear phase FIR filter design (5 marks)

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