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Question about sample rate and aliasing


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I've been going through Craig's excellent "Max your Mix" book. As usual, it's well written, super-clear, full of examples, and all in all a really good resource.

 

I have a question about a riff in Chapter 3, page 52, in the section entitled "How Sample Rates Affect Mixing".

 

sounds generated inside the computer, such as what"s generated by virtual instruments, can generate harmonics that interact with the program"s sample rate. This can cause a type of distortion called aliasing. (Acoustic or electric sounds recorded through an audio interface won"t have this issue, because the interface itself will remove ultra-high frequencies that could otherwise be a problem.)

 

I don't want to reignite a sample-rate war; I'm just trying to understand an issue that appears to be an oft-cited reason as to why 44.1 kHz is adequate for representing the sound we can hear. When Craig says "the interface itself will remove ultra-high frequencies that could otherwise be a problem", I believe this refers to the anti-aliasing filter that ensures no frequencies above the Nyquist frequency (22.05 kHz in this case) will be present at the A/D converter.

 

The crux of my issue is that with all current technology I know about, an anti aliasing filter that truly removed all frequencies above 22.05 kHz would inevitably have an affect on some signal below 20 kHz. Some frequencies below 20K would be attenuated, or phase shifted, or both. That's just a real-world engineering limitation.

 

If we had an ideal filter that could lop off everything above 22.05 kHz, without touching anything below 20 kHz, then sure, 44.1 kHz would be a sufficient sampling rate. But we don't. So it's not. Right? What am I missing?

 

Thanks.

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The "perfect filter" has always been the Achilles Heel of sampling, and not something that's mentioned too often in conjunction with the Nyquist theory. In terms of practical reality, a "typical" brickwall filter is a 96dB/oct Butterworth filter. But - remember that most interface converters are not running at 44.1 kHz, but at 96 or 192 kHz, regardless of what sample rate you're using in your DAW. So with 96 dB/octave at 96 kHz, there isn't a whole lot happening below 22.050 kHz, and most of the phase shift issues will have happened above that.

 

A linear-phase brickwall filter would solve one problem (no phase shift), but that drastic a slope would introduce pre-ringing, which is explained in the book so I don't need to go into it here :)

 

So no, digital audio isn't perfect...but I think it beats dragging a rock through yards of plastic, and then using insane amounts of EQ (aka the RIAA curve) in the process. FWIW, I always suspected that the reason why SACD sounded better was because the sample rate was so high, the filter requirements were extremely relaxed.

 

Anyway, I really appreciate your comment, as you know these books are updated periodically, and this is a great subject to treat in a little more depth in the next revision (probably 2Q 2022). Thank you!!

 

Hey - are you going to review the book on Sweetwater.com :) ?

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remember that most interface converters are not running at 44.1 kHz, but at 96 or 192 kHz, regardless of what sample rate you're using in your DAW. So with 96 dB/octave at 96 kHz, there isn't a whole lot happening below 22.050 kHz

 

I did not know that. That is a key piece of knowledge. Are you saying that even typical consumer grade interfaces (Focusrite Scarlett, etc.) are always sampling at 96 kHz or higher? I'm surprised that interface vendors don't tout that - it's a pretty significant benefit.

 

Hey - are you going to review the book on Sweetwater.com :) ?

 

Sure, as soon as I finish it.

 

Thanks again.

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I did not know that. That is a key piece of knowledge. Are you saying that even typical consumer grade interfaces (Focusrite Scarlett, etc.) are always sampling at 96 kHz or higher? I'm surprised that interface vendors don't tout that - it's a pretty significant benefit.

 

You can pretty much assume that the ADC's sampling rate is the highest sampling rate supported by the interface. For example, the Neat USB mics had 96 kHz A/D converters, which they touted even though most consumers were probably going to use them at 44.1 or 48 kHz. An analog-to-digital converter's spec sheet will indicate the sample rate range it accommodates. I believe your DAW will "downshift" the sample rate to that of your project.

 

However, this is my understanding, not something I've verified independently, so I could be wrong with respect to input filtering. I also think D to A conversion is a different animal, because by that time, any aliasing has already been baked into the signal. So before I'd add any new information to the book, I'd talk to some interface manufacturers to make sure my understanding is correct. But again, I really appreciate your bringing this up, will pursue it further, and report back.

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The problem with Butterworth class filters used as brick wall filters is as the cutoff slope increases it also increases the ripple in the passband. So you lose the benefit of flat passband response of Butterworth filters.

 

Active filter circuits have inherent noise. Cascading multiple filter circuits to achieve 96dB/oct cutoff has the tradeoff of increasing noise - each filter stage in series accumulates noise.

 

There is no perfect brick wall filter in the analog domain. They all have tradeoffs.

 

Murata used to sell modules for A/D conversion that were active brick wall filters. They were used in many devices in the 1980s/1990s. If you look at the schematics of the legacy Lexicon digital reverbs (200, 224, etc) you will see brick wall filter circuits that were unconventional, probably close to the Murata modules.

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