Digital Drive: This Wasn't as Bad as Expected... by Todd Krieger

"I agree completely with the former assertion, and this amplitude modulation is interpretable as flat frequency response convolved with a gradual amplitude damping envelope"

I think what you mean by a "damping envelope" as the filter function itself. But the function does the *opposite* of damp. It **induces** "ringing." As stated before, to reduce modulation, which flattens HF response. And the "ringing" helps reject artifacts above half the sample rate frequency.

"that arises due to the upsampling operation."

If you took a 20-bit 8x oversampling DAC (very common in the late '90's), and removed the actual D/A portion of the DAC following the oversampling section, and just used the oversampled signal as the output, you would have created an 20/352 upsampler. And aside from synchronous conversion in this case, the filter process is basically the same. Or in other words, an upsampler is an oversampling DAC minus the D/A section.

"In the non-oversampling case, this is the often-seen sinc damping"

If there is no oversampling, there is no filter function the base media signal is convolved with. The "sinc" function is used in oversampling/upsampling DACs *only*, and the base signal is convolved with this "sinc" function. The windowed "sinc" FIR function is the function that attains a "brickwall" frequency response. One that is flat, with a steep cutoff right below half the sample rate frequency.

"in upsampling, it depends on the asynchronicity and requires some calculation to ascertain the behavior."

I've heard from the late Julian Dunn, the upsample conversion can be "synchronous" by being 320x oversampled followed by 147x downconversion. I think in reality, there are *two* conversions, which is somewhat "lossy" compared to synchronous conversion.

"The upsampler's damping envelope will have a steeper rolloff than the classic sinc behavior, and will also have some peaking."

You cannot have a steeper rolloff than the "sinc"/"brickwall" filter function. The "sinc" function and the "brickwall" filter are one and the same. If you widened the FIR window, covering more of the "sinc" function, the "more-perfect" the brickwall filter's steep cutoff becomes.

"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"

You are getting carried away with "damping." In digital audio, there is *no* damping going on. It may *appear* damped relative to a "sinc" filter, but it is *not* damped in the classic sense.

The ringing is not "reduced," but *induced* by the digital filter. The FIR function is what *injects* a ringing pattern into the signal. A "time-resolute" filter (Wadia), which has a more-gradual rolloff, injects less "ringing" than a classic "sinc" filter. As I said earlier, this induced "ringing" attains a flatter response by reducing HF modulation and to attain rejection of artifacts above half the sample frequency.

"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"

The ringing frequency is half the base sample rate frequency. No way to get around that. Otherwise one would not get the proper "brickwall" response.

"Incidentally, this is the major strength of non-OS, limited only by the response of the analog electronics."

The non oversampling DAC just takes the *raw* CD data, and converts it directly to an analog signal. The image about half the sample frequency is attenuated solely by the analog post filter, as opposed to mostly by the digital oversampling filter. The analog post filter should have a steeper cutoff slope to reject most of that image.

"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."

The phase error is more of a function of the *symmetry* of the FIR coefficients than the amount of ringing that takes place. One FIR DAC could be a classic sinc with ringing, another FIR DAC could be a "time-resolute" function with almost no ringing, yet both have zero average phase error.

"To me, time smear is a much broader term which looks to be different from your perspective."

"Time smear" is simply the ringing components of the DAC's time response.

"Brickwall filter is an ambiguous term."

No it is not. It is a sharp cutoff filter made expressly to reject the images above half the sample rate frequency.

"The point of the post-filter ("brickwall" or not) is to roll off steeply enough to exclude high frequency images."

The post filter is almost *never* a "brickwall" filter. (Unless if it's also the main filter, like on the first Sony players.) Because the "brickwall" filter has already taken place in the oversampling DAC or upsampler. The purpose of the post filter is to "smooth out" the oversampled/upsampled signal, and since the sample rate of the oversampled is much higher in frequency, the post filter can be *very* gradual, and at a stop band frequency somewhere between half the base sample rate and half the *oversample* frequency rate.

"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 it rolls off quickly enough to reject the first image, it is *not* a gradual filter. A "brickwall" filter is *not* a gradual filter. The near-perfect vertical slope is where the term "brickwall" comes from. Conversely, a gradual filter does *not* completely reject the first image.

"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)."

An upsampler uses the exact same FIR window algorithm techniques as an oversampling DAC. I have to kindly say Doug is wrong. (Until a company comes out with an upsampler that expressly specifies such a response.) Remember, there is no damping going on whatsoever in a digital filter. The ringing is **always** induced by the filter function.

"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."

All digital filters have interpolation. Once can create a "trapezoidal" response by altering the filter coefficients in the DAC's "kernel." But the DAC would *still* interpolate in the "trapezoidal" case.

"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."

Dither is applied in the A/D *recording* process. The dither noise "toggles" the least-significant bit (LSB), where the bit would *not* toggle *without* the added noise. This toggled signal is then *stored* on the recorded media. When played back, this toggled signal running with a typical digital filter creates a resultant playback signal whose level is *below* the LSB.

But dither has no use whatsoever in the D/A process itself, unless one wants to merely raise the noise floor.

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

Different yes, but not necessarily "better."

"Key word is *significant*. Firstly, the post-filter phase shift is additive."

Actually, it's "subtractive"... [-;

"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."

It is impossible for the max phase error of a symmetric FIR filter to *exceed* 90 degrees (which is pi/2). With an analog filter, full pass band to full stop band shifts the phase angle -180 degrees. (This is what I meant by "subtractive.")

"Comparable, assuming non-brickwall filter, nor even a marginally steep filter because of the additive nature of the phase error."

It can be "brickwall" too. As long as the FIR coeffiecients are symmetrical.

"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 think you are saying because *analog* "brickwall" have poor phase response, this is done in the digital domain, since it can be done in the digital domain with better phase characteristics. And hence this is true.

Over 95 percent of all DACs sold in the past decade use "brickwall" digital filters.

"I still have a hard time believing this is true."

Would I lie to you? [-;

You may notice I said certain things several times. As I said, this is not the easiest stuff to understand. You may want to look up "Julian Dunn" on Google. This guy forgot more about digital processing than either of us will ever know. He passed away in the past year, and he will be missed.