FFT of Unsteady Temperature Data Resulting a Peak at 0 Hz
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Hi all,
I have a data that was sampled at 50 Hz for 120 seconds. When I apply fft, dominant frequency seems to be 0 Hz which I initially thought it could actually very well be. However, when I apply same fft to different set of data acquired from the experiment, I get the same peak at 0 Hz, which does not seem to be correct as I expect it to show relatively high frequency(ies) ( this is due to nature of experiment in which the unsteady temperature data is acquired, and the second set of data is expected to show some form of periodicity).
As you may see below in the code, DC offset is removed by "detrend" and a low pass filter is applied ( the result was the same even before low pass filtering).
Can you please take a look at the code (data is attached as well) for any possible corrections or recommendations? If everything is okay with the code, I will appreciate some comments on the physical meaning of the frequency analysis result in this particular case.
Best.
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/287308/image.jpeg)
Fs = 100; % Sampling frequency
T = 1/Fs; % Sampling period
dt = 0 :T:120-T; % Time vector
nfft= length(S2TR3_0); %Length of FFT
nfft2 = 2.^nextpow2(nfft) ;
S2TR3_0 = detrend(S2TR3_0);
figure
plot(S2TR3_0)
fy = fft(S2TR3_0,nfft2);
fy = fy(1:nfft2/2);
xfft = Fs.*(0:nfft2/2-1)/nfft2;
plot(xfft,abs(fy/max(fy)));
%low pass filter
cut_off = 2/Fs/2;
order = 256;
h = fir1(order,cut_off);
con = conv(S2TR3_0,h);
figure
plot(con);
fh = fft(h,nfft2);
fh = fh(1:nfft2/2);
fh = fh';
mul = fh.*fy;
figure
plot(abs(mul));
3 Comments
Daniel M
on 25 Apr 2020
No, sampling rate is the same as Fs. You are thinking of Nyquist rate, which is half of Fs, and is typically used for filtering (as you did with cut_off = 2 / (Fs/2) ).
For the second comment, he is saying that he can visually identify an underlying 0.1 Hz oscillation in the time-domain data. 0.1 Hz means one oscillation every 10 seconds.
Accepted Answer
Daniel M
on 25 Apr 2020
Edited: Daniel M
on 25 Apr 2020
Data looks fine. You shoud plot using semilogy to better visualize the higher frequencies. Your data shows a typical 1/f noise pattern, seen in white and pink noise dominated data. (Fig 1).
You can also try removing this 1/f curve by taking the gradient of the data, this is a rough method. (Fig 2)
Compare these semilogy plots with the periodic data and see if you can spot the differences now.
3 Comments
Daniel M
on 25 Apr 2020
I've attached three files for you. Put them all on your path and you can call them from anywhere.
Create the plots using this line of code
plotFFT(S2TR3_0,Fs,[],[],0,'semilogy',1);
plotFFT(gradient(S2TR3_0),Fs,[],[],0,'plot',1);
I'm also going to paste the contents of the plotFFT function, for the casual browser.
function [H,F,Y] = plotFFT(x,fs,begtime,endtime,demean,plotType,side,varargin)
% [H,F,Y] = plotFFT(x,fs,begtime,endtime,demean,plotType,side,varargin)
% This function takes a signal, x, and the sample rate, fs, and
% plots the FFT between begtime and endtime (defaults to
% beginning and end of signal). Times are in seconds, not
% indices.
%
% Inputs:
% x - must be a signal from one channel
% fs - the sampling frequency
% begtime/endtime - beginning and end in seconds. default is full amount
% demean - 1 or 0 to detrend data. 0 is default
% plotType - 'plot' (default), 'semilogy', 'semilogx', 'loglog'
% side - input to figurebig()
% varargin - plotting options (color, linestyle, etc.)
%
% Outputs
% H - figure handle
% F - one-sided frequency vector
% Y - one-sided Fourier transform
T = 1/fs; % sampling period
flipBack = false;
%%% Do some input error checking
if size(x,1) ~= 1
if size(x,2) == 1
% make it a row vector
x = x.';
flipBack = true; % return the outputs as column vectors
else
error('x must be a vector')
end
end
if nargin < 3 || isempty(begtime) || begtime < 0
begtime = 0;
end
if nargin < 4 || isempty(endtime) || endtime > (length(x)-1)*T
endtime = (length(x)-1)*T;
end
if begtime >= endtime
error('begtime must be before endtime')
end
if nargin < 5 || isempty(demean)
demean = 0;
elseif ~(demean==1 || demean==0)
error('demean must be true or false')
end
if nargin < 6 || isempty(plotType)
plotType = 'plot';
elseif ~any(strcmp(plotType,{'plot','semilogy','semilogx','loglog'}))
error('Incorrect plotType')
end
if nargin < 7 ||isempty(side)
side = 0;
end
% check if user passed 'Visible' into varargin
% [~,visloc] = ismember('Visible',varargin);
% if visloc == 0; visloc = []; end % avoid error in figurebig
visloc = find(strcmp('Visible',varargin)); % ismember errors if varargin is not cellstr
% Get indices from beg/end times
begind = floor(begtime*fs+1);
endind = floor(endtime*fs+1);
X = x(begind:endind); % new signal
if demean
X = detrend(X);
end
L = length(X); % length of signal
N = L; % n-point fft. This could be an input.
Y2 = fft(X,N); % fourier transform, 2-sided
t = (0:L-1)*T; % time vector
% Create one-sided frequency vector including Nyq freq
% This is the same for both even and odd numbered vectors
Ny = fix(N/2)+1; % Nyq index
F = linspace(0,1,Ny)*fs/2; % frequency vector, 1-sided
Y2 = abs(Y2/N); % 2-sided, scaled by N
Y = [Y2(1) 2.*Y2(2:Ny)]; % get positive freqs, scale power by 2 for non-dc components
%%% Make the plot
H = figurebig(side,varargin{[visloc,visloc+1]});
subplot(3,1,1)
plot(t,X,varargin{:})
grid minor
xlabel('Time [s]')
ylabel('Signal')
axis tight
subplot(3,1,[2 3])
switch plotType
case 'plot'
plot(F,Y,varargin{:})
case 'semilogy'
semilogy(F,Y,varargin{:})
case 'semilogx'
semilogx(F,Y,varargin{:})
case 'loglog'
loglog(F,Y,varargin{:})
end
xlabel('Frequency [Hz]')
ylabel('|P(f)|')
axis tight
grid on
H = tightfig(H);
if flipBack
% x was input as a column vector. Return F and Y as column
% vectors
F = F.';
Y = Y.';
end
end
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