## 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)