Digital Signal Processing (Department Elective-II) — Winter 2018

Adiscrete –time signal x(n) is given below : X(n) = {1,2,1,-2,1,2,3,4,14} ↑ Sketch and label carefully each of the following signals:

x(n-2) (ii) x(-4-n) (iii) x(n/2)

List advantages of Digital Signal Processing over Analog04 Signal Processing.

Find the linear convolution of following pairs of discrete07 sequences

x (n) = {1,2,3,4,12,4,6} h (n) = {4,3,2,1}11 (ii) x (n) = {1,2,1,2,1,2,1} h (n) = {1,2,3,4,3,2,1}11

Obtain Fourier transform of single sided exponential pulse x(n) = an u(n)

Check the following systems for time invariance and Linearity : (i) y(n) = n[x(n)]2 (ii) y(n) = a[x(n)]2+b x(n)

Calculate DTFT of following signals

x(n) = [ ¼ ,¼, ¼, ¼ ] (ii) x(n) = 2( ¾ )n u(n)

Explain Inverse system, minimum phase system and all pass system. Determine Inverse of the system characterized by y(n)=0.5y(n-1)+x(n) assuming zero initial conditions.

03

Find the Z Transform of u(n-1)

The impulse response of t he LTI system is h(n)={2,4,5,6}. ↑ Determine the response of the system to the input signal x(n)={1,1,2,3} ↑

Determine the inverse z-transform of the function X(Z) = , |Z| >1

Find Z-transform of x(n) = [2(4)n – 4(2)n ] u(n)

State and prove the differentiation property of Ztransform.

Determine the response of the system, y(n) = y(n-1) - y(n-2) + x(n) to the input signals. x(n) = δ(n) - δ (n-1)

Define DFT.

Find the IDFT of Y(K)={1,0,1,0}

Explain 8-point DFT from two 4 point DFTs using radix-2 Decimation in frequency (DIF) FFT algorithm.

Find the Circular convolution of following pairs of discrete sequences

x (n) = {3,2,3,4} x (n) ={ 1,3,1,3,2,1}12 ↑ ↑

Obtain the value of X(4) for 8 point DFT if x(n) = {1,-1,0,2,1,-2,-1,1}

Derive DIT FFT flow graph for N = 4 hence find DFT of x(n) = {1, 2, 3, 4}

Write a note on windowing.

Determine H(Z) by using impulse invariant method if H(s) = and sampling time is 0.01 sec.

Obtain Direct Form I & II realization of a system described by y(n) – 1/6 y(n – 1) + 1/3 y(n-2) = x(n) + 2x(n-2)

Compare Decimation in Time and Decimation in Frequency.

Explain Floating point Digital signal processors.

With the help of a neat sketch, explain Digital Signal Processor architecture.