[sdiy] Novation peak NCOs

[rsdio at audiobanshee.com]

I have to make a correction in response to the quoted comment. Naively generated square, ramp, triangle, and any waveform with a discontinuity in the zeroth or first derivative have an infinite series of harmonics. There is no sampling rate that is fast enough to exceed infinity, so there’s no such thing as not having an aliasing problem to start with. You will always need BLITs or sums of harmonic series to avoid aliasing, unless you want to say that “a little” aliasing is almost as good as no aliasing at all.

Harmonics are almost vanishingly small in amplitude as their harmonic number increases, but that doesn’t mean they disappear. Dither mathematics (see Vanderkooy and friends’ papers) shows us that signals with an amplitude less than the LSB of a finite bit depth can still be preserved in a signal, so that proves we can’t completely ignore the really small amplitude harmonics. It’s not quite the same as them not being there at all.

Brian


On Apr 20, 2017, at 3:01 PM, paula at synth.net wrote:
>  In all seriousness, speed comes cheaply in FPGAs and a one bit DAC running at 24Mhz is also not expensive in terms of resources. That aside, remember if you generate a fast enough wave you don't have an aliasing problem to start with, so no BLITs, oversampling or other things needed to remove it, as it's not there to start.