[sdiy] Generating a large number of CV outputs

[Josh Rohs]

>
> So I'm having a hard time seeing where these images could come from, or
> how you'd ever detect them. You definitely couldn't hear them.
>
> This is highly context-specific. Depends on 1) your sample rate or more
particularly, 2) the ratio of your sample rate to signal bandwidth 3) as
Roman said, the presence of any nonlinearity in the path

You are right that there is no such thing as an instantaneous step in the
real world, but for audio purposes I think it's reasonable to consider the
continuous time impulse response to be a "boxcar" considering the rise time
in relation to the sample period.

We can think of the DAC output as our discrete signal passed through a
0-order hold of period 1/Fs; the discrete signal contains images at integer
multiples of the sample rate. These images are the *same* level as the
baseband signal in the discrete domain - I think this is what Tom was
getting at. Only when we pass the discrete signal through the DAC (0-order
hold) do we shape the output spectrum(including those images), which you
can picture as a train of scaled pulses convolved with the frequency
response of the ZOH.

The ZOH is basically a crappy lowpass filter. Attenuation at FS/2 is like
4db. for a high bandwidth signal, this is *not acceptable* generally, so
use reconstruction filters to 1) attenuate the images and 2) possibly
correct for passband droop due to the SIN(X)/X attenuation of the ZOH. the
second one is probably done more in non-audio applications. Basically, we
try to filter our steppy signal back into the perfect band limited version
we intended, but there is no causal brick wall filter, so this is
theoretically impossible. The best you can hope for is to push those images
far down enough that they're below the noise floor/threshold of human
hearing.

Re: being able to hear those images: if you sample high enough, it likely
won't be a problem, in a perfect world. but since we're talking about
synthesizers here, nonlinearities will undoubtedly exist, as roman
references. All it takes is mild intermodulation to bring those images back
into baseband.

As always, this is all dependent on context/application.
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