# Fourier transform power dependent on frequency

## Homework Statement

this is something i noticed doing homework rather than homework itself. I plot fft output from different frequency signals, i am not sure why power changes with increasing frequency?

## Homework Equations

if i take (with matlab notation):

time = 0:0.01:10
y = fft(sin(2*pi*f*time))

with f = 5
then the maximum amplitude of the fft output is about 498.

with f = 10
the maximum amplitude of fft output is 492.

3. My attempt at a solution

I understand the amplitude is 'halved' in both cases because this fft is ambiguous so the energy is spread over two peaks. But why is the energy less when the frequency increases? I have more cycles in the case with more frequency, but I suppose this means I have less samples. Is it usual to normalise this in some way? It seems like this is something you wouldn't want if you were dealing were plotting energy return from doppler shifts.