compute the energy of the signal x from its frequency spectrum x in matlab

To compute the energy of the signal x from its frequency spectrum X, you can use the Parseval's theorem which states that the energy of a signal in the time domain is equal to the energy of its frequency spectrum.

To implement this in Matlab, you first need to compute the power spectrum of the signal x using abs(X).^2, take the sum of all the power values, and then multiply it by the frequency resolution (which is Fs/N, where Fs is the sampling frequency and N is the length of the signal).

Here's the code snippet for computing the energy:

main.m
% Calculate the power spectrum of signal x
X = fft(x);
Pxx = abs(X).^2;

% Calculate the energy using Parseval's theorem
Fs = 1000;  % Sampling frequency
N = length(x);  % Number of samples
f_res = Fs/N;  % Frequency resolution
energy = sum(Pxx)*f_res;
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The variable energy will contain the energy of the signal x.