Question

Clear steps, please.

Consider the following LTI system where, Q -5, and w 2000m rad./sec. a) Use MATLAB to determine magnitude response and phase response of the filter. b) What type of filter is it? c) What will be the output of this filter if input xio- 5Cos(1000). Show all calculations step by step as shown in Lecture-21 . d) Verify your answer of part (e) by using Simulink model. Attach the snapshot of Simulink model and output. e) What will be the output of this filter if input x(0) SCos(2000xt). Show all calculations. f) Verify your answer of part (e) by using Simulink model. Attach the snapshot of Simulink model and output. g) What will be the output of this filter if input xt)-5Cos(4000π). Show all calculations. h) Verify your answer of part (g) by using Simulink model. Attach the snapshot of Simulink model and output. i) Using MATLAB find the poles of H(s). Is the system stable? j) Find and sketch h(t) in MATLAB

Answer 1

a. Matlab code:

s=tf('s');
h=400*s/(s^2+400*s+2000^2);
margin(h)

b.

This is a band pass filter

c.

for input x=5cos(100t)

w=100

G(w)= 0.0001 + 0.0100i magnitude is 0.0100 and angle is 1.5608 rad or  89.4807 deg

out put is Y = 0.01*5cos(100t+89.4807) = 0.05cos(100t+89.4807)

d.

File Tools View Simulation Help 0.1 008 004 002 0.04 Rnady T-10.000

e.

for input x=5cos(2000pit)

w=2000*pi

G(w)= 0.0050 - 0.0705i magnitude is 0.0707 and angle is -1.5001 rad or  -85.9993 deg

out put is Y = 0.0707*5cos(2000pi*t-85.9993) = 0.3535cos(2000pi*t-85.9993)