Number of samples for doing FFT

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I have a set of 10006 samples which resembles 10 period s of a 50 hz signal which is sampled with 50 KHZ.

as you know the freqeuncy of bins are calculated via SF/N where SF is sampling frequency and N is the number of samples.

I want to have the magnitudes of the frequency in integer multiples of 5 HZ up to 9 KHZ (for example: 5 , 10 , ..., 1025, 1030...,8000, 80005..9000).

so if I do the fft with 10006 samples my frequency bins are not any more the integer multiples of 5 and instead they are integer multiples of 50000/10006. and if I truncate my samples then i will have integer multiples of 5 Hz bins but my samples are not any more resembling exactly 10 periods which means I have leakge effec !

so I am wondering how to have exactlu 5 HZ bins and with out having the spectrum distorted by leakage effect ?!!

Answer 1

[Matt J]

If you zero-pad to 20K samples then you will have SF/N=2.5Hz. You can then discard every other frequency sample if you want frequency sampling of 5 Hz.