[linux-audio-dev] Audio sampling and fft accuracy.

[James Courtier-Dutton]

Hi,

If I have a sample 2kHz sine wave signal at 50% peak.
I then add a white noise signal at 20%.
I then do a FFT transform.
If I design the FFT so that 2kHz is at the center of one of the FFT 
buckets, how close will the FFT figure be to the 50% sine wave input.
Obviously, there will be a variation due to the amount of noise. So the 
output of the FFT buckets will be 50+-error.
Will this variation as a result of noise decrease as I use more and more 
samples per fft block? I.e.Will the +-error value decrease?
I would think it should decrease, as a result of the general averaging 
the fft routine will make to the noise signal. I would think that as the 
noise was random, it should average out to zero over time.
I.e. 20% noise samples. Average each sample, the average should be zero 
as one reaches infinity number of samples.

So, if my reasoning above is correct. I can draw the following conclusion:
A 2kHz signal sampled at 8kHz and then FFTed, the 2kHz bucket will be 
less accurate than a 2kHz signal sampled at 16kHz and then FFTed.

Now, I just need to work out how much more accurate it would be.

James