I ended up doing 'ZOH' after noticing that you get really strange
results if you upsample a signal with zero-padding and then try to use
it as the frequency of an oscillator... the oscillator's frequency drops
by the upsampling factor. Another wa to say the same thing: the DC gain
of a zero-padding upsampler is 1/N where N is the sampling factor. You
could correct this by multiplying the zero-padded signal by N but then
what of someone tries to downsample it again... it then gets multiplied
by N unless the downsampler averages all the N samples... and then we're
back to something that resembles the ZOH filtering effect on the way
back down.
If I weren't able to specify a choice of upsampling methods, an
alternative would be to make a special ugen that filters its input but
only looks at 1/N samples.
cheers
Miller
On 4/9/25 1:07 PM, Christof Ressi wrote:
Hi,
I have made a PoC for adding upsampling and reblocking support to
SuperCollider: https://github.com/supercollider/supercollider/pull/6702
One thing I have been thinking about is the default upsampling method.
Currently, I'm using zero-order-hold (ZOH), aka "sample and hold",
which is also the default for Pd's [inlet~]. The other practical
alternative would be zero-padding. Letting the users choose the method
is not a real option, so I need to settle on a good default.
Generally, upsampling is done by zero-padding + low pass filtering.
ZOH is basically a low-quality low-pass filter. It's like a FIR filter
that consists of a series of 1s and the frequency response is that of
a Sinc function. AFAICT, it introduces high frequency noise, but I'm
wondering how relevant that is when the output runs through an
antialiasing filter anyway.
Zero-padding without low pass filtering results in repetitions of the
original spectrum above the original Nyquist frequency. (It's like
multiplying the signal with an impulse train, which results in the
spectrum being convolved by an impulse train, resulting in a regular
repetition.) I think that an *unfiltered*//zero-padded signal can lead
to strange result. For example, a slowly moving ramp would almost look
like an impulse train.
In my understanding, a zero-padded signal *must* be filtered, while an
unfiltered ZOH signal may be acceptable for many use cases. Is this
correct? @Miller: Is this maybe also the reason why Pd 0.44 has
switched from "pad" to "hold" as the default upsample method in [inlet~]?
Zero-padding has the advantage that low pass filtering can fully
restore the original signal, which apparently is not the case for a
ZOH signal. On the other hand, it's always possible to zero-pad the
input signal after the fact.
At the moment I'm tending to keep ZOH as the default upsampling
method, but I would be curious about other people's opinions.
Christof
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