Re: Question about upsampling methods

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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