# Problem 1 Write MATLAB Program to compute and plot the frequency response of a causal LTI discrete-time system with a transfer function given by for 0     . What type of filter does it represent? H(z)  0.15(1 z2 ) 10.5z1 0.7z2 Problem 2 Repeat Problem 2 for the following transfer function: H(z)  0.15(1 z2 ) 0.70.5z1 z2 What is the difference between the two filters in problem 1 and problem2, respectively? Which one will you choose for filtering and why? Problem 3 1. Find this filter impulse response. 2. Find the output of the filter when the input x[n] using linear convolution. 3. Find the filter frequency response using a. MATLAB (freqz) and b. MATLAB (FFT). 4. What was the effect of the filter on the signal? Explain! 5. Is the frequency response of the filter consistent with the result obtained in part 2? Explain. 6. Find the filter frequency response by hand. Is this result consistent with the one obtained in part 3? 7. What type of a filter is this one (LP, BP, or HP). 8. Repeat all parts from 1 to 7 for the following causal FIR filter y[n] = 0.5 x[n] -0.5 x[n-1] Given the following signal x[n]= [20 18 22 17 23 19 21 17 18 14 16 12 14 11 12 9 10 7 8 4 7 ] and a causal FIR filter characterized by the following difference equation: y[n] = 0.5 x[n] + 0.5 x[n-1] Ikhlas Abdel-Qader Page 1 of 1 5/14/2020 Problem 1

Write MATLAB Program to compute and plot the frequency response of a causal LTI discrete-time system with a transfer function given by for 0     . What type of filter does it represent?

H(z)  0.15(1 z2 ) 10.5z1 0.7z2

Problem 2

Repeat Problem 2 for the following transfer function: H(z)  0.15(1 z2 )

0.70.5z1 z2

What is the difference between the two filters in problem 1 and problem2, respectively?

Which one will you choose for filtering and why?

Problem 3

1. Find this filter impulse response.

2. Find the output of the filter when the input x[n] using linear convolution.

3. Find the filter frequency response using

a. MATLAB (freqz) and

b. MATLAB (FFT).

4. What was the effect of the filter on the signal? Explain!

5. Is the frequency response of the filter consistent with the result obtained in part 2? Explain.

6. Find the filter frequency response by hand. Is this result consistent with the one obtained in

part 3?

7. What type of a filter is this one (LP, BP, or HP).

8. Repeat all parts from 1 to 7 for the following causal FIR filter

y[n] = 0.5 x[n] -0.5 x[n-1]

Given the following signal

x[n]= [20 18 22 17 23 19 21 17 18 14 16 12 14 11 12 9 10 7 8 4 7 ]

and a causal FIR filter characterized by the following difference equation:

y[n] = 0.5 x[n] + 0.5 x[n-1]

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