# how to obtain the frequencies from the fft function

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sharvari samant on 30 Sep 2013
Commented: KR on 15 Nov 2020
after the fft of the input signal,how to get the frequencies?
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irem asci on 6 Apr 2020
I have 10 seconds of EEG recording that I have used fft on. How can I obtain the frequencies?
numberOfSamples = 20000
samplingRate = 2000
electrodeTimeSeries = eegFile.EEG1;
timeSeries = electrodeTimeSeries(1:numberOfSamples);
y = fft(timeSeries);
posFreq = y(1:(numberOfSamples/2));%
spec = abs(posFreq);

dpb on 30 Sep 2013
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

Wayne King on 30 Sep 2013
Edited: Wayne King on 7 Nov 2013
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 Frisch on 12 Nov 2020
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.
% 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 on 15 Nov 2020
Thanks, Daniel. Re-downloading easyFFT resolved the issue. Thanks again for all of your help!

Daniel Frisch on 31 Aug 2020
You can use my little tool easyFFT. It automatically calculates the frequency vector in addition to the FFT.
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KR on 12 Nov 2020
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'