What is the reference value to calculate dBFS from an FFT of normalised audio?

[Ashley2608]

I am working on a spectral analyser and want to display the spectrum of an incoming signal. So far I have calculated the power using an FFT.
I then calculate the magnitude from the FFT output.

I know that to get the amplitude in dB the calculation is

amplitude = 20 * log10 ( mag )


to calculate the dBFS amplitude I use

amplitude = 20 * log10 ( mag / ref )

however I don't know what the reference value should be, since I am working with audio that has been normalised (range +1 to -1) and stored as a float.
Can anyone point me in the right direction?

Thanks!

[hugoderwolf]

There was a thread recently on this. I'll just repost my answer.

A sine of Amplitude A will give you a bin magnitude of N * A / 2 (if sine frequency fits the bin exactly), where N is your FFT length. So if you want the dB scale in your analyzer to have some actual quantitative meaning, it would be appropriate to scale it so that a 0dB sine will give you a 0dB bin amplitude.

So your dB value would be 20 * log(2 * magnitude / N). That's what most analyzers do.

[Ashley2608]

Brilliant. That's exactly what I needed
Thanks!