I. Compute the impulse response h[n] for n=0, 1, 2,3 ,4 of the following LTI sys

Question

I. Compute the impulse response h[n] for n=0, 1, 2,3 ,4 of the following LTI systems a. y[n]=x[n]+0.85y[n-1] c. y[n]=2x[n]-x(n-1-0.5x(n-2] 2. Using Matlab function 'zplane', draw a pole-zero diagram of the LTI systems give in problem1. 3. Use Matlab to display the magnitude and phase response of the LTI systems give in problem1 4. Generate 1024 samples of pseudo random numbers with zero mean and unit variance using Matlab function 'rand'. Then use 'std', 'mean' and 'hist' to verify the results. Use Matlab to display the magnitude and phase response of the LTI systems with 5. multiple poles, a. b. multiple zeors multiple poles and zeros. c. 6. Draw the system structure in direct form I, direct form II, parallel and cascade form for 1 (b).

Explanation / Answer

1)

a)The impulse response is given by H(jw)= 1/(1-0.85e-jw)

b)The impulse response is given by H(jw)=(1-0.2e-jw)/(1-0.3e-jw-0.4e-2jw)

c)The impulse response is giveny by H(jw)=(2-1e-jw+0.5e-2jw)

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