[sdiy] Digital accumulator VCO core?

Brian Willoughby brianw at audiobanshee.com
Tue Feb 16 02:25:41 CET 2021

On Feb 15, 2021, at 11:13, Richie Burnett wrote:
> Ideally we would use an infinite sinc function as our band-limited impulse, and we would integrate this to give a band-limited step.  This would give perfect band-limiting right at the Nyquist frequency with no approximations. The downside is that we would need to correct and infinite number of samples before and after each discontinuity in the sawtooth waveform to achieve perfection!  Relaxing our quest for perfection by allowing some approximations makes the process realisable.

... and the approximation is to window that sinc function before and after the peak so that it's not an infinite number of samples. The amplitude of the sync drops with 1/abs(x) so that a window centered around 0 is only truncating very tiny sample values.

I just realized that I should have written sinc as cos(x)/x because that's symmetric around x == 0.

The minimum phase conversion simple moves the peak of the band-limited impulse closer to the first sample, rather than the mid-point.

>> On a separate note, has anyone come across something that's like a
>> spectral "gate"? like a normal time-domain noise gate, but for each
>> frequency separately: i.e. a frequency will pass through only if it's
>> above a certain threshold.
> I believe such things are used for noise reduction, but I don't know.

Definitely. The thresholds for each bin can be trained by a snapshot of the "noise" and then the audio will only be present in a band when it's louder than the "noise floor." Of course, there are artifacts associated with modifying the amplitude of individual bins because the signal being processed is not an ideal repeating period that stretches to infinity.

Brian Willoughby

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