[sdiy] Generating a large number of CV outputs

[mskala at northcoastsynthesis.com]

On Thu, 14 Dec 2023, Tom Wiltshire wrote:

> The basic principle is that a given set of DAC output samples don't have
> a single interpretation, but many. Yes, the samples *could* represent a
> waveform below Nyquist, and they'd all be exactly where we expect them
> to be. But they *could equally well* represent a waveform *above*
> Nyquist and they'd *still* all be exactly where we expect them to be.

One way I think of it is that even if DAC output doesn't have
theoretically perfect discontinuous steps in the time domain, the smooth
curves between the sample moments end up looking like a filtered version
of such discontinuous steps.  And unless the filtering is a perfect brick
wall in the frequency domain - which, as you say, is only going to happen
with a lot of effort, not by accident - then some of the higher
frequencies of the stair-step signal will still exist.

> higher and higher frequencies. If we want to limit the DAC's output to
> signals within a certain band, we *actually have to do that*, we can't
> assume it is already done for us. Maybe we can't *hear* them, but that

It's all the more true when the DAC is using temporal oversampling like
the PWM, delta-sigma, and variants that featured in this thread earlier.
Some parts of the system are pushing around signals containing harmonics
of the sample rate, and the output is directly derived from such signals.
"Image" frequencies are just intermod products between sample-rate
harmonics and the desired signal.  It's a lot to ask that the image
frequencies wouldn't appear in the output at least a little bit, and
that's certainly not something we can expect by default, nor a natural
expectation from the fact the signals are continuous.

-- 
Matthew Skala
North Coast Synthesis Ltd.