[sdiy] Digital accumulator VCO core?

Tom Wiltshire tom at electricdruid.net
Mon Feb 15 23:32:29 CET 2021

The point as not to remove the aliases by *filtering* but by *cancellation*.

Imagine you could create a waveform that consisted of only “anti-aliases” that would eliminate the aliased harmonics when applied to the original signal. That’s what we’re doing.

Yes, the usual scenario is that the sample rate is fixed and therefore the band-limited data only needs to be derived once. You can do all the hard sums offline, generate one massive look-up table of the band-limited edge correction, and then you just paste the right bits into the right places and all the aliasing disappears. That’s why I described it as “magical”!


> On 15 Feb 2021, at 22:02, Brian Willoughby <brianw at audiobanshee.com> wrote:
> I don't agree with this 5-step simplification. Once you create a naive raw impulse, the data already includes an infinite series of harmonics that are aliased and cannot be removed by filtering. Even two passes of a filter cannot remove the aliases that fall in between the in-band harmonics.
> In contrast, you can synthesize a band-limited impulse easily using the sin(x)/x formula. There's no need to low-pass filter a synthesized band-limited impulse. The windowed version just leaves out values of sin(x)/x for large values of abs(x)
> What I don't know about is the math to convert a standard band-limited impulse into a minimum-phase band-limited impulse. Anyone?
> Either way, a synthesized band-limited impulse can be converted to a band-limited step via integration, and this can be done in advance. I'm assuming that the sample rate of the converter is fixed, and thus the band-limited data need only be synthesized once.
> Brian Willoughby
> On Feb 15, 2021, at 04:06, Richie Burnett <rburnett at richieburnett.co.uk> wrote:
>>> If you do a polyblep you correct the sample just before and just after the transition to "blend" the fractional-sample-position step into whole samples, but I don't get what the curve is supposed to be or how you design it.
>> Ok, here goes...  (See attached JPG image.)
>> 1. Start with a raw impulse (A).
>> 2. Pass this through a boxcar FIR filter to get a band-limited impulse (B).
>> 3. Pass this through the same boxcar filter again to get an even more band-limited impulse (C).
>> 4. Now integrate this band-limited impulse to get a band-limited step (D).
>> 5. Finally subtract a naive step from the band-limited step to get (E).
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