how to obtain the frequencies from the fft function

after the fft of the input signal,how to get the frequencies?

[irem asci]

I have 10 seconds of EEG recording that I have used fft on. How can I obtain the frequencies?

numberOfSamples = 20000                           
samplingRate = 2000                               
eegFile = readtable('Hit_0_EEG1.txt');
electrodeTimeSeries = eegFile.EEG1;               

  timeSeries = electrodeTimeSeries(1:numberOfSamples);
  
  y = fft(timeSeries);   
 
  posFreq = y(1:(numberOfSamples/2));%
  
  spec = abs(posFreq);

[Matan Dor hai]

fs = 2000; % sample rate N = len(your_data); % 20000 in your case fshift = (-N/2:N/2-1)*(fs/N); Y = fftshift(fft(your_data); Y = abs(Y).^2 / N; plot(fshift,Y) % 2 sided fft

fshift = (0:N/2-1)*(fs/N); Yshift = Y(N/2+1:end); plot(fshift,Yshift) % right sided fft

Answer 1

[Wayne King]

dpb is correct, you can use that to create a meaningful frequency vector

For an even length signal, the most common interval is (-Fs/2, Fs/2]

   Fs = 1000;
   t = 0:1/Fs:1-0.001;
   x = cos(2*pi*100*t)+randn(size(t));
   xdft = fftshift(fft(x));
   df = Fs/length(x);
   freq = -Fs/2:df:Fs/2-df;
   plot(freq,abs(xdft))

For an odd-length signal, it's common to have an open interval (-Fs/2,Fs/2) where the starting point is -Fs/2+ df/2 and the ending point is Fs/2-df/2

       Fs = 1000;
       t = 0:1/Fs:1;
       x = cos(2*pi*100*t)+randn(size(t));
       xdft = fftshift(fft(x));
       df = Fs/length(x);
       half_res = df/2;
       freq = -Fs/2+half_res:df:Fs/2-half_res;
       plot(freq,abs(xdft))

Of course for a real-valued signal, if you are only interested in magnitude, you only need 1/2 the frequency axis and magnitudes.

If you have the Signal Processing Toolbox, you can use periodogram to get a power spectrum or power spectral density estimate that will output a frequency vector for you.

[Daniel Michael]

Are you sure the frequency order is not the following? Not sure why Matlab does not include this in the documentation.

freq = Fs/N*[(0:N/2) -1*((N/2-1):-1:1)]

Unrecognized function or variable 'Fs'.

Answer 2

[dpb]

Frequency is totally dependent upon the sample rate of the time signal and duration.

Sampling relationships --

Fmax=1/2dt;  T=Ndt;  df=Fmax/(N/2);   T=1/df

Answer 3

[Daniel Frisch]

easyFFT is not part of Matlab itself, but you have to download it and put the path where it is located to Matlab's path, for example using the addpath() function.

I also helped you with PCA. You have to differentiate between the PCA vector (coeff) in the 3D multivariate space, and the time signals in x,y,z data(:,2:4) or the time signals in the PCA base system, score.

addpath('path/to/folder/of/easyFFT.m')

% Generate random data
L = 1000;
Fs = 5000;
t = (1:L)'/Fs;
f = 200;
data = [ t, sin(2*pi*f*t), cos(2*pi*f*t), t*0];
data(:,2:4) = data(:,2:4) + randn(size(data(:,2:4)))*.1; % add some noise

% Extract data
t = data(:,1);
L = size(data,1);
Accel = data(:,2:4);

% Perform PCA
[coeff,score,latent] = pca(Accel);  % need to identify the dominant tremor axis of the 3D accelerometer

% Plot multivariate data in 3D 
figure()
plot3([zeros(1,3);(coeff(:,1).*sqrt(latent))'], [zeros(1,3);(coeff(:,2).*sqrt(latent))'], [zeros(1,3);(coeff(:,3).*sqrt(latent))'], 'DisplayName','PCA Base')
hold on
scatter3(data(:,2), data(:,3), data(:,4), 'DisplayName','Data')
axis equal
xlabel('x'), ylabel('y'), zlabel('z')
legend;

% Plot time data, separate for each PCA axes
figure();
plot(t,score, 'DisplayName','Accel along PCA axes');


% 1D Time signal along most dominant tremor axis 
score1 = score(:,1); % extract signal projected on most dominant tremor axis coef(:,1) 
[Y,f] = easyFFT( score1, length(score1), 1, Fs ); 
figure();
plot(f, abs(Y), 'DisplayName','Dominant Tremor FFT');

[KR]

You are a legend! Thank you for clarifying how to use your easyFFT. However, what am I doing wrong here? I have downloaded easyFFT and saved into the following path:

addpath('D:\Matlab\easyFFT.m');

But I get this error:

Warning: Name is nonexistent or not a directory: D:\Matlab\easyFFT.m 
> In path (line 109)
  In addpath (line 86)
 

I imagine this would be an easy fix and I should be able to figure it out after I play with it for a bit, but if you can spot my error, that'd be great!

Also, thank you so much for fixing the pca! I spend too long trying to resolve this, so I greatly appreciate you taking the time to help me :). I have tried this code and it works :)!

Thanks again for your help!

[Daniel Frisch]

You must add the folder, not the file itself. Sorry my addpath-line was a bit misleading.

addpath('D:\Matlab')

[KR]

That was silly of me - thank you for identify that error. I have run the code, and it works!

Thanks again - I greatly appreciate your help!

Just quickly, I know that I can right click and extract the x- and y-values shown in the figure above, but is there a function that I can use to extract these values, such as dsearchn?

Thanks again for your help!

[Daniel Frisch]

You want to find the maximum? Just use the max function on the Y values that you used for the plot. It gives you the maximum value and the index.

https://de.mathworks.com/help/matlab/ref/max.html

[M,I] = max(Y)

[KR]

Thanks for your help, Daniel! I will be able to try the max function to obtain the max peak, once I resolve an issue I am having.

I had no issues performing the easyFFT yesterday, but for some reason, I am getting the following error today:

[Y,f] = easyFFT(score1,length(score1),1,Fs); 

Error: File: easyFFT.m Line: 20 Column: 20
Invalid expression. Check for missing multiplication operator, missing or unbalanced delimiters, or other syntax
error. To construct matrices, use brackets instead of parentheses.

I have downloaded and saved easyFFT to path: 'E:\Matlab', and have used addpath('E:\Matlab'); any ideas of what I am doing incorrectly?

Again, thank you for your time and help!

[Daniel Frisch]

I'm not sure, maybe download easyFFT again, make sure you use Matlab R2020b, and otherwise send me a working example to daniel.frisch\at\posteo.de.

[KR]

Thanks, Daniel. Re-downloading easyFFT resolved the issue. Thanks again for all of your help!

Answer 4

[Daniel Frisch]

You can use my little tool easyFFT. It automatically calculates the frequency vector in addition to the FFT.

[KR]

Hi Daniel,

Do you mind identifying my error in using your easyFFT function? Please note that I need to perform the easyFFT on the first component derived from pca (which I haven't been able to work yet).

data = table2array(acceler);
t = data(:,1);
L = size(data,1);
Accel = data(:,2);
Fs = 5000;
Fn = Fs/2; 
coeff = pca(Accel); %need to identify the dominant tremor axis of the 3D accelerometer
figure()
plot(pca(Accel))
legend({'X';'Y';'Z'})
[Y,f] = easyFFT(Accel); %error states 'undefined function or variable 'easyFFT'

[Daniel Frisch]

Hi, the "undefined function or variable" error means that the function is not on the path. Either put the file easyFFT.m in your current folder, or add the folder containing it via the addpath() function.

Answer 5

[Jiahaw Fu]

Answer 6

[Mark Newman]

The FFT gives you a list of results. Each item in the list represents a sinusoid with a different frequency. The position of each item in the list tells you its frequency. See the following video for more details: https://www.youtube.com/watch?v=3aOaUv3s8RY

Answer 7

[Dan]

here's a simple wrapper that might help (here dim refers to the matrix dimension to loop the 1-D FFT over):

function [X, f] = run_fft(x, dt, dim, shiftSwitch)
if nargin < 3 || isempty(dim), dim = 2 ; end
if nargin < 4 || isempty(shiftSwitch), shiftSwitch = false ; end
N = size(x, dim) ;
if dim == 1
  n = size(x, 2) ;
else
  n = size(x, 1) ;
end
NFFT = 2 ^ nextpow2(n) ; % for zero-padding
f = (1 / dt) * (-NFFT / 2 : NFFT / 2 - 1) / NFFT ; % f = 1 / (2 * dt) * linspace(0, 1, NFFT/2 + 1) ; % f = (0 : 1 : N - 1) * fs / N ; % fk = k fs / N where k=0,1,2,...N-1 --- % Map the frequency bin to the frequency (Hz)
if dim == 2, f = f( : ) ; end
if dim == 2, X = zeros(NFFT, N) ; else X = zeros(N, NFFT) ; end
for kx = 1 : N
  if dim == 1
    xk = x(kx, :) ;
  else
    xk = x(:, kx) ;
  end
  nank = isnan(xk) ;
  xk(nank) = 0 ; % turn nan's into zeros for zero-padding
  Xk = fft(xk, NFFT) ;
  if shiftSwitch 
    Xk = fftshift(Xk) ;
  else
    f = fftshift( f ) ;
  end
  if dim == 1
    X(kx, :) = Xk ;
  else
    X(:, kx) = Xk ;
  end
end