Digital Signal Processing — Winter 2022

07

List advantages of Digital over Analog signal processing with application of DSP. If the continuous-time signal

x(t) = 2 cos (400 πt) + 5 sin (1200 πt) + 6 cos (4400 πt) + 2 sin (5200 πt) is sampled at a 8 kHz rate generating the sequence x[n], find x[n].

07

Explain classification of signals with examples. Obtain the linear convolution of following sequences:

x[n]={1,1,0,1,1} and h[n]= {1,-2,-3,4}.

Find the response of the following difference equation:

y[n] - 5 y[n-1] + 6 y[n-2] = x[n], for x[n] = u[n].

07

List properties of Discrete Time Fourier Transform. Prove (1) Shifting and (2) Convolution of two sequences properties. Determine Ztransform of the signal:

x[n] = δ(n+1) + 3 δ(n) + 6 δ(n-3) - δ(n-4).

07

List properties of ROC for the Z-Transform. Determine the inverse Ztransform of the system function

H(z) = 1 / [(1 - 0.2 z-1) z-2]

07

Obtain direct form Irealization of the difference equation, y[n] = b x(n) + b x(n-1) + b x(n-2) + b x(n-3) – a y(n-1) – a y(n-2) – a y(n-3)23 List properties of DFT. State and Prove any two of them.

07

Obtain direct form Irealization for the second order filter given by, y[n] = 2b cos w y(n-1) – b2 y(n-2) + x(n) – b cos w x(n-1)00 Give relationship between DFT, DTFT and Z Transform.

07

Explain Radix-2 Decimation In Frequency (DIF) Algorithm. Describe IIR filter design by Impulse Invariant method.

07

Explain Goertzel algorithm. Explain multiplier-Accumulator (MAC) hardware in DSP

processors.