how to calculate fast Fourier transform with a 128-point window on these data with non-uniform sampling frequency

Hi everyone

I have provided you with my MATLAB code and data. These samples were recorded at a non-uniform sampling frequency, so I used the NUFFT command to convert the Fourier.

Now, if I want to use fast Fourier transform with a 128-point window on these data with non-uniform sampling frequency to calculate the power spectrum, and then divide the frequency range of all power spectra into eight equal parts and divide the area under the 8-channel curve. What calculator code should I use to calculate?THANKS SO MUCH

This is my code:

%% load Data

DATA3 = [];DATA4 = [];FFT3 =[];M7=[];

for j =1:13

data3 = load(strcat(strcat('als',num2str(j)),'.ts'));

DATA3 = [DATA3;data3];

t3 = data3(:,1); f3 = (length(data3)/300))*(0:(length(t3)-1))/length(t3);

fft3 = nufft(data3(:,2:13),t3,f3);FFT3 = [FFT3;fft3]; M6 = abs(fft3);M7 = [M7;M6];

end

FFT4=[];M9=[];

for j = 1:16

data4 = load(strcat(strcat('control',num2str(j)),'.ts'));

DATA4 = [DATA4;data4];

t4 = data4(:,1); f4 = (length(data4)/300))*(0:(length(t4)-1))/length(t4);

fft4 = nufft(data4(:,2:13),t4,f4);FFT4 = [FFT4;fft4]; M8 = abs(fft4);M9 =[M9;M8];

% f4 = (0.8167/2)*(0:(length(DATA4)-1))/length(DATA4);

end

Answer 1

[Mathieu NOE]

hello

see my suggestion below

the result is in Area

clc
clearvars

load('DATA3.mat');
t3 = data3(:,1);

%% uniform resampling of data on 128 samples
nfft = 128;  % fft length
newt3 = linspace(min(t3),max(t3),nfft); % equally spaced time vector 
dt = mean(diff(newt3)); % new time increment
Fs = 1/dt;      % sampling frequency
newdata3_2_13  = interp1(t3,data3(:,2:13),newt3,'linear');


%% fft 
fft_spectrum = abs(fft(newdata3_2_13))/nfft;
% one sidded fft spectrum  % Select first half 
    if rem(nfft,2)    % nfft odd
        select = (1:(nfft+1)/2)';
    else
        select = (1:nfft/2+1)';
    end
fft_spectrum = fft_spectrum(select,:);
freq_vector = (select - 1)*Fs/nfft;
figure,semilogy(freq_vector,fft_spectrum);

%% divide the frequency range of all power spectra into eight equal parts 
freq_points = linspace(min(freq_vector),max(freq_vector),8+1); % equally spaced freq vector 

     for cj = 1:numel(freq_points)-1
         start = freq_points(cj);
         stop = freq_points(cj+1);
         ind = find(freq_vector>=start & freq_vector<=stop);
        Area(cj,:) = trapz(freq_vector(ind),fft_spectrum(ind,:));   % Area under curve : 
                                                                    % rows = 8 (as many as parts) , cols = 12 , as many as signals
     end

[NGR MNFD]

Hello Dearthanks for your suggestion but for this data should use a nonuniform fft like nufft,because has a different sampling frequency .Doesn't the MATLAB code of FFT make a difference? because your code matlab is about uniform resampling and this code matlab use for uniform frequency While we don't have anything like that here.Thank you for your advice again

[Mathieu NOE]

hello

sure the original data has a non uniform time vector , but why wouldn't we resample the data (interp1) at a fixed sampled rate and use the regular fft ?

If you plot the original and resampled data you will see perfect match

[NGR MNFD]

hello dear ...

how?

I do not understand you,These are the data registered by the Physinet site, and I did not register, so I cannot make any changes in it, and I want to perform this operation on this data.

[Mathieu NOE]

hello again

what is your issue ? there is nothing special to do on the original data.

I simply suggested to resample the data into a uniform spacing so you can easily use the regular fft

see :

%% uniform resampling of data on 128 samples
nfft = 128;  % fft length
newt3 = linspace(min(t3),max(t3),nfft); % equally spaced time vector 
dt = mean(diff(newt3)); % new time increment
Fs = 1/dt;      % sampling frequency
newdata3_2_13  = interp1(t3,data3(:,2:13),newt3,'linear');

[NGR MNFD]

hello again dear.

You are absolutely right. I thought there is a way to go the same way with nufft non-uniform sampling method. Now with your method, the data and the label to enter the neural network do not match, I don't know what changes should I make in the code? Thank you for your help.

this is my code and workspace matlab

clc,clear all,close all;

Area3=[];

for j =1:16

data3 = load(strcat(strcat('control',num2str(j)),'.ts'));

t3 = data3(:,1);

%% uniform resampling of data on 128 samples

nfft = 128; % fft length

newt3 = linspace(min(t3),max(t3),nfft); % equally spaced time vector

dt = mean(diff(newt3)); % new time increment

Fs = 1/dt; % sampling frequency

newdata3_2_5 = interp1(t3,data3(:,2:5),newt3,'linear');

%% fft

fft_spectrum = abs(fft(newdata3_2_5))/nfft;

% one sidded fft spectrum % Select first half

if rem(nfft,2) % nfft odd

select = (1:(nfft+1)/2)';

else

select = (1:nfft/2+1)';

end

fft_spectrum = fft_spectrum(select,:);

freq_vector = (select - 1)*Fs/nfft;

% figure,semilogy(freq_vector,fft_spectrum);

%% divide the frequency range of all power spectra into eight equal parts

freq_points = linspace(min(freq_vector),max(freq_vector),8+1); % equally spaced freq vector

for cj = 1:numel(freq_points)-1

start = freq_points(cj);

stop = freq_points(cj+1);

ind = find(freq_vector>=start & freq_vector<=stop);

area3(cj,:) = trapz(freq_vector(ind),fft_spectrum(ind,:)); % Area under curve :

% rows = 8 (as many as parts) , cols = 12 , as many as signals

end

Area3=[Area3;area3];

end

Area4=[];

for j =1:13

data4 = load(strcat(strcat('als',num2str(j)),'.ts'));

t4 = data4(:,1);

%% uniform resampling of data on 128 samples

nfft = 128; % fft length

newt4 = linspace(min(t4),max(t4),nfft); % equally spaced time vector

dt = mean(diff(newt3)); % new time increment

Fs = 1/dt; % sampling frequency

newdata4_2_5 = interp1(t4,data4(:,2:5),newt4,'linear');

%% fft

fft_spectrum = abs(fft(newdata4_2_5))/nfft;

% one sidded fft spectrum % Select first half

if rem(nfft,2) % nfft odd

select = (1:(nfft+1)/2)';

else

select = (1:nfft/2+1)';

end

fft_spectrum4 = fft_spectrum(select,:);

freq_vector4 = (select - 1)*Fs/nfft;

figure,semilogy(freq_vector4,fft_spectrum4);

%% divide the frequency range of all power spectra into eight equal parts

freq_points = linspace(min(freq_vector4),max(freq_vector4),8+1); % equally spaced freq vector

for cj = 1:numel(freq_points)-1

start = freq_points(cj);

stop = freq_points(cj+1);

ind = find(freq_vector4>=start & freq_vector4<=stop);

area4(cj,:) = trapz(freq_vector4(ind),fft_spectrum4(ind,:)); % Area under curve :

% rows = 8 (as many as parts) , cols = 12 , as many as signals

end

Area4=[Area4;area4];

end

data = [Area3',Area4']';

label=[3*ones(1,13)';4*ones(1,16)'];

% % % creat simple perceptron

net = perceptron('hardlim','learnp')

net.trainparam.epochs = 200;

net = train(net, data,label);

view(net)

Y = net(data);

[Mathieu NOE]

hello again

sure, I can clearly see that data and label are not same size +

but I do not understand why you created label this way and how the dimensions (1,13) and (1,16) are related to size(data) = 232 x4 ?

label=[3*ones(1,13)';4*ones(1,16)'];

[NGR MNFD]

Hi ...

My purpose of area calculation is to extract the feature from the power spectrum and then feed it to the neural network. I scored the levels based on two classes, sick and healthy, for example, class 1 and 2 or class 3 and 4.(label=[3*ones(1,13)';4*ones(1,16)'];)

In your opinion, what should I do so that the size of the two will be similar and I will be closer to my goal?

[Mathieu NOE]

hmmm

I am not really the expert here for the neural training - tried to figure out the issue by reading the doc for function train but it's quite outside my area of expertise - sorry !!

[NGR MNFD]

thanks so much dear