Discrete Time Signal & System - May 2013

Electronics Engineering (Semester 6)

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) Classify the following system on the basis of linearity and time variance/invariance:
(i) y[n] = 4x[n] - 2y[n-1]
(ii) y[n] - 2ny[n-1] = x[n]
(iii) y[n] + 2 y²[n] = 2x[n] - x[n-1]
(iv) y[n] - 2 y[n-1] = 2^x[n] x[n]
(v) y[n] = x[-n] (5 marks) 1 (b) Find the number of complex addition and complex multiplication required to find DFT for 16 point signal. Compare them with number of computations required, if FFT algorithm is used.(5 marks) 1 (c) Prove that discrete time harmonics are not always periodic in frequency. (5 marks) 1 (d) Compare IIR and FIR.(5 marks) 2 (a) Determine causal, non-causal and both sided signal associated with z-transform.
x(z) = [1 + 1.5z^-1 + 0.5z^-2]^-1(10 marks) 2 (b) If x[n] = [3,2,1,2] and h[n] = {1,2,1,2}, then determine linear convolution.(10 marks) 3 (a) Consider a sequence x[n] = {1,2,1,2,0,2,1,2}. Determine DFT using DITFFT.(10 marks) 3 (b) Find DFT of the sequence x[n] = {1,2,3,4} and using this result and not otherwise, find DFT of
(i) x₁[n] = {1,0,2,0,3,0,4,0}
(ii) x₂[n] = {1,2,3,4,0,0,0,0}
(iii) x₃[n] = {1,2,3,4,1,2,3,4}.(10 marks) 4 (a) The transfer function of discrete time system has poles at z=(1/3),z=(+-j/2) and z=-2(+-)j and zeros at z=0 and z=-1.
(i) Sketch pole-zero diagram.
(ii) Derive the system transfer function.
(iii) Develop difference equation.
(iv) Find if the system is stable.(10 marks) 4 (b) Derive the composite radix for δ=2.3 algorithm. Draw the flow chart. (10 marks) 5 (a) Explain Overlap add and Overlap save method.(10 marks) 5 (b) Determine the steady state response of the system
H(z) = (3z²)/(z² -z + 1)for the input
x[n]=(0.6)ⁿ + 2(0.4)ⁿ cos(0.5nπ - 100⁰).(10 marks) 6 (a) Show DF-I, DF-II, cascade and parallel realization for
(10 marks) 6 (b) Let
let the input x[n] = 4 u(n) and the initial conditions be
y[-1]= 0, y[-2] = 12. Find:-
(i) Zero input response.
(ii) Zero state response.
(iii) Total response.(10 marks)

Write short notes on any four:-

7 (a) Properties of DTFT.(5 marks) 7 (b) Goertzel Algorithm.(5 marks) 7 (c) Mapping between s-plane and z-plane.(5 marks) 7 (d) Applications of DSP to Biomedical field.(5 marks) 7 (e) TMS 320C5X series processor.(5 marks)