FAKULTI KEJURUTERAANUNIVERSITI KEBANGSAAN MALAYSIAKL3063: Digital Signal Processing

MATLAB Assignment 1

Instruction: Answer all these questions and submit your answers along with the printouts of MATLAB script and plots.DEADLINE: 5pm, Thursday 13 March 2008. No excuse.

1. Generate and plot the samples (stem function) of the following sequence over the indicated interval in MATLAB:

a)

b) where w(n) is a Gaussian random sequence with zero

mean and unit variance.

2. Determine the autocorrelation sequence and the crosscorrelation sequence for the following

sequences:

What is your observation?

3. The finite input sequence is given as , while an infinite impulse response is given as

. Determine the convolved signal .

4. Determine the results of the following polynomial operations using MATLAB:

a) X1(z) = (1 – 2z-1 + 3z-2 – 4z-3)(4 + 3z-1 – 2z-2 + z-3)

b) X2(z) = (z2 – 2z + 3 + 2z-1 + z-2)(z3 – z-3)

5. A causal, linear and time-invariant system is given by the following difference equation:

a) Find the system function H(z) for this system.

b) Plot the poles and zeros of H(z) and indicate the region of convergence.

c) Find the unit sample response h(n) of this system.

KL3063 Iskandar Yahya [Iskandar@vlsi.eng.ukm.my]Page 1

d) Is this system stable? IF the answer is yes, justify it. If the answer is no, find a stable unit sample response that satisfies the difference equation.

KL3063 Iskandar Yahya [Iskandar@vlsi.eng.ukm.my]Page 2