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Hi,
In topic "Power Spectral Density Estimates Using FFT (https://www.mathworks.com/help/signal/ug/power-spectral-density-estimates-using-fft.html)", why are squared dft values multipled by (1/(fs*N))?
fs = 1000;
t = 0:1/fs:1-1/fs;
x = cos(2*pi*100*t) + randn(size(t));
N = length(x);
xdft = fft(x);
xdft = xdft(1:N/2+1);
psdx = (1/(fs*N)) * abs(xdft).^2;
psdx(2:end-1) = 2*psdx(2:end-1);
freq = 0:fs/length(x):fs/2;

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Askic V
Askic V 2022-11-10

0 个投票

It is because of Parseval's theorem, which expresses the energy of a signal in time-domain in terms of the average energy in its frequency components
In this case, n and k are integers, but actually these are samples i.e. discrete time intervals, so they can be considered as n*deltaT, in such case it is
deltaT is a sample time period i.e. deltaT = 1/Fs where Fs is a sampling frequency.
That is why 1/(fs*N)!

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