fourier transform ans amplitude

Hi everyone, good work, why is the converted signal divided by sqrt(n)^2 when finding P values ​​after the Fourier transformation of the gaussian pulse on the matlab website?

Fs = 44100; % Sampling frequency

T = 1/Fs; % Sampling period

t = -0.5:T:0.5; % Time vector

L = length(t); % Signal length

X = 1/(0.4*sqrt(2*pi))*(exp(-t.^2/(2*(0.1*1e-3)^2)));

n = 2^nextpow2(L);

Y = fft(X,n);

f = Fs*(0:(n/2))/n;

P = abs(Y/sqrt(n)).^2; %???

Answer 1

[Hassaan]

Dividing by sqrt(n)^2 after performing the FFT on a Gaussian pulse or any signal in MATLAB is a normalization step to ensure that the signal's power or energy is consistently represented across the time and frequency domains, adhering to Parseval's theorem. This step is crucial for accurate signal analysis and interpretation in various scientific and engineering applications.

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[Erkan]

Thank you for your answer. I will contact you with a problem I am trying to resolve.

[Hassaan]

You are welcome!