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Cosine Fourier Transformation
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clear all; close all; clc; | |
W = 4; | |
Fs = 100; % large frequency to replicate continuous data (dt) | |
t = 0:1/Fs:W-1/Fs; | |
N = length(t); | |
x = cos(2*pi*t); | |
% 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; | |
end | |
% Inverse Fourier Transform | |
xr = zeros(1,length(t)); | |
for i1 = 1:length(t) | |
xr(i1) = sum( X.*exp(1i.*f*t(i1)) )/2/pi/Fs; | |
end | |
figure(1); | |
subplot(3,1,1); | |
plot(t,x); | |
grid on; | |
title('x(t)=cos(2\pit)'); | |
xlabel('Time (s)'); | |
ylabel('Magnitude'); | |
subplot(3,1,2); | |
plot(f,X); | |
grid on; | |
title('X(\omega)'); | |
ylabel('Magnitude'); | |
xlabel('Frequency (\omega)'); | |
subplot(3,1,3); | |
plot(t,xr); | |
grid on; | |
title('Reconstructed x(t)'); | |
xlabel('Time (s)'); | |
ylabel('Magnitude'); | |
ylim([-1 1]); |
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