This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
clear all; close all; clc; | |
W = 2; | |
Fs = 100; % frequency meant to replicate continuous data | |
t = 0:1/Fs:W-1/Fs; | |
N = length(t); | |
x = cos(2*pi*t); | |
% Sampled x | |
fs = 20; % sampling frequency | |
Ts = 1/fs; | |
num = W*fs; % # of (discrete) samples to get | |
n = 0:num-1; | |
xn = cos(2*pi*n*Ts); | |
% Continuous Fourier Transform | |
f = -10:1/Fs:10; | |
X = zeros(1,length(f)); | |
for i1 = 1:length(f) | |
X(i1) = sum( x.*exp(-1i*f(i1).*t) )/Fs; % divide by Fs to replicate dt (infintesimaly small period of time) | |
end | |
% Discrete Time Fourier Transform | |
f2 = -10:1/Fs:10; | |
Xs = zeros(1,length(f2)); | |
for i1 = 1:length(f2) | |
s = 0; | |
for i2 = 1:length(n) | |
s = s + xn(i2)*exp(-1i*f2(i1)*i2); | |
end | |
Xs(i1) = s; | |
end | |
% Inverse Discrete Time Fourier Transform | |
n2 = 0:length(n)-1; | |
xsr = zeros(1,length(n2)); | |
range = 0:1/Fs:2*pi-1/Fs; | |
for i1 = 1:length(n2) | |
s = 0; | |
for i2 = (1:length(range))+floor(length(f2)/2) | |
s = s + Xs(i2)*exp(1i*f2(i2)*i1); | |
end | |
xsr(i1) = s/2/pi/Fs; % divide by Fs to replciate infintesimaly small dt | |
end | |
figure(1); | |
subplot(2,1,1) | |
plot(t,x); | |
grid on; | |
title('x(t)=cos(2\pit)'); | |
xlabel('Time (s)'); | |
ylabel('Magnitude'); | |
subplot(2,1,2); | |
stem(n,xn); | |
title('x[n]=cos(2\pinTs)'); | |
xlabel('n'); | |
ylabel('Magnitude'); | |
figure(2); | |
subplot(2,1,1); | |
plot(f,real(X)); | |
grid on; | |
title('X(\omega)'); | |
xlabel('Frequency (\omega)'); | |
ylabel('Magnitude'); | |
subplot(2,1,2); | |
plot(f2,real(Xs)); | |
grid on; | |
title('Xs(\omega) (DTFT)'); | |
xlabel('Frequency (\omega)'); | |
ylabel('Magnitude'); | |
figure(3); | |
subplot(2,1,1); | |
stem(n2,real(xsr)); | |
title('Reconstructed x[n]'); | |
xlabel('n'); | |
ylabel('Magnitude'); | |
subplot(2,1,2); | |
stem(n2,xn); | |
title('x[n] (original)'); | |
xlabel('n'); | |
ylabel('Magnitude'); |
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment