## Digital Signal Processing - May 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)** Fro the given causal sequences x(n) = {8, 9, 2, 3} and h(n) = {4, 3, 6} find the cross correlation.(5 marks)
**1(b)** State the condition for stability of LTI system and determine for the given discrete time system h(n) = (0.3)^{n}u(n) + 5δ(n), is stable or not.(5 marks)
**1(c)** Differentiate IIR and FIR systems.(5 marks)
**1(d)** For the causal signal x(n) = {2, 2, 4, 4} compute four point DFT using DIT-Fft.(5 marks)
**2(a)** Check whether following system y(n) = 2x(n-1) + x(2n) is:

a. Linear or non Linear

2. Causal or non-causal

3. Time variant or Time invariant

4. Static or Dynamic(10 marks)
**2(b)** Draw the radix 2 DIT flow graph and find the DFT of the sequence x(n) = {10, 11, 8, 5} using FFT flow graph.(10 marks)
**3(a)** A For x(n)={2 3 →4 5 1 3}, plot the following Discrete Time Signals:

1) x(n-1) 2) x(n)u(-n) 3)x(n-1)u(n-1) 4) x(-n)u(n) 5) x(2n)(10 marks)
**3(b)** Determine whether or not the following signals are periodic.

If periodic specify its fundamental peroid,

1. x(n) = sin(0.25πn+0.4)

2. x(n) = cos(0.5nπ) + sin(0.25nπ)(10 marks)
**4(a)** For the FIR digital filter with impluse response given by

h(n) = 2δ (n-4) sketch the magnitude response of the filter.(10 marks)
**4(b)** State any five DFT properties.(10 marks)
**5(a)** Find circular convolution of x_{1}(n) = {5, 6, 2, 1} and x_{2}(n) = {3, 2, 1, 4} by computing DFT of x_{1}(n) and x_{2}(n).(10 marks)
**5(b)** Compute Linear Convolution of causal sequence x(n) = {7, 6, 4, 5, 2, 4, 5, 2, 3} and h(n) = {1 2 3 1} using fast overlap save method.(10 marks)
**6(a)** Write a detailed note on Carl's Correlation Coefficient Algorithm.(10 marks)
**6(b)** Write a detailed note on DSP Processor and Architecture.(10 marks)