Redbook 44.1 kHz standard: theoretically sufficient timbral resolution?

While there will always be some who think otherwise, like most science-minded people I do not entertain the notion that somehow we can perceive frequencies above 20 kHz. Our hearing has upper limits, just like we cannot perceive any colors in the UV region, above the for us visible spectrum (unlike bees, for example, who can see stunning colors and color shapes in flowers where we simply cannot). Accordingly, missing high frequency content above 20 kHz would not form an argument against the Redbook CD 44.1 kHz standard. In this context is also worth noting that in the chain for vinyl playback ultrasonic content is greatly attenuated in order not to destroy cutting equipment, among others; this makes for a rather thin technical argument that vinyl is significantly superior to CD in this regard.

Of course, a greater bandwidth can always be advocated for purposes of avoiding artifacts in the audio band, yet this issue is frequently tackled by upsampling of 44.1 kHz digital to much higher frequencies (like 4 x 44.1 kHz = 176.4 kHz in my own DAC) and shallow filtering from there, so that for example phase issues in the audio band, such as introduced by the infamous 'brickwall' filtering, are avoided. I do find noteworthy the argument put forth by Chris Montgomery in his article "24/192 Music Downloads...and why they make no sense",

http://xiph.org/~xiphmont/demo/neil-young.html

that ultrasonic content is actually harmful because with a lot of audio equipment it leads to intermodulation distortion products in the audio band (and this can be tested with the files that he posts).

The argument that the sampling rate of 44.1 kHz is insufficient is mostly based on the stairstep model, which is the result of a fundamental misunderstanding of the application of the Nyquist theorem in digital that lead to standards around that frequency cut-off (44.1 or 48 kHz). That the stairstep model is false has been convincingly argued, among others, by Chris Montgomery in the above cited article.

Even more strongly, his video,

https://www.xiph.org/video/vid2.shtml

demonstrates that for any sinewave signal the 44.1 kHz bandwidth is sufficient, as it shows on an oscilloscope that even from a 20 kHz sinewave signal the analog waveform is reconstructed perfectly by a DAC, without any stairsteps (watch the first 9 minutes of the video, it will be stunning for those who are no familiar with this).

It has been suggested that any complex waveform can be synthesized from sinewaves, and thus according to the Nyquist theorem any music signal up to 20 kHz frequency can be perfectly represented by 44.1 kHz digital. Yet the following article by Chris Tham, "Exploring Digital Audio Myths and Reality Part 1" argues otherwise:

http://www.audioholics.com/audio-technologies/exploring-digital-audio-myths-and-reality-part-1

While Chris Tham concurs with Chris Montgomery's argument that the idea that digital is 'discontinuous' is a myth and that the stairstep model is bogus, he also points out that square waves and sawtooth waves cannot be represented accurately by 44.1 kHz digital, see figures 7, 8 and 9 in the article.

He concludes:

"Some could argue that we don't listen to sawtooths or square waves, therefore Figures 6-8 are not significant. But we do - some musical instruments have harmonic characteristics very similar to sawtooth waves. And pop/rock music often contain music generated by synthesizers - sawtooth and square waves are fundamental building blocks for digitally synthesized music."

Indeed, it has been suggested that the waveforms of trumpet sound are similar to sawtooth waves, and the similarity, the asymmetry in the waveform, is seen in the graphs in section 1.6.1 in the following article:

http://www.feilding.net/sfuad/musi3012-01/html/lectures/005_sound_IV.htm

It is also noteworthy that in digital synthesis trumpet sound often appears to be emulated using sawtooth waves. Yet strangely enough, I do not find notable weakness in 16/44.1 digital when it comes to reproduction of trumpet sound. I find the medium very convincing in this area. On the other hand, compared to top-level analog it shows, to my ears, some weakness in reproduction of violin or saxophone sound, sounds that are very rich in overtones. Having said that, I have not yet heard the very best playback in digital; here is the witness of someone who owns the Berkeley Reference DAC, next to very advanced vinyl playback:

http://audioshark.org/dac-reviews-9...e-alpha-dac-review-6331-page2.html#post106059

From the post:

"A little backround, IMHO current digital state of the art still misses the best of analog on two marks: 1) reproduction of accurate timbres of instruments especially ones with significant high frequency overtones, 2) reproduction of the soundstage and spacing of instruments within that soundstage. [...] It was immediately apparent that the BADA Reference was doing something on issue 1 that I hadn't previously heard from Digital. In its own way, the BADA was as much a breakthrough on issue 1 as the Light Harmonic was on issue 2. There is a certain rightness about the best recordings through the BADA Reference. It flatters some of the most difficult to reproduce instruments like pianos and massed strings. Best of all, it didn't matter if it was Redbook or a HD source. The Redbook performance is striking. The BADA makes the format wars conversation almost silly."

So here it is argued that the timbral performance of Redbook digital matches the one of hi-rez; I have read somewhat similar testimonies about that DAC elsewhere.

So what is going on? Is the 44.1 kHz standard indeed theoretically, on a technical level, insufficient when it comes to proper timbral resolution of just acoustic instruments (disregarding odd non-sine waveforms from synthesizers), even if some people suggest that it does not matter in practice?

And what about the technical argument that ultrasonic frequency content from hi-rez digital can be harmful to sound reproduction in practice, because a lot of the downstream equipment cannot handle the bandwidth and causes intermodulation distortion products? (You can test this in your own equipment with the files Chris Montgomery posts in his above cited article.)

Orb said:

Why we going around in circles again..again...again...again...

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I was asking a specific technical question, based on sinewaves vs. other waveforms, which I do not think has been extensively discussed in the past. So, no I do not think we go around in circles again. Rather, I would appreciate an answer to my specific question (and perhaps the follow-up question in my post too).

Thanks
Al

Well, then I'll wait for someone else who actually wants to answer my question(s) -- hopefully in terms that I and others who do not have a physics degree either can understand, without too many mathematical formulas but perhaps with a few useful graphs.

After all, this is what this forum should be for, and I have put considerable effort into my post.

Thanks
Al

Orb said:

Did you see Al's question about sinewaves?
Probably makes more sense to focus on that if anyone wants to help.

Click to expand...

Yes, please. And thanks for your answers so far, Amir and Orb.

Groucho said:

I don't believe it. If the incoming 19997 Hz triangle or square wave is antialias filtered prior to the ADC, the ADC will see nothing but a 19997 Hz sine wave, so the ability of the system to preserve the amplitude should be just the same as if it was nothing but a sine wave we were sampling - which he agrees can be reproduced perfectly. In other words it will perfectly reproduce what our ears would hear assuming they can't hear above 22 khz.

In fact, I think he is naively generating sample values for a 'triangle wave' at a 44100 kHz sample rate and assuming that his audio editor's waveform interpolation is the same thing as anti-alias filtering. It isn't. It is the same as the reconstruction filter of a DAC, so he is effectively applying a reconstruction filter to a waveform that was already aliased - like sampling a high bandwidth triangle wave without an anti-aliasing filter and then playing it back over a DAC, hence the 'wobbles'.

So you can rest easy. This isn't digital audio's 'dirty secret'; digital audio does reproduce brass, and even synthesiser waveforms perfectly (as long as we accept that they are bandwidth-limited).

Click to expand...

Thank you, Groucho, this was very helpful!

So if what you say is correct, then the same problems should also apply to his depiction of the 4001Hz 0dB sawtooth wave sampled at 44.1kHz (Fig. 7 in his link, http://www.audioholics.com/audio-technologies/exploring-digital-audio-myths-and-reality-part-1).

***

(Anti-aliasing filters, which Groucho mentions, restrict the bandwidth before a signal sampler, e.g, an analog/digital converter, see the wiki link, https://en.wikipedia.org/wiki/Anti-aliasing_filter. That link also leads to an explanation of reconstruction filters, which perform the same function of bandwidth limiting at the DAC level.)