Re: Question about upsampling methods

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
>>
>>
>

---
[email protected] - the Pure Data mailinglist
https://lists.iem.at/hyperkitty/list/[email protected]/message/4FJQN73I6OCQ6QKTSCSTXDF4NDNYF3WT/

To unsubscribe send an email to [email protected] mailing list
UNSUBSCRIBE and account-management -> https://lists.iem.at/