Normalising FFT data (FFTW)

Question

Using FFTW I have been computing the FFT of normalized .wav file data. I am a bit confused as to how I should normalise the FFT output, however. I have been using the method

Answer 1

Surprisingly there is no single agreed definition for the FFT and the IFFT, at least as far as scaling is concerned, but for most implementations (including FFTW) you need to scale by 1/N in the forward direction, and there is no scaling in the reverse direction.

Usually (for performance reasons) you will want to lump this scaling factor in with any other corrections, such as your A/D gain, window gain correction factor, etc, so that you just have one combined scale factor to apply to your FFT output bins. Alternatively if you are just generating, say, a power spectrum in dB then you can make the correction a single dB value that you subtract from your power spectrum bins.