Energy Spectrum of a signal after FFT in Matlab
The cited passage gives a method for obtaining the energy in the harmonics of a specific frequency.  If your frequency of interest is $f_0$, then take a section of samples of length $N$ where $N = \frac{4 F_s}{f_0}$ and compute the $N$-point FFT.  Now you can find the energy of the second harmonic by squaring the magnitude of the $4k+1 = 9$th FFT bin. To account for errors in estimating $f0$ you can sum the squared magnitudes of bins 7 through 11.

Below is some example code that might give an idea of what the algorithm in question does:

%% Generate an example signal
Fs = 5e3;                     % Sampling rate
f0 = 151;                     % Frequency of interest
t = (0:Fs-1)/Fs;              % Time samples
x = cos(2*pi*f0*t);           % Pure sinusoid @ f0
noise = 0.1*randn(size(x));   % Gaussian noise
y = (x&gt;0)-(x&lt;0) + noise;      % Introduce harmonics and noise

%% Compute energy in the harmonics of f0
N = round(4*Fs/f0);           % Determine record length
Y = fft(y(1:N))/N;            % Compute N-FFT (normalized)
Y2 = Y.*conj(Y);              % Magnitude squared
K = floor(N/2/4);             % Number of harmonic "bins"
for k = 1:K
    idx =  4*k+1+(-2:2);      % Five indices centered at 4k+1
    Pyk(k) = sum(Y2(idx));    % Sum of energies around 4k+1
end

%% Plot the results
[Pyy,Fyy] = pwelch(y,[],[],[],Fs);
plot(Fyy,10*log10(Pyy));
hold on;
F = linspace(0,Fs-Fs/N,N);
Fk = F(1+4*(1:K));
plot(Fk,10*log10(Pyk),'ro');
title('Power Spectral Density');
xlabel('Frequency (Hz)')
ylabel('Power/Frequency (dB/rad/sample)')
data2 = sprintf('Energy in Harmonics of %d Hz',f0);
legend('Power Spectral Density Estimate', data2);
hold off;




As far as finding a "signature" in the data, you can see that the algorithm could be very useful for that.  However, it is very important to note that the algorithm presumes some fundamental frequency of the signal in question.  If the signal in question has a fixed period, but the shape of the signal over that period changes with time, then this algorithm would be useful.  However, if the frequency varies with time, then this algorithm is not a good fit for your application.

If you are simply looking to estimate the spectrum of a signal, then maybe this page will be of help: FFT for Spectral Analysis (mathworks.com)