MATLAB: How to complete the fourier Analysis using Matlab

digital signal processingfftfourierfourier transformMATLABplottingsignal processingtransform

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

Best Answer

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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hello

I modifed a bit your code and tested it with a two tone signal

see the line with peak_fr_sorted_values


clc
%% dummy data
Fs = 1e3;
samples = 1e4;
t = (0:samples-1)'*1/Fs;
signal = 0.7*cos(2*pi*50*t)+0.4*cos(2*pi*100*t)+0.1*randn(samples,1);
[data_filt_ft, fr] = fr_t(signal, Fs);
%% Peak detection Part
% In this part, we have defined a threshold value. So, all peaks above
% threshold value will be detected.
temp_fft = data_filt_ft;
 
% Normalize the FFT
temp_fft = temp_fft/max(temp_fft);
 
% threshold
th = 0.02; % i.e. 1% of maximum amplitude
temp_fft(temp_fft < th) = 0; %you can skip this step by commenting this.
 
% Plot FFT after thresholding
figure; plot(fr, temp_fft);
xlabel('Frequency(Hz)'); ylabel('Amplitude');
grid on;
 
% find peaks of the remaining data
[peak_ft, peak_loc] = findpeaks(temp_fft);
 
 
%Sort amplitude values into ascending order
[peak_ft_sorted_values,peak_ft_sorted_index] = sort(peak_ft,'ascend');
% frequency corresponding to peak
[peak_fr] = fr(peak_loc);
% and now sorted according to amplitude (above)
peak_fr_sorted_values = peak_fr(peak_ft_sorted_index)
 
% this fuction returns the fourier transform of the signal
function [ft, f] = fr_t(x, Fs)
L = length(x);
% NFFT = 2^nextpow2(L); % Next power of 2 from length of y
NFFT = L;
 
X = fft(x,NFFT)/NFFT;
f = Fs/2*linspace(0,1,floor(NFFT/2+1));
 
ft = abs(X(1:floor(NFFT/2+1)));
% ft = 20*log10(ft);
% plot(f,ft);
 
end

Best Answer

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