## 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 x_{1}(n)=(-3)^{n} for n=0,

1,

2,

3 0 otherwise and x_{2}(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 x_{1(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) =2^{n}u(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)