Digital Signal Processing — Summer 2023

Find which of the signals are causal or non-causal.

x(n)=u(n+4)-u(n-2)

x(n)=(1/4)n u(n+2)-(1/2)n u(n-4)

x(n)=u(-n)

Consider the analog signal X (t)=3 cos 100лt a

Determine the minimum sampling rate required to avoid aliasing.

Suppose that the signal is sampled at the rate Fs =200 Hz .What is the discrete-time signal obtained after sampling?

What is aliasing effect and how it can be eliminated?

Obtain the linear convolution of x(n) = {1,2,0,1}& h(n)= {0,1,0,1}

Perform the circular convolution of the two sequences x1(n)={2,1,2,1} and x2(n)={1,2,3,4}

Determine the impulse response h(n) for the system described by the second-order difference equation y(n)-3y(n-1)-4y(n-2)=x(n)+2x(n-1)

Determine the direct form I , form II and cascade realization for following system. Y(n)=x(n) - x(n-1) + 2 x (n-2) -3 y(n-1)+4y(n-2)

Find the z transform for x(n) = u(-n-1).

Explain with suitable example recursive and non-recursive system.

List out the properties of Ztransformation with suitable detail.

Prove the periodicity of DTFT.

Compute 4 point DFT of the given sequence x[n]={1,0,1,0}

Explain various properties of ROC.

Derive the lattice structures of FIR filters.

List out the properties of z-transform.

List out and prove properties of DFT.

Explain Notch filters with respective waveform.

Explain bilinear transformation method for FIR filter design.

Derive the Ztransformation for x(n) = an (sinw0n) u(n)

Find out inverse z transform of X(z) = 1+z-1 / (1- z -1 + 0.5z -2)1

Perform the circular convolution of two sequence X1(n) = {1,3,5,3} and X2(n) = {2,3,1,1}

Explain Radix-2 Decimation in Time algorithm.

Derive the frequency sampling structures of IIR filters.

Determine auto-correlation of the following signal: x(n) = {1 ,2, 1, 1}

Determine the eight point DFT of the signal x(n)={1,1,1,1,1,1,0,0} and sketch its magnitude and phase.