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buelligan
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Keith Howard's Ringing False: Digital Audio's Ubiquitous Filter

This is an excellent and informative article. I am a fan of Keith's writing. What we all must remember is that the data on a disc do not trace out the waveform at higher frequencies. The data points on the disk are the skeleton for the digital filter to flesh out. His point about the ringing pattern of the digital filters time domain response being directly responsible for replicating the higher frequency components of the waveform is one that many detractors of digital audio seem to be unaware. It is pretty close to magic that the algebraic sum of all the ringing patterns should end up replicating the waveform so completely, yet that is exactly (nearly) what happens. It should be noted that J. Peter Moncrief (IAR) made exactly the same point back in about 1989 in his review of the first Theta Digital DSP(and custom, advanced reconstruction algorithm)-based D/A converter. It also makes me question the validity of designs that use no digital filter (47 Labs, Zanden). Note: if I understand correctly, the Wadia has no ringing of a single sample, but uses a different algorithm, based on multiple samples, to reconstruct the high frequencies, i.e. it definitely has a sophisticated digital filter.

Anyway, very interesting reading Mr. Howard. I don't mind having my brain twisted, so keep asking the intersting questions!

Editor
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Re: Keith Howard's Ringing False: Digital Audio's Ubiquitous Fil


Quote:
It is pretty close to magic that the algebraic sum of all the ringing patterns should end up replicating the waveform so completely, yet that is exactly (nearly) what happens.

I also found this mind-boggling when I learned of it back in the early 1980s, hence my 1986 Stereophile article on it: www.stereophile.com/reference/25/

That this process works for a frequency only just below half the sample rate seems counterintuitive, but it is most definitely true, as can be witnessed when you playback a 20kHz sinewave from a test CD. Despite there being only slightly more than 2 sample points per cycle, any properly designed CD player outputs a clean sinewave.

John Atkinson
Editor, Stereophile

buelligan
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Re: Keith Howard's Ringing False: Digital Audio's Ubiquitous Fil

Dear Mr. Atkinson,

Humblest apologies; You are indeed the one who wrote the first article I ever saw that made the point about the sinx/x ringing patterns summing to replicate the waveform. I guess memory leaks happen to non-silicon memory systems too.

It's been a long time since I read Mr. Moncrieff's article, but I think he did drive the point a little harder about how incomplete the data are on the disc and how much work (math) the reconstruction has to do.
If memory serves (not terribly well, sometimes), he also indicated that the ADC doesn't just directly sample the input waveform, but, in conjunction with the input filtering, should output samples in such a way that placing the apex of each sinx/x pattern will replicate the signal. It must be the reconstruction filter's partner in crime.

In any case, it is fair to say that both articles form the basis of my understanding of digital audio, such as it is.

All the best,
Buelligan

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Re: Keith Howard's Ringing False: Digital Audio's Ubiquitous Fil

Dear Keith,

Certainly sinx/x reconstruction is theoretical. Since the domain (valid time axis) of the sinx/x function is minus infinity to plus infinity. The universe is only 13 billion years old, give or take, and protons and neutrons (and thus, our DACs and digital media) will eventually decay into energy, so we will never capture all the pre- and post-ringing required to theoretically, completely reconstruct a waveform. (You know, re-reading the above makes me think I may just have too much time on my hands.)

When you say "The stepped representation contains the desired signal plus above-Nyquist images,",

I take this to mean the data samples off of the digital media in question. I am also assuming that we are talking about a 44.1 kHz sampling rate. And in players where there is no digital filtering, there is no oversampling.

As I mentioned in my first post, my understanding of digital audio, right or wrong, was formed by JA's aforementioned article and Peter Moncreiff's review of the Theta DSPro. The point that Mr. Moncreiff took pains to make in his review, as I remember it, it that the data on CDs does not, in fact, contain all of the desired signal, at least above about 2 kHz. He even had graphics comparing data points he captured from the digital output of the transport (shown as dots, for clarity, on the o-scope trace) on the disc, lined up temporally with waveform captures of the analog output (I'll be really mad if he just drew them on a graphics program!) that showed some interesting results. They showed the analog waveform actually undulating up and down within the disc data sampling interval and other interesting, and counter-intuitive behaviors. He also showed similar graphs (and results) with sampled-and-held PAM signals that would be created from the disc data.

Most interestingly, he showed graphically/described verbally, that simple averaging and rounding of a connect-the-dots derived waveform would lack the complexity and intricacy of the analog waveform produced by the Theta. If Moncreiff's observations and assertions are valid, then digital filterless players reconstruction of below-Nyquist signals, would not be as good (i.e. informationally complete).

Needless to say, methodology is everything here and since I haven't read the article since the early nineties, I can't comment substantively on exactly how he did it. The above two articles were the genesis of my posts in response to your article.

I would love to read (and HATE to prepare for, research, measure, document the data for, and write) an article comparing and analyzing very fine details of the actual analog waveforms produced by machines such as the Theta, DCS, etc., with the data points on the disc. With tremendous respect (and no regard for the misery such a task would cause you) I submit that you are the man for the job. Whatever the results, reading it would be edifying and enjoyable.

DISCLAIMER/DISCLOSURE: I am a high-end retailing refugee (escaped 12 years ago) who sold and admired Theta DACs. I am coveting the Gen VIII with an intensity that is painful. I have no other vested interest in the outcome, except to understand what is going on.

All the best Keith,

Buelligan

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