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In Reply to: Why you should not put this on your site, Teresa. posted by raphsdad on September 14, 2006 at 18:00:44:
And Digital is know for having a hard time passing 10kHz sine wave and square waves as well while analog is able to do it more accurately. The chart does clearly state it is a 10kHz sine wave does it not?Actually this link is tame compared to a couple of other, what I consider important web sites.
"Analog is Music, Digital is mathematics"
Happy listening,
Teresa
Follow Ups:
No. Misleading in that it shows 'CD audio' as a very crude stepped wave whereas the audio, ie the analogue conversion, the output, would be a very close approximation to the sine wave. That graph more or less represents the data used by the DAC to start rebuilding the analogue waveform.Yes, digitization throws away a lot of information. BUT, as Nyquist showed, it can be recovered surprisingly accurately. That's why there's a DAC. That's what it does.
"Yes, digitization throws away a lot of information. BUT, as Nyquist showed, it can be recovered surprisingly accurately"It is actually more subtle than that.
What Nyquist-etc show is that sampling a band-limited signal and reconstructing it with a very specific filter at replay is a 100% lossless operation. This is still without quantisation, i.e. they are talking about an analogue sampled system.
Quantising ('digitising') the individual samples reduces the information due to the granularity of the quantizer. But this granularity can be pushed down to good-enough levels. In practice 20-22 bit is possible, giving signal-to-quantisation distortion levels of over 100dB. In short: the quantisation loss can be made arbitrarily small (but requires some competence).
The required reconstruction filter is the Sinc function. Sadly this cannot be realised in this universe, but it can be approximated to levels that are quite decent. Even so the human ear constitutes an additional reconstruction filter, making it debatable whether, for audio, one must strictly adhere to the Sinc reconstructor. After all, many people listen quite happily to non-oversampling non-filtered DACs.
So what's left of digital's harmful processes?
Ah yes, the 'sampling a band-limited signal' thingy. Nyquist-... don't teach you how to band-limit an arbitrary signal. And that's where the rub is.
You cannot have harmless band-limiting AND a totally flat frequency response to 20kHz AND a sampling rate of only 44.1kHz.
That's where CD seems to fail.
It is the CD manufacturers insistence on reaching out to 20kHz (do we really need this? Tell me which analogue tape machine or LP does so at all levels?) that causes a lot of the problems. Why? Because of the band-limiting anti-aliasing filter being flat out to 20kHz and then -100dB or less at 22kHz. Too steep. Analogue filters needn't apply here, and regular digital filters cause pre/post-ringing(*).
Solutions?
1)
You can reach out pretty harmlessly with digital to 20kHz, but then you'll need a sampling rate of more than 44.1kHz. Probably around 60kHz, earlier studies indicate 50kHz bu that seems to be a bit right.2)
Forget the flat-to-20kHz requirement. Allow the system's frequency response to droop monotonously above, say 15kHz, to reach -3dB at 18kHz and less than -60dB at 22kHz. That way you can make pretty decent band-limiters.Almost no-one is doing so. That's bad. But there is hope. Some manufacturers of ADCs and some recording engineers are picking up on this.
---
Much longer than I intended to reply, and no analogue contents. Sorry for that.
(* That's at the ADC side. At the DAC side we need those filters
to ring. This often not-understood dichotomy is one of the reasons of many people in the industry doing the wrong thing half of the time: they apply DAC filter lore to ADCs!)
Regarding ADC's - I'm surprised to hear you say that they are problematic. I assumed even at 16/44 they have been pretty much 'perfect' in their capture of a signal for many years.Apart from which, most are now 24-bit and much higher sampling. 16/44 masters are created in software from higher resolution recordings.
I assumed the same for many years.In reality just about any commercially available ADC chips*, including top models like the PCM1804, do their anti-aliasing filtering with linear-phase half-band FIR filters with relatively short length:
-this is cheap in silicon
-only 6dB attenuation at fs/2
-often only about 80dB of stop-band rejection above fs/2 (i.e. full-band aliasing occurs at levels coincident with the source's ambience and fine detail)
-filter impulse response with pre and post echo, about 1 ms wide (upper 60dB of impulse). You rang, mylord?All of this is very poor. Luckily indeed that many have reverted to 88.2kHz or 176.4kHz recording followed with downsampling in the DAW, hopefully using better filters.
(* There exist pro ADC units that do better, notably dCS and a few others. These do not rely on commercial ADC chips from TI/BB/Crystal/AKM but rather on in-house developed discrete solutions, often with much more rigorous AA filtering)
--
One filter I have made is:
.flat to 15kHz
.-3dB at 18kHz
.-130dB at 20kHz
.600us impulse width (almost twice as fast as a regular CD-audio AA filter)
This is a 'safe' filter in that it allows even for cheap DACs with primitive half-band reconstruction filters to play without imaging.Another filter I have is more like (don't have the details here):
.flat to 16kHz
.-3dB at 24kHz (!)
.-130dB at 28kHz
.400us impulse width
This filter is remarkable in that it deliberately allows aliasing to occur, folding back in the 16-22kHz band. The reasoning is two-fold: many adults (including me) don't hear beyond 15kHz, and above ~12kHz the human ear cannot distinguish pitch, so aliasing occuring above 12kHz is perceived as a brightening, and not as a mixing-in of dissonant tones. dCS follow the same strategy.
I use this filter mainly for recording analogue-master LPs, often with purely acoustic contents and innately smoothly rolling off above 12kHz or so. In short: when the source programme is not rich in treble contents.All work in progress. Present filters are long and computationally intensive, and FIR/linear phase. I want to arrive at much shorter filters, asymmetrical FIR, and somewhere between linear phase and minimum phase.
Very interesting indeed! I can just about follow the concepts, but far be it from me to critique.I whole-heartedly agree that it was very foolish to adopt sampling rates in recording that weren't factors of the defacto 16/44 RBCD, I honestly don't understand why this ever happened.
Regarding our hearing, again I think we have to be careful in differentiating 'band-width', 'frequency-response' and 'time-domain resolution' or 'coherence'.
An anecdote;
my own hearing rolls off over 15 KHz (I'm 46), but I was nonetheless very easily able to hear the difference in Max Townshend's home development/reference system (listenin to DVDA and SACD) when he switched out his 'super-tweeters' - not subtle at all - and these drivers produce no sound pressure even remotely within the range of my hearing.
Actually, more correctly, they produced almost no sound pressure within the range of my hearing - I doubt the crossovers used completely 'brick-wall', but they were probably rolled off to the threshhold of audibility ( at least -60dB or thereabouts) by 16KHz or so, at 'realistic' in-room levels.
"Forget the flat-to-20kHz requirement. Allow the system's frequency response to droop monotonously above, say 15kHz, to reach -3dB at 18kHz and less than -60dB at 22kHz. That way you can make pretty decent band-limiters.IOW, return to multi-bit, 4x or 8x oversamplng DACs with well-implemented analogue low-pass filtering?
No, this is about band-limiting, thus prior to the sampling ADC.
In practice the filter I propose (really not me, but Craven, Lagadec, et al.) has to be inserted in the digital domain, after an oversampling ADC. I have Matlab prototypes that take in a normally-sampled 88.2kHz stream and convert it to 44.1kHz for CD mastering.
Ok, that sounds intersting.However, I still think that it ultimately boils down to simple lack of 'time-domain resolution' (which isn't the same thing as band-width or frequency response) and that this is intractable.
IMV, a 44.1Hz sample rate doesn't actually 'resolve' above about 8KHz (if that), whatever the various threorums say about 'reconstructing' frequencies above this with anti-aliasing et al.
Anyway, in the D/A process (which I would maintain is where the real conumdrum lies) you mentioned 'ringing' on signal edges with complex over-sampling filters, there is also the issue of phase-shifting of harmonic content (loss of 'time domain' coherence). Both of these profoundly effect perceived timbre, despite measuring as tiny numbers as 'THD'.
"time-domain resolution' (which isn't the same thing as band-width or frequency response) "It is exactly the same thing.
Time and frequency are two sides of one coin.
Time and frequency are two sides of one coin.I agree - two factors. A musical instrument can produce an immensely complex sound and a commensurately complex waveform, which is composed of many simultaneous harmonic components. Tiny changes, almost at the threshold of 'measurability', in the relationship of these harmonics can (and do, in 16/44) change timbre quite radically.
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