Question

please complete only F, H, and J only. step by step clearly. please follow the questions. also type any codes you used.

100 Consider the following LTI system, where, Q = 5, and wo 200π 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 x,(t)-5Cos(100t). Show all calculations step by step as shown in Lecture-20 d) Verify your answer of part (c) by using Simulink model. Attach the snapshot of Simulink model and output e) What will be the output of this filter if input x:0-5Cos(2000m). 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 x3(t) -5Cos(4000xt). Show all calculations. h) Verify your answer of part (g) by using Simulink model. Attach the snapshot of Simulink model and output. ) Using MATLAB find the poles of H(s). Is the system stable? j) Find and sketch h(t) in MATLAB Instructions: . Make a report, it should be typed, hand written solutions are not accepted . Report should contain table of contents Upload ONE PDF file that contains the solution, codes and figures Hand written solutions will result in a grade of o include page numbers at the bottom of every page You must submit the solutions in the same order as the questions . . . You must start o new page for each part AND correctly number the problem solutions

Answer 1

(f)

untitled* - Simulink File Edit View Display Diagram Simulation Analysis Code Tools Help 0.01 uniikxl euntitled simout 4000 pi 2+4000 * pis 2000 pi)2 Ready View 1 warning auto(ode3) 100%

Block Parameters: Sine Wave Sine type: Time based Time (): Use simulation time Amplitude: Bias: Frequency (rad/sec): 2000*pi Phase (rad) -pi/2 Sample time: -1 Interpret vector parameters as 1-D OK Cancel Help Apply

simulation result: output is available in scope.

-4 10 -2 -6 -8 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01 0 Offset-0

(h)

Input frequency w = 4000pi

Block Parameters: Sine Wave Sine type: Time based Time (t): Use simulation time Amplitude: Bias: Frequency (rad/sec): 4000* pi Phase (rad) -pi/2 Sample time: -1 Interpret vector parameters as 1-D OK Cancel Help Apply

simulation result:

4 2 0 -1 -2 -3 -4 0.001 0.01 0 0.002 0.003 0.0040.005 0.006 0.007 0.008 0.009 Offset-0

MATLAB code for solving the part (j) is given below in bold letters.

% (j)
clc;
close all;
clear all;

% define the frequency variable s as symbolic variable
syms s;

% define the parameters of the transfer function
w0 = 2000*pi;Q = 5;

% Define the transfer function
H = s*(w0/Q)/(s^2+s*(w0/Q)+w0^2);

% obtain the inverse laplace transfer function of H(s), impulse response h(t)
h = ilaplace(H);

% define time vector
t = 0:1e-5:0.01;
h_t = subs(h);

% plot the system impulse response
figure;
plot(t,h_t,'linewidth',2);grid on;xlabel('time');
ylabel('Amplitude');title('h(t)');

RESULT:

h(t) 1500 1000 500 0 -500 1000 0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01 time