Hi there, Welch and FFT are very different by nature. The FFT is used to get the spectral estimate over the netire signal but it is sensitive to non stationarity. So if you want to have a better estimate for signal with non stationary components, use Welch. Welch spectra breaks down the signal in segment and use a hanning function. The number of segments in Welch depends on the overlap you use and the length of your segment. From this you can define your degrees of freedom (DOF). The welch spectra has a lower frequency resolution fompare to a simple fft as you are averaging a series of fft obtained on each segment. The DOF is conventionaly used to tell how statistically robust is your welch sepctra (e.g. DOF>16 is considered as a good start in ocean wave statistics).
The following script breaks down the welch method. so you can see how it is rlated to the FFT. This is based on welch (1967).
I hope this helps
samprate=fs; %sampling frequency
nfft=length(Waveburst); % enter here any time series quantity (here we have 2048 sampes rows in one burst column)
% get the corresponding time vector (timestamp of the record)
dt=1/fs;%Time or space increment per sample
t = (0:nfft-1)/fs; %Time of 1 burst in decimal minutes
% segmentation in averaging windows
xwin=512; %length of averaging segment
noverlap=xwin*0.5; % number of samples corresponding to a 50% overlap (0.5)
K=(nfft-noverlap)/(xwin-noverlap); % Number of segment that data were divided in
% obtain modified periodogram for each segment
HanningW=hanning(xwin); %generate the anning indow for the given segment length
centreseg=noverlap; % initial centre of the segment
for i=1:K % get the fft on each modified periodogram. This will ony work for 50% overlap and if the signal length is a multibple of the window length
Ak(:,i)=(1/xwin).*fft((Waveburst(centreseg-noverlap+1:centreseg+noverlap,1).*HanningW),xwin); % periodogram are obtained by multiplying the hanning window to each data segment then we realised and fft to obtaine modified periodogram
centreseg=centreseg+noverlap; %shift the centre of the segment at the end of the previous segment;
end
U=(1/xwin).*sum((HanningW).^2); % we need to correct the spectra estimate as we applied a window
Ik=(xwin/U).*abs(Ak).^2; % spectra estimate of each periodogram
%average the periodograms to obtain thepriodogram of the entire signal.
%So we obtain the magnitude of each frequency component in the signal.
%However when k>N/2 the sequences reapeat (2 sided spectra)
P=(1/K).*sum(Ik,2)';
% apply Nyquist limit to avoid repetion and obtained 1 sided spectra
Nyquist = xwin/2+1;
P=P(1:Nyquist); % truncate the spectral estimate within the boundary of the Nyquist
P(2:end-1) = P(2:end-1)*2; % now to obtain the amplitude of each frequency, we need to multiply the magnitude of the 1 sided spectra by 2 as we shiched from 2 sided to one sided spectra
Fx1 = (0:Nyquist-1)*samprate/xwin; % these are the corresponding frequencies for thhe PSD in P
Pxx1 = P/samprate; % the is the power spectra density for each frequency
% compare to welch
figure
plot(Fx1,Pxx1)
hold on
[psd freq]=pwelch(Waveburst(:,1),xwin,noverlap,nfft,samprate); %use hamming window by default
plot(freq,psd,'r')
