CSE-304 Digital Signal Processing Assignment 2 Spring 2012 BEE1-AB

Due date : 18/04/2012 12:00pm Q1) Given the pole-zero plot of a certain system:

Specify which of the following statements is true, false or cant be determined from the information given.

a. The system is stable b. The system is causal c. If the system is causal, it must be stable d. If the system is stable, it must have a two-sided impulse response.

Q2) For each of the pole-zero plots in figure below 5.15, state whether it can correspond to

1. an allpass system; 2. a minmum phase system; 3. a system with real impulse response; 4. an FIR system; 5. a system with a stable inverse.

In each case, specify any additional constraint on the ROC in order for the property to hold.

Q3) Consider the system function given below :

Draw the corresponding pole-zero plots. Give the system function for corresponding minimum phase system, elaborating with the help of pole-zero plots. Q4) Given a system be defined by

1. Is this system stable/causal 2. Find the impulse response h[n]. 3. Find the z-transforms Hi(z) of all possible inverses for this system. In each case, specify a region of convergence, and whether the inverse is stable and/or caussal. Q5) The input signal, its Fourier transform and the filter frequency response (magnitude and group delay) are shown in the figure below (refer to P5.34-1 3rd Ed. Oppenheim):

The input signal and filter frequency response

The 4 possible outputs signals are shown in the Figure below (Refer Fig. P5.34-2), but only of them is the correct output. Identify which one is the correct output and justify your choice.

Possible output signals

Q6)

Q7) Practice problem