FFT and PSD - normalize values

Prashant Kumar answered . 2025-07-07 20:01:08

Normalizing the FFT and PSD values in MATLAB to ensure that the amplitude values are not affected by the time window or the number of points requires some adjustments. Here are the steps to achieve consistent amplitude values:

1. FFT Normalization: Normalize the FFT by dividing by the total number of points and adjusting for the peak amplitude.

2. PSD Normalization: Normalize the PSD by adjusting for the signal's length and amplitude.

Here's how you can modify your MATLAB code:

%% R is the signal data points extracted from the timetable Datos03
%% tiempo is the signal time points.
%% L is the number of data points (Length of the signal)
    
% Time domain
plot(Datos3.Time, Datos3.VarName1)
R = Datos3.VarName1;
tiempo = seconds(Datos3.Time);

% FFT
Fs = 10240;           % Sampling frequency
T = 1/Fs;             % Sampling period       
L = length(tiempo);   % Length of signal

Y = fft(R);
P2 = abs(Y/L);
P1 = P2(1:L/2+1);
P1(2:end-1) = 2*P1(2:end-1);
f = Fs*(0:(L/2))/L;

% Normalization for FFT
P1 = P1 / max(P1) * max(abs(R)); % Normalize to the peak amplitude of the signal

% Plot FFT
figure;
plot(f, P1)
xlim([0 400])
title('FFT')
xlabel('Frequency (Hz)')
ylabel('Amplitude')

% PSD
[SignalSpectrum, SignalFrequencies] = periodogram(R, [], [], Fs);

% Normalization for PSD
SignalSpectrum = SignalSpectrum / max(SignalSpectrum) * max(abs(R))^2 / L; % Normalize to the peak amplitude of the signal and adjust for signal length

% Plot PSD
figure;
plot(SignalFrequencies, SignalSpectrum)
xlim([0 400])
title('PSD')
xlabel('Frequency (Hz)')
ylabel('Power/Frequency (dB/Hz)')

Explanation:

• FFT Normalization: After computing the FFT, normalize the amplitude by dividing by the total number of points and scaling it to match the peak amplitude of the original signal.

• PSD Normalization: After computing the PSD using the periodogram function, normalize the power spectral density by adjusting for the signal's length and scaling it to match the peak power of the original signal.

These adjustments should help you achieve consistent amplitude values in both the FFT and PSD plots, regardless of the time window or the number of points. This way, the amplitude values will accurately represent the signal's characteristics

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