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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