[sdiy] A new shade of pink (noise)

[Richie Burnett]

Usually I think the choice of terminology is clear cut...  The filter before 
an ADC is an anti-aliasing filter.  The filter after a DAC is an 
anti-imaging or reconstruction filter.  (Barring a few weird speciality 
cases like intentionally under-sampling RF and stuff.)

The case where I have to think about it is the filter used when you resample 
digital audio from one sample rate to a new sample rate.  Like when playing 
back a digital recording at a different speed/pitch (transposing).  The 
sampled data in the digital domain has an infinite number of repeating 
images of the original spectrum due to the sampling process, so we use 
interpolation to reconstruct what the analogue signal originally did 
*between* the sample points, then we pick new values from the interpolated 
curve to form the output samples at the new sample rate.  If we skipped 
using a filter to do the interpolation there would be images from the 
sampling process, and when we proceeded to change the sample rate these 
images would also alias to new frequencies because the output sample rate is 
finite.  Everything above the Nyquist frequency for the new output 
sample-rate must fold over (alias.)  So is the resampling (interpolating) 
filter an anti-aliasing filter, an anti-imaging filter, or BOTH !?

-Richie,



-----Original Message----- 
From: Brian Willoughby
Sent: Wednesday, November 25, 2020 12:53 AM
To: Synth-diy
Subject: Re: [sdiy] A new shade of pink (noise)

I'll add another voice of agreement that "reconstruction filter" is the best 
name.

In my estimation, it's a great word to use because it's a subtle reminder 
that digital audio is *not* a stair-stepped approximation of continuous 
analog audio. As everyone here already knows, proper use of sampling 
requires a signal to be filtered (band-limited) before it's digitized, and 
then reconstructed through a filter after the DAC. Calling that final stage 
a "reconstruction filter" emphasizes that it's returning the same, 
continuous, analog signal that went into the process - without the jagged 
edges that you *might* see on your computer screen.

That said, I am guilty of saying "aliasing" when "imaging" would be more 
appropriate.

Would it be correct to say that half of the images are mirror images? In 
terms of high frequencies being output lower than low input frequencies?

Between Nyquist and the sample rate, would you call those frequencies 
"images" or "aliases"?

I assume we can all agree that frequencies above the sample rate are aliased 
down below the sample rate.

Sounds like I'm going to have to review some terminology. That's always a 
good idea, though, anyway.

Brian


On Nov 24, 2020, at 13:31, Eric Brombaugh <ebrombaugh at gmail.com> wrote:
> Yes - the secret sauce of how Stenzel got 128 voices of anti-aliased 
> oscillators out of a lowly STM32F373 with the Streichfet was an 
> eye-opener. Lots of optimizations that are only obvious *after* someone 
> tells you how they work.
>
> I agree 100% on the use of "anti-image" or "reconstruction" for the 
> filtering that happens after a DAC - I prefer reconstruction. As I became 
> more familiar with the subtleties of discrete-time processing I also 
> became more conscious of the difference between imaging and aliasing and 
> began to strive to use the terms correctly.
>
> Eric
>
> On 11/24/20 1:14 PM, Richie Burnett wrote:
>> Thanks for that link Eric.  Very interesting, I always wondered how they 
>> achieved 128 voice poly on the Streichfet.
>> The section towards the end about using BLEP techniques to emulate 
>> "variable sample rate playback with Zero-Order-Hold" on a modern DSP with 
>> fixed sample rate is very interesting.  To me this is the secret to 
>> getting that gritty PPG type sound when playing back wavetables at low 
>> pitches.  I would call the additional spectral content "Imaging" rather 
>> than "Aliasing" though, because it is produced by repeated images of the 
>> spectrum due to the sampling process that aren't being supressed properly 
>> during playback.  Not aliasing that I think of happened during recording 
>> of the wavetable.  A lot of people do seem to call the filter that 
>> follows a DAC an "Anti-aliasing filter" though, when it is really an 
>> "anti-imaging filter" in my opinion, or even "reconstruction filter" is a 
>> better description, I think.
>> -Richie,

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