Generating Frequency domain with FFT function of accelerometer data

Hello,

I have accelerometer data that are recorded in excel sheet.

I would like to extract the frequency domain features from the data.

In order to do that, I need to convert the data into frequency by using the FFT function.

First of all, I generate the whole frequency of the data with this code:

freX = fft(accX)/N;
freX_2 = abs(freX);
freX_1 = freX_2(1:N/2+1);
freX_1(2:end-1)= 2*freX_1(2:end-1);
f_freX = fs*(0:(N/2))/N;

It works fine.

Now, I need to cut the data into windows with 200 data point for each window.

However, my code is hitting errors and I couldnt debug it.

for i =1:number_of_windows % there are 700 windows
   % generating the frequency domain
   a = fft(accX((1+(i-1)*s_win):(i*s_win)));
   freX_2 = abs(a/N); 
   freX_1 = freX_2(1:N/2+1); 
   %error: Index exceeds the number of array elements (200).
   
   
   % extracting the frequency domain features
   meanfreX(i) = meanfreq(freX_1(1+(i-1)*s_win):(i*s_win)); % mean frequency
   peakX(i) = findpeaks(freX_1(1+(i-1)*s_win):(i*s_win)); % peak frequency
   medfreX(i) = medfreq(freX_1(1+(i-1)*s_win):(i*s_win)); % median frequency
   powX(i) = ((abs(freX_1(1+(i-1)*s_win):(i*s_win))).^2)/s_win; %power spectrum
   
end

My whole code look like these:

clear all;
close all;
% Load the data for treadmill subject


t1= xlsread('data1',1);

% 1st column is accelerometer on X axis
accX = t1(:,1) ;

% set up window length
window = 2;

% set up frequency signal
fs = 100;

% set up size window
s_win = window*fs;

N = length(accX);
number_of_windows = floor(N/s_win);

% Fourier Transform
for i =1:number_of_windows % there are 700 windows
   % generating the frequency domain
   a = fft(accX((1+(i-1)*s_win):(i*s_win)));
   freX_2 = abs(a/N); 
   freX_1 = freX_2(1:N/2+1); 
   %error: Index exceeds the number of array elements (200).
   
   
   % extracting the frequency domain features
   meanfreX(i) = meanfreq(freX_1(1+(i-1)*s_win):(i*s_win)); % mean frequency
   peakX(i) = findpeaks(freX_1(1+(i-1)*s_win):(i*s_win)); % peak frequency
   medfreX(i) = medfreq(freX_1(1+(i-1)*s_win):(i*s_win)); % median frequency
   powX(i) = ((abs(freX_1(1+(i-1)*s_win):(i*s_win))).^2)/s_win; %power spectrum
   
end

Please help me debug the fourier transform.

Thank you.

Answer 1

[Raunak Gupta]

Hi,

In the line

freX_1 = freX_2(1:N/2+1); 

freX_2 is built to have 200 elements but when you are calculating freX_1, the indexing is done with N/2 which is essentially the size of full accX and not of freX_2. In the above line if you replace N with s_win, I think the error will be resolved. But again when I see down you have taken freX((1+(I-1)*s_win) :(i*s_win)) which can be correct if freX_1 has size s_win. I think the code in the for loop should only work for a single window. Also you have used findpeaks which will return variable number of frequencies as local maxima. Instead I think you want max frequency so I have replaced it with max(freX_1) for it work.

So, I think the for loop may be written like below for it to work.

for i =1:number_of_windows % there are 700 windows 
    % generating the frequency domain 
    a = fft(accX((1+(i-1)*s_win):(i*s_win))); 
    freX_2 = abs(a/s_win);  
    freX_1 = freX_2(1:s_win/2+1);  
    % extracting the frequency domain features 
    meanfreX(i) = meanfreq(freX_1); % mean frequency
    peakX(i) = max(freX_1); % peak frequency 
    medfreX(i) = medfreq(freX_1); % median frequency 
    powX(i) = (sum(abs(freX_1).^2))/s_win; %Average power spectrum 
end

[An Van]

Thank you, I could finally get this part done.