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Pete,

The definition and methods of computing Fourier transforms vary.

In mathematics it is often useful to scale the transform so that it is a unitary operator - or in plain speak the spectrum has the same norm (rms value) as the time based signal (functions on a circle [Fourier series vs World Series] or on the real line).

Look at the terms of a Fourier series as +/- frequencies (i.e. sine and cosine series vs complex number series); the 0th term has a different scaling factor from the other terms. The 0th term has an extra factor of 2. Of course the non-zero terms in the sine/cosine series result from +/- frequencies as complex valued terms considering negative frequencies.
RM

I add here a simple Windowing Demo from RITEC.

In this simulator, the user can generate single or dual frequency signals, and apply several different types of windows on them to view the effects of non-bin-centered data, whereby leakage of energy to adjacent bins occurs; a result of processing finite-duration records.

There are several types of windows available in this simulator including: Hann (Hanning / Raised Cosine), Bartlett, 4-term Blackman-Harris, Flat-Top, and Hamming windows. The spectral content is amplitude corrected with the appropriate window Amplitude Correction Factor.

https://www.ritec-eg.com/Libra...se-Factor-basic.html

RM

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