Using the function x(t) = e^(-100t) *u(t) from t= 0 to 0.2 s Wc =300*2*pie Fc =

Question

Using the function x(t) = e^(-100t) *u(t) from t= 0 to 0.2 s

Wc=300*2*pie Fc= 300Hz   Wo = 400*2*pie

Use numerical Method to calculate and plot |X(jw)| , |W(jw)| , |Y(jw)| , |F(jw)| with MATLAB

I'm having trouble with one of the functions in the code, XW = CTFourierTransform(t,dt,xt,w) i am getting an error saying the function is undefined. The code I have is below.

clear all;
close all;

fc = 300;% fc=300Hz
f0 = 400;% f0=400Hz;
wc = 2*pi*fc;
w0 = 2*pi*f0;

dw = 0.2*pi;
fw = 800; % the maximum frequency 800 Hz is used for evaluation
ww = 2*pi*fw;
w = -ww:dw:ww;

dt = 0.0005;
t = 0:dt:0.2;
xt = exp(-100*t);

XW = CTFourierTransform(t,dt,xt,w); % Perform Fourier Transform for
% continuous-time signal

plot(w/(2*pi),abs(XW));

xtr = ICTFourierTransform(w,dw,XW,t);% Perform inverse Fourier
% Transform for continuous-time signal
figure;
hold on;
plot(t,xt,'r');
plot(t,real(xtr),'b');
hold off;

tic;

% Multiply xt by e^(j*wc*t) to get yt.
yt= exp(-100*t).*exp(1j*wc*t);
% Fourier transform yt to get YW.
YW=CTFourierTransform(t,dt,yt,w);
% Put YW throught the low-pass filter.
WW=YW;
% Compute for loop length ahead of time to decrease computation time.
WWlength=length(WW);
count = round(0.5*f0/fw*WWlength);
for x = 1:count
WW(x) = 0;   
end
for y = 3*count:WWlength
WW(y) = 0;   
end

% Bring WW into the time domain.
wt= ICTFourierTransform(w,dw,WW,t);

% Multiply wt by e^(-j*wc*t) to get ft.
ft= wt.*exp(-1j*wc*t);

% Bring ft into the frequency domain.
FW=CTFourierTransform(t,dt,ft,w);

% Finally create the graph.
figure
plot(w/(2*pi),abs(XW),'r');
hold on
plot(w/(2*pi),abs(YW),'g');
plot(w/(2*pi),abs(WW),'b');
plot(w/(2*pi),abs(FW),'k');
xlabel('f (Hz)')
title('Signal Graph')
legend('|X(jw)|','|Y(jw)|','|W(jw)|','|F(jw)|','Location','Best')
hold off;

% The task for the students is ended here,
time = toc;
fprintf('The running time is %6.4f seconds ',time)

x( )-e-100tu(t) t = 0 to 0.2 (s) 0,-300. 2 Using numerical method, calculate and plot the following: jct y(t) w(t) x(t) Low pass filter

Explanation / Answer

Save CTFourierTransform function and ICTFourierTransform  type script in your matlab so that the function will executes and gives you required results

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