Hi Miller,
On 09.04.2025 14:09, Miller Puckette wrote:
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...
Yeah, that's exactly one of the cases I thought about...
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.
Yes, that's what I figured. Actually, you can do that by multiplying the
signal with an impulse train at the original frequency
(Impulse.ar(s.sampleRate)) and then applying a lowpass filter, but a
dedicated UGen could be nice.
So I guess I will stick with ZOH unless somebody convinces me of the
opposite :)
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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