Digital Signal Processin (EX-703 (C)) - Important Questions

Discuss the concept of sampling and reconstruction of signals.

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

Explain what is meant by a linear time-invariant causal system.

Determine the z-transform and ROC of the following discrete-time sequences: (i) x(n) = a^n u(n), (ii) x(n) = -a^n u(-n-1), (iii) x(n) = a^n u(n) for M <= n <= N-1 and zero otherwise.

Determine the inverse z-transform x(n) of the second-order rational function X(z) = 1 / (1 - 1.5z^-1 + 0.5z^-2) for the three cases: (i) ROC |z| > 1 causal, (ii) ROC |z| < 0.5 anti-causal, (iii) ROC 0.5 < |z| < 1 two-sided.

Explain the properties of the z-transform for causal signals.

Determine the linear convolution / system response y(n) = x(n)*h(n) for the given finite sequences h(n) = {1, 2, 1, -1} and x(n) = {1, 2, 3, 1}.

Explain the relationship between multiplication of two DFTs and circular convolution.

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

Compute the N-point DFT of the sequence x[n] = 1 for n = 0 and 0 otherwise for 0 <= n <= N-1.

Explain the design of FIR filters using the window method.

Explain the design of an IIR filter using the Butterworth method.

Explain about Linear Mean Square Estimation.

Write short notes on any two of the following: (i) Wiener filter, (ii) Optimal filtering using ARMA model with suitable examples.