Digital Signal Processing (EC-601) - Important Questions

Define stability, causality and invertibility for discrete-time LTI systems. How is stability determined from the impulse response?

Solve the second-order linear constant-coefficient difference equation for y[n], n >= 0 for given input sequence and initial conditions y[-1], y[-2].

Discuss Direct Form-I and Direct Form-II implementations of discrete-time systems. What are the main differences between these implementations?

For an LTI system with impulse response h[n] = (0.5)^n u[n], determine the frequency response H(e^{jc9}) and explain the frequency domain representation of discrete-time signals and systems.

Determine the z-transform of exponential sequences including x[n] = -a^n u[-n-1], x[n] = a^n u[n] + b^n u[-n-1] and x[n] = (1/2)^n u[n]. Specify ROC in each case.

Represent the system described by the given state-space equations using a signal flow graph.

Prove and explain the convolution in time and scaling in time-domain properties of the z-transform.

Determine the 4-point circular convolution of two given length-4 sequences using concentric circles method.

State and prove any four properties of the DFT (e.g., linearity, circular time/frequency shifting, time reversal).

Explain the concept of Discrete Fourier Series (DFS) and derive its expression. Discuss its important properties.

Compute the 8-point DFT of the given sequence using the radix-2 decimation-in-frequency FFT algorithm showing all intermediate stages.

Determine the DFT of a given sequence using the Radix-2 FFT algorithm with detailed steps and final result.

Explain the decimation-in-time FFT algorithm and how it decomposes the DFT computation into smaller DFTs with butterfly diagram.

Compare and contrast the impulse invariant transformation and bilinear transformation methods for IIR filter design.

Write short notes on any two: (i) Design techniques for IIR and FIR digital filters (ii) Design of FIR filter using windowing method (iii) Bilinear transformation for high-pass IIR filter from Butterworth analog prototype.