On Wed, Jun 13, 2012 at 6:14 PM, katja katjavetter@gmail.com wrote:
There should be an (optional) amplitude compensation for up- and downsampling, as an amplitude effect would be inconvenient in the case of a variable-speed sound-on-sound looper.
Katja
I think that a consideration here to justify a scaling effect is to deliver the same rate of power.
I like looking at this problem with sinc functions, because the spectrum becomes easy to see, and the energy is easy to calculate.
The function with sampling rate f_s and unit spectrum from -f_s/2 to f_s/2 is f_s*sinc(t*f_s). This function when it's convolved with itself, equals itself.
and if you have f1 < f2, f1*sinc(t*f1) convolved by f2*sinc(t*f2) = f1*sinc(t*f1) which is important for comparing interpolators at different frequencies.
The L2 norm of f_s*sinc(t*f_s) = f_s. Here's the term that grows larger when we increase f_s.
In a given block, you're always writing N samples. Your goal is to write N orthogonal functions that fills all the values in some interval and keep normalized the power during that interval.