Digital Signal Processing - May 18

Computer Engineering (Semester 7)

Total marks: 80
Total time: 3 Hours
INSTRUCTIONS
(1) Question No. 1 is compulsory.
(2) Attempt any three from remaining five questions.
(3) Assume suitable data if required.
(4) Figures in brackets on the right hand side indicate full marks.

1(a) Evaluate DFT of x(n)= cos(0.25$\pi$n). (5 marks)

1(b) Determine the energy and power of signal given by x(n)= (1/3)$^n$u(n). (5 marks)

1(c) Find the circular Convolution of the following causal signals.
x$_1$(n)= { 3,2,4,1 } and x$_2$(n)= { 2,1,3 }

(5 marks)

1(d) Define BIBO Stable system. (5 marks)

2(a) A State the following DFT properties:

• 1) Linearity
• 2) Periodicity
• 3) Scaling
• 4) Convolution
• 5) Time Reversal

(10 marks)

2(b) Consider the following analog signal
x(t)= 5 cos2$\pi$(1000t)+ 10 cos2$\pi$(5000t) to be sampled.
I) Evaluate the Nyquist rate for this signal.
II) If the signal is sampled at 4 KHz, will the signal be recovered from its samples?

(10 marks)

3(a) For the causal LTI digital filter with impulse response given by h(n) = $\delta$(n)-2$\delta$(n-1)+$\delta$(n-2)+2$\delta$(n-3) sketch the magnitude response of the filter. (10 marks)

3(b) Design radix 2FFT flow graph for x(n)= {2,1,3,1} (10 marks)

4(a) Check whether the system y[n] = x[n] + 2x[n-2] is :

• i) Static or Dynamic
• ii) Linear or Non-linear
• iii) Causal or Non-Casual
• iv) Shift variant or Shift Invariant

(10 marks)

4(b) Compute linear convolution of the causal sequences x[n]= { 3,4,2,1,2,2,1,1 } and h[n]= {1, -1} using overlap add method. (10 marks)

5(a) For x(n)= {3,↑ 2,1,6,4,5} 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-1)u(n)
• 5) x(n-2)

(10 marks)

5(b) Perform Cross correlation of the causal sequences
x(n)= { 3,3,1,1 } y(n)= { 1,2,1 }

(10 marks)

6(a) Write a detailed note on TMS 320 (10 marks)

6(b) Explain the significance of Carl's Correlation Coefficient Algorithm in digital signal processing. Evaluate Carl's Coefficient for two causal sequences
x[n]= {1,3,4,2} and y[n]= {1,2,2,1}

(10 marks)