Digital Signal Processing — Winter 2019

How Digital signal processing is better than Analog signal processing? Explain in brief.

Adiscrete time signal is given by x(n)= { 2, 1, 1, 2, 1 } ↑ sketch the following signal: (1) x (n+1) (2) x (n – 2) (2) x (n) u (n-1) (4) x (n - 1) δ (n -1)

A Digital communication link carries binary coded words representing samples of an input signal x (t) = 3 cos600π t + 2 cos1800π t a The link is operated at 10000 bits/sec and each input sample is quantized into 1024 different voltage level.

What is the sampling frequency & folding frequency?

What is the Nyquist rate for the signal x (t)? a

What are the frequencies in the resulting discrete time signal x (n)?

What is the resolution Δ?

Determine the autocorrelation of the sequence x (n) ={1,5,1,2} ↑

Obtain the linear convolution of x (n) = {1,2,2,1} h(n) = {1,2,1}

Determine the response of the system y (n) =5/6 y (n-1) - 1/6 y(n-2) + x(n) to the input signal x (n) = δ(n)

Prove that LTI system is stable if its impulse response is absolutely summable. Test the stability of a system where impulse is h (n) = an u(n).

Prove that LTI system is causal if its impulse response h (n)= 0 for n < 0

Determine if the following discrete time systems are (1) Causal or non causal (2) Linear or non linear

y(n) = cos x(n)

y(n) =x(n2)

Determine the inverse Ztransform of the following using partial fraction expansion method. X(z) = z3/(z-1)(z-1/2)2 |z| ˃ 11

Find the Ztransform and sketch ROC of x (n)= an u(n) + δ (n-3)

State & prove differentiation property of Ztransform.

Find the inverse Ztransform of the following using long division method. (1) X(z)= z / z-1 |z| ˃ 1 (2) X(z)= z / z-a if |z| ˂ |a|

Describe the relationship between DFT & Z- transform.

Explain linearity & periodicity properties of DFT.

The transfer function of a causal LTI system is H(z)= (1-z -1 ) / (1+3/4 z-1) (1) Find the impulse response of the system. (2) Find the output of the system to the input x (n) = (1/3)n u(n) + u (-n-1) (3) Is the system stable?

Compute the DFT of the following: (1) x (n) = δ (n) (2) x (n) = δ (n – n )0

Find the circular convolution of the following sequences: x (n) = {1,2,3,4} h(n) ={2,1,1,2}

Consider the LTI system initially at rest, described by the difference equation, y (n) =1/4 y (n-2) + x(n) (1) determine h(n) of the system (2) Determine direct form –II, parallel form & cascade form realization of this system.

Explain frequency Aliasing.

Write the properties of

humming window

hanning window

Explain bilinear transformation method of designing IIR filter.

Find inverse DFT of X(K) ={1,2,3,4}

The transfer function of analog filter is H(s) = 3 / (s+2) (s+3) with T = 0.1 sec s Design IIR filters using bilinear transformation.

Explain Radix-2 decimation in frequency FFT algorithm.