EEE 352 Analog Communication SystemsBET V A

Assignment I Z-Transforms with MATLAB

Note:1). Write your name and registration number clearly on the first page.2). There are four questions in this assignment. Type (preferred) or write clearlyyour answers to all questions, showing all the detailed steps.3). Please submit your completed assignment (hardcopy only!) to me on Thursday 11 March. Late submission after this date will be penalized!

Q1. Given below is a channel transfer function in Z domain:

H(z) = z / (z-1)(z-0.8)

a) By using partial fraction method, show that the above expression can be written as:

H(z) = C1 z / (z-1) + C2 z / (z-0.8)Determine the values of C1 and C2.

b) Using the above form of partial fractions or otherwise show that inverse channel impulse response h(n) is given by:

h(n) = 5*[1 - (0.8)^n]U(n)

c) Using the following MATLAB code confirm h(n) identified in part b) of Q1.(You are supposed to submit your code alongwith this part with results)

>> clear all %clears all variables recently used >> syms z>> f = z/((z-1)*(z-0.8)); % channel transfer function>> iztrans(f) % returns inverse Z-transform

Q2. Generate a pole-zero plot in Z domain using following MATLAB code.

>> clear all>> den = [1 -1.8 0.8];>> p = roots(den) % returns poles of channel transfer function>> z = roots([0 1 0]) % zero of channel transfer function>> zplane(z,p) % pole-zero plot of channel transfer function

a) Submit figure of pole zero plot in printed form.

b) Determine the impulse response of the system ‘h’ for N terms. Set N =10 for first ten terms of impulse response of channel. You may use the following MATLAB command.

>> num = [0 1 0];>> h = impz(num,den,N) %returns a column vector having first N

%terms of impulse response

Q3. Observe the frequency response of the channel in MATLAB:

a) By using MATLAB command freqz() write a code for generation of magnitude and phase response of the system.

b) Submit alongwith a plot of magnitude spectrum over a normalized

frequency range which extends from 0 to (rad/sample).

Hint: use >> [H,f] = freqz()Then plot abs(H) versus frequency

Q4. For an input signal step signal u(n) to channel where u(n) = 0 for t<0 and u(n) = 1 for t>=0:

a) Verify its Z-transform as shown below:

b) For given U(z) obtain its magnitude and phase response in MATLAB. Submit the printed plot with this part.

c) Observe mag and phase response of output signal Y(z) when it passes through the channel having transfer function H(z).(Submit your observation)