Digital Signal Processing — Winter 2024

Describe the process of conversion of an analog signal into a digital signal.

What is the significance of ROC in Z-transforms? Explain by using suitable example.

Draw and explain the block diagram of a digital signal processing system. Also explain an application of digital signal processing in detail.

Define the following:

Time invariant system.

Static System.

Linear System.

Explain the process of up-sampling and down-sampling using suitable examples.

State and prove the conditions for a system to be

Causal

Stable with respect to the impulse response of a system.

Compute the convolution of the signals 𝛼n −3 ≤ n ≤ x(n) = { 0 elsewℎere 1 0 ≤ n ≤ ℎ(n) = { 0 elsewℎere

Describe the relationship between Fourier Transform and Z-Transform.

State and prove the convolution property of Z-transform.

Consider the system

Determine the poles and zeros.

Determine the impulse response of the system.

Compare DTFT and DFT.

State and prove the time shifting property of Z-Transform and state its significance.1

Define ROC. Determine the Z-transform and the ROC of 1n n ≥ 0

Explain Minimum Phase System in brief.

Draw and describe the Direct form – Istructure realization of IIR system.

Consider the sequences x (n) = {0,1,2,3,4} x (n) = {0,1,0,0,0} and s(n) = {1,0,0,0,0}12 and their 5-point DFTs

Determine a sequence y(n) such that Y(k)=X (k)X (k).12

Is there a sequence x (n) such that S(k) = X (k)X (k)313

Describe the use of Inverse System. Explain Inverse System in brief.

Draw the structure of radix 2 DIT FFT algorithm

Let x (t) be an analog signal with bandwidth of 3000Hz. Considering a N=2n point a DFT to compute the spectrum with resolution less than or equal to 50Hz. Determine

Describe the effects of coefficient quantization in FIR filters.

Determine the coefficients {h(n)) of a linear-phase FIR filter of length M = which has a symmetric unit sample response and a frequency response that satisfies the condition 1 k = 0,1,2,3 2𝜋k H ( ) = {0.4 k = r 0 k = 5,6,7

Explain pipelining and MAC architecture of a digital signal processor.

Explain sampling rate conversion by a non-integer number.

Explain forward linear predictive filter in detail.

Design a two-stage decimator for the following specifications D=100 Passband: 0 ≤ F ≤ 50 Transistion Band: 50 ≤ F ≤ 55 Input sampling rate: 10,000 Hz Ripple: δ =10-1, δ =10-3.12