Question

please complete this project.

100 Consider the following LTI system, 5, and wo = 2000π rad/sec. where, Q 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 (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)-5Cos(2000zt). 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

a) matlab code:

clc;

clear all;

s=tf('s');

q=5;

w0=2000*pi;

p=w0/q;

g=p*s/(s^2+p*s+w0^2);

margin(g); % magnitude and phase response using bode

Bode Diagram Gm- Inf, Pm -180 deg (at 6.280+03 rad/s) 10 20 35 45 45 10 10% Frequency (rads)
b) This is a band pass filter

c)d)

C) 2O 0032 OwE loc H (Su)-

simulink:

Function Block Parameters: Gc3 Transfer Fcn The numerator coefficient can be a vector or matrix expression. The denominator coefficient must be a vector. The output width equals the number of rows in the numerator coefficient. You should specify the coefficients in descending order of powers of s. Parameters Numerator coefficients (1257 0] Denominator coefficients [1 1257 3.948e07] Absolute tolerance auto State Name: (e.g., 'position') Apply OK Cancel Help

Source Block Parameters: Sine Wave output a sine wave Olt) Amp Sin(Freq*t+Phase) + Bias Sine type determines the computational technique used. The parameters in the two types are related through: Samples per period 2*pi / (Frequency Sample time) Number of offset samples Phase Samples per period (2*pi) Use the sample-based sine type if numerical problems due to running for large times (e.g. overflow in absolute time) occur. Parameters Sine type: Time based Time (t): Use simulation time Amplitude Bias Frequency (rad/sec) 100 Phase (rad): 1.57 Sample time: Interpret vector parameters as 1-D

output:

1257s den(s) Gc3 Sine Wave Scope1

f)

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Source Block Parameters: Sine Wave Sine Wave Output a sine wave Olt) Amp Sin(Freq*t+Phase) Bias Sine type determines the computational technique used. The parameters in the two types are related through Samples per period 2*pi / (Frequency Sample time) Number of offset samples Phase Samples per period (2*pi) Use the sample-based sine type if numerical problems due to running for large times (e.g. overflow in absolute time) occur Parameters Sine type: Time based Time (t): Use simulation time Amplitude: Bias Frequency (rad/sec) 2000*pi Phase (rad) 1.57 Sample time: Interpret vector parameters as 1-D Apply Cancel OK Help

1257s den(s) Gc3 Sine Wave Scope1

File Tools View Simulation Help Ready T:10.000