Digital Drive: Re: Erroneous Stuff... by csown

Hi Todd,

Folks are in town, so it's tough to pull away for some quiet writing time. Before starting, I think I should mention this conversation feels like it's moved a bit toward one arguing semantics. I can probably afford a couple more cycles, but it starts getting too time-consuming because these things usually end up as definitions and re-definitions of terms. I'm sure it's safe to say that we both agree that Doug's article has some errors. As an educated person reading a technical article, the author's perspective must always be in doubt. Taking things at face value is extremely dangerous. As always, buyer beware.

The amplitude response is totally dependent on the digital filter function.
(snip)
I do not know what you mean by "damping envelope" in the event of asynchronous sample conversion, but upsampling does not "damp" anything.

I agree completely with the former assertion, and this amplitude modulation is interpretable as flat frequency response convolved with a gradual amplitude damping envelope that arises due to the upsampling operation. In the non-oversampling case, this is the often-seen sinc damping; in upsampling, it depends on the asynchronicity and requires some calculation to ascertain the behavior. The upsampler's damping envelope will have a steeper rolloff than the classic sinc behavior, and will also have some peaking.

"The damping envelope of the upsampler is steeper than that of typical zero-order-hold, thus it gives an effect of being a gradual filter, but one that allows frequency-dependent high frequency images."

It looks like you mean "less ringing," which has everything to do with the *function* of the DAC's or upsampler's digital filter, but nothing whatsoever to do with upsampling itself. If it looks like what I think you're saying, you are correct that it equates to a more gradual response.

*sort of*. One effect of the gradual damping curve is that HF ringing is reduced. However, the fact that you upsample means you are allowing some of those "frequency-dependent high-frequency images" I referred to earlier, which means you are getting ringing at frequencies quite closer to the audible band than you would have gotten if you simply used standard FIR. Incidentally, this is the major strength of non-OS, limited only by the response of the analog electronics.

Incidentally, I think the crux of this issue is that your interpretation of time smear is that it is due to poor impulse response (i.e., pre-ringing). I believe it is also due to absolute phase error, but these two issues are inextricably linked with each other. I see the picture more easily from the absolute phase error perspective. Impulse response is usually associated with high frequency aspects of the sound, whereas if you look at the full-band bode plot, you can easily see that the delay has much greater effect on tone. Music is harmonically rich, and we worry not just about the delay and damping in high frequencies, but the lower frequencies also. To me, time smear is a much broader term which looks to be different from your perspective.

There are DACs that *do* have such a response. Wadia comes to mind. Some DACs totally forgo the digital filtering altogether, like 47 Lab, Audio Note, and Ack. But to the best of my knowledge, I have yet to see an upsampler manufactuer actually state such filters being incorporated in the upsampler chips. They specify a "brickwall" filter in the D-D conversion. (The link to my original response.)

Brickwall filter is an ambiguous term. The point of the post-filter ("brickwall" or not) is to roll off steeply enough to exclude high frequency images. A gradual rolloff filter with oversampling can be construed as a brickwall filter as well, because it rolls of quickly enough to exclude the first image. If they are not specific about the filter type in the datasheet, other than specifying "brickwall", you still have no idea what the hell type of filter they are using, and they are not bound to use a 12th-order Chebyshev II or whatever the standard might be. It might even be proprietary info and you won't be able to get that information except by studying the bode plots.

"I might be missing some details about the behavior of upsampling LPF filter behavior."

This is where the the author made his erroneous assumption. The LPF is very similar to that in most DACs. Just about all of them specify a "brickwall" response. (The DCS Purcell might be different, but I'm not sure. If Wadia would ever make an upsampler, I am sure it would be closer to the author's description. But because it's Wadia's filter function of choice, not because it's inherent upsampler technology.)

I was talking here about the LPF-ing nature of the upsampling operation. This is the damping envelope mentioned above, the point I said earlier that you missed - the upsampler has a damping envelope which is essentially a gentle LPF operation. Doug is correct in attributing "LPF" behavior to the upsampler (minus post-filter).

"In essence, the high frequency bands give an averaging effect to the 'fundamental' frequency. This is what 'linearizing' means here."

In the context of a "more-gradual" filter, true. But the upsampling is not what is responsible for that.

I think you're still missing what linearizing means. I believe you're thinking about something like a trapezoidal filter. It's not the same as interpolation, i.e., connecting the samples. Here, it is ensuring that the voltage output represents the bit level being output. You essentially modulate that bit level with a dither signal, making it more accurate. It's the same as dither over the LSB - adding noise ensures the noise floor stays *apparently* constant, when in fact it is not really zero, and can never be.

The phase error that has been specified for symmetric-window FIR filtered DACs as the *average* phase error, which is indeed zero. But if you took the individual phase errors relative to the original analog signal, and took the samples that had the most extreme errors, it would be close to +90 degrees and -90 degrees. (But not exactly +/- 90 degrees.) Because the samples do not always occur on the "peaks" of HF signals.

You're right on this one - you didn't correct me... :) (actually, I think we had different definitions of pure phase response). FIR window gives a Pi/2 to -Pi/2 zigzag line across the band and yields an average phase of zero. I see what you were saying with the phrase "phase accuracy in Redbook playback is a misnomer." That is a correct statement.

Oversampling the process that *defines* a FIR filter. There is no FIR filter that does *not* use oversampling. The two terms are inseparable.

Correct. FIR = oversampling. oversampling is a subset of upsampling. The two yield quite different results when implemented.

"But the analog post-filter mucks up this phase performance really bad"

Only if it has a "brickwall" response, like the original Sony players. A gradual post-filter used after most oversampled and upsampled signals do *not* suffer significant phase error. Because the phase shift takes place around half the *oversampled* frequency, not half of the base sample rate.

Key word is *significant*. Firstly, the post-filter phase shift is additive. Additionally, the band for "interpretability" is subject to question. The maximum phase error acceptable in many imaging applications is -Pi/4 to Pi/4, which is quite smaller than in audio. I suppose it is up to the listener (the absolute rule is -Pi, but you run into nonlinearity then), but I prefer phase error not to exceed -Pi/2.

"I still have better phase response than most every D/A out there."

> The average phase response will be comparable to that of a FIR DAC.

Comparable, assuming non-brickwall filter, nor even a marginally steep filter because of the additive nature of the phase error. If what you are saying about brickwalls (high order shoddy-phase-response analog post-filters) is true, then all upsamplers are using brickwalls and indeed that is *most* DACs nowadays. I still have a hard time believing this is true.

"No steep analog post-filter means that this is the worst the phase error gets."

You have this backwards. The average phase error of an *analog* brickwall (steep) filter shifts 180 degrees by the location the full stop band is attained. This is why they are not implemented in modern DACs.

Yes, the latter assertion is correct. And I made no contradiction here, because I refer to post-filterless non-oversampling DACs. Pi is the worst it will get unless there is some odd post-filtering (some non-OS DACs nowadays are correcting for the sinc rolloff, so I suppose not all of them will have as good of phase response as the dAck! - this is something I won't compromise on in my design, it's been proven in the listening).

By the way, I did find other erroneous stuff on that paper. The author talks about "dithering" in the D/A process. Dither is only implemented in either the *A/D* process or a digital *downconversion* (downsampling) process. It uses noise to attain a "pseudo linearity" to below the level of the media's least-significant bit, in the *encoding* of the digital media.

... and decoding, too. This is the same principle as the differential non-linearity stuff. For differential linearity, instead of dither being applied to noise floor, it is being applied in a very fine way to *each individual bit*. This is possibly only because of the way upsampling "leaks" in low-amplitude high-frequency images. So each bit has its own dithering signal, in addition to the overal dithering for the LSB you mentioned above. I don't think he's particularly clear about differentiating these two. I guess you can call one of them "noise floor dithering", and the other one "plateau dithering" or some crap like that.

Best,

-Chris