Fourier transform-normalizing

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Ken W 2015-12-19

Dear All,

I confused with the normalizing and scaling of power spectral density. Below is my computation procedure,

Data length = 16384;

Sampling frequency, Fs = 10 Hz;

Nyquist frequency = 5 Hz;

Fast Fourier transform (FFT) of 16384 data points;

Discard the DC component Take the first half FFT components i.e. from 2 to 8193 ((16384/2)+1, Nyquist theorem);

Bandwidth = 5/8192 = 0.000610351;

For each of the 8192 components;

Power = Real^2 + Imaginary^2;

Spectral energy = (2 x Power)/N;

Power spectral density = spectral energy/Fs;

The last step power spectral density is divided by Fs or bandwidth? Why need to have this dividing?

Thank you.

MATLAB Mathematics Fourier Analysis and Filtering

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