How to complete the fourier Analysis using Matlab ?

Question

Megh 2015-1-11

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https://ww2.mathworks.cn/matlabcentral/answers/169590-how-to-complete-the-fourier-analysis-using-matlab

评论： Katherine Zheng 2022-3-18

Hello !!

I have tried using the Matlab tutorial for FFT and DFT but I'm having extreme difficulty understanding the code and how I can use it in my question. My experience with matlab is only in data manipulation and plotting, so I'm struggling with the concepts.

So here is the question...

To compute the Cn coefficient given by

Cn = 1/T * ∫ f(t)*e^(-2*pi*n*t/T) dt,

in which T is the period, and then Amplitude is

sqrt(Re(Cn)^2 + Im(Cn)^2)
F = n/T

then... how can I plot Amplitude vs Frequency using matlab functions. So far I have this function and req as mentioned above.

f(t) = e^-t from -3 to 3
T = 6
F = -10:1:10

I would like to plot using matlab, but so far I'm doing integral manually and then just iterating values, and plotting them in matlab, can I use fft function or any other function to speed up the process ??

Many thanks

Megh

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dpb 2015-1-11

在 MATLAB Online 中打开

There's a complete example of computing/plotting the one-sided PSD at

doc fft

that should be pretty easy to follow what it's doing.

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Answer 1

Rick Rosson 2015-1-11

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https://ww2.mathworks.cn/matlabcentral/answers/169590-how-to-complete-the-fourier-analysis-using-matlab#answer_164606

编辑：Rick Rosson 2015-1-11

在 MATLAB Online 中打开

doc fft
doc fftshift
doc abs
doc angle
doc plot
doc stem
doc xlabel
doc ylabel
doc grid
doc xlim
doc ylim

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Megh 2015-1-13

Thanks !!

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Answer 2

Youssef Khmou 2015-1-11

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/169590-how-to-complete-the-fourier-analysis-using-matlab#answer_164611

在 MATLAB Online 中打开

Try to study and alter this example :

Fs=10;
t=-3:1/Fs:3;
x=exp(-t);
plot(t,x)
N=1000; % N points for frequency computation
fx=fftshift(fft(x,N))/sqrt(N);
fx=fx.*conj(fx);
 % frequency axis
f=(-N/2:N/2-1)*Fs/(2*N);
figure; plot(f,fx);

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Megh 2015-1-13

Thanks !!

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Answer 3

Megh 2015-1-13

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/169590-how-to-complete-the-fourier-analysis-using-matlab#answer_164805

编辑：Megh 2015-1-13

在 MATLAB Online 中打开

Ughhh I tried using above answers but It felt unsure about lots of operation (Since I have yet to understand many of the FFT properties and theorems) ... Well I chose the following code which I'm more confident about the mathematical operations.

This code works for now, well I still need to figure out the better way.

% clear the memory and workspace 
clc, clear, close all 
syms t fr
g_t = sin(2*pi*t);  % function
T = 10;             % period of the function
a = -5; b = 5;      % to integrate from a to b 
n = -100:1:100;     % n is an integer by DEFINATION
freq = n./T;
% Integrate function
f = g_t*exp(-2*pi*fr*i*t);
Cn = 1/T * int(f,t,a,b);
% get the amplitude and phase spectra function
Amp = sqrt(real(Cn)^2 + imag(Cn)^2);
Pha = atan(imag(Cn)/real(Cn));
% Do this to combat datapoints/frequency in which function yields
% infinty or division by zero error, take the limit 
% NEED TO FIND BETTER Way
AmpV = zeros(1, length(freq));
for n = 1:length(AmpV)
    try AmpV(n) = subs(Amp, 'fr', freq(n));
    catch AmpV(n) = limit(Amp, fr, freq(n));
    end
end
% Plot the discrete Amplitude spectrum
figure(1)
stem(freq,AmpV)
xlim([-10 10])
xlabel('\bfFrequency in Hz')
ylabel('\bfAmplitude')
title('\bfAmplitude spectra of F_{t}')