If I want to add 3dB per octave to signal (e.g. to flatten out the power spectrum of an exponential sine sweep), is it really just as simple as...
- Take the Fourier transform of the time-domain signal, let's call this A(f).
- Multiply this by the square root of the frequency (square root because power goes like amplitude squared)?
- Maybe normalize by the lowest frequency, so that there's unity gain for that frequency.
- Take the inverse Fourier transform to get back to the time domain.
Mathematically, the filter would be, simply,...
A'(f) := A(f) * sqrt ( f / f_low )
Is this right, and/or is there a better way?
(I've searched around and...it seems this is such a simple matter that people don't post how to do this.)