fft frequency shift | Forum for Electronics

Thank you for your answer.
If I use a particular length fft, not necessarily radix 2, will this correct the situation ?

So that everyone comprehends what I did, here are some details:

ω0 = 50
f1(t,x) = sin(ω0*2*pi*t*x)
N=1024 number of points
x = 1 to 18 , step 1
frequency range is then 0 to approximately 900 Hz
abs(fft) values, red multiplier character .
Curve fitting g1(x) = 0.5 – 0.42*(x/820)^1.8 , the blue line .

And, maybe, an image file; freq_shift.png

If there’s a general formula to correct for this, without
adjusting the size of the fft all the time, then that is preferable
and likely useful.