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Digital Signal Processing : Question Paper Dec 2016 - Computer Engineering (Semester 7) | Mumbai University (MU)

## Digital Signal Processing - Dec 2016

### Computer Engineering (Semester 7)

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) A perform covolution operation between given function in time domain if x1(n)=(-3)n for n=0,
1,
2,
3 0 otherwise and x2(n)=u(n)-u(n-4)
(5 marks)
1(B) Find whether the given signal is energy signal or not x((n)=u(n)-u(n-6).(5 marks) 1(C) State the stability criteria of discrete time sytem and determine the given IIR system is stable or not y(n)=5x(n)+12.(5 marks) 1(D) Find IDFT of X(k)={2,
1-j,
0,
1+j}.
(10 marks)
2(A) Consider the following analog signal
x(t)=2sin(100 * ∏ * t) The signal x(t) is sampled with a sampling rate Fs=50Hz. Determine the discrete time signal . Plot the discrete time signal. And also calculate total numbe of samples.
(10 marks)
2(B) If x1(n)={1,→
2,
3,
6} find X1(K) and p (n)={1,→
6,
3,
2} Find P(K) using X1(K).
(10 marks)
3(A) A Chek whether following systems are:
i) Static or Dynamic
ii) Linear or Non-linear
iii) Shift invariant or variant
iv) Causal or Non-causal.
a) y(n) =2nu(n)
b) y(n)=4x(n)+x(n-2)
(10 marks)
3(B) For x(n)={8,
5,→
2,
4,
2,
2}, plot the following Discrete Time signals:
1) x(n+2)
2) x(n)u(-n)
3) x(n-1)u(n-2)
4) x(-n-1)u(n)
5) x(2n-1)
(10 marks)
4(A) State any five DFT properties.(10 marks) 4(B) Draw the radix 2 DIT FFT and find the DFT of the sequence x(n)={2,
3,
4,
1,
0,
0,
0,
0} using FFT flow graph.
(10 marks)
5(A) Compute LinearConvolution of causal sequence x(n)={5,
6,
2,
4,
1,
4,
5,
2,
3} and h(n)={2,
1,
3,
1} using fast overlap and method.
(10 marks)
5(B) For the FIR digital filter with impulse response given by h(n)=δ(n)+2δ(n-2)+3δ(n-3) sketch the magnitude response of the filter.(10 marks) 6(A) Write a detailed note on TMS 320.(10 marks) 6(B) Write a detailed note on Carls' Correlation Coefficient Algorithm.(10 marks)