

all 3 comments

[–]cypherpunks 2 points3 points  (0 children)

A finite-length Fourier transform does give you frequency bands. You can only get infinitely narrow peaks if you start with an infinitely long time series.

Basically, it's provable that RMS power (square root of sum of squares of sample values) is preserved by an FFT. Every frequency shows up in the output.

So don't worry and use those algorithms.

[–]SadisticFlower 0 points1 point  (1 child)

You can control the width and shape of the 'bins' by controlling sampling frequency and/or windowing the data. A lower sampling frequency will result in a reduced frequency selectivity, i.e. frequencies close to the target frequency will bleed over, this creates effective 'bins'. If you window the data with say a hamming or hann window you can reduce the amount of bleeding beyond the edges of the 'bin' (i.e. greater attenuation of spurious frequencies).

[–]ThatcherC[S] 0 points1 point  (0 children)

What would you call a low sampling rate? From what I can tell, as the sampling frequency goes down, the Nyquist cutoff also goes down, so you don't get accurate response in higher frequencies.