Digital Drive: A DAC's "Brickwall Filter" is *Not* the Analog Post Filter... by Todd Krieger

"You are restricting 'damping' to time domain artifacts only. But it can be applied to any domain."

In signal theory, there are only two "domains." The time domain, and the frequency domain. In the context of Redbook digital audio, the ringing has a much bigger impact in the time response than the frequency response.

"Upsampling is asynchronous oversampling, i.e., it is oversampling using non-integer multiples of the sampling frequency."

Upsampling does not *have* to be asynchronous. You can set the upsample frequency to 88.2 or 176.4 kHz (as opposed to 96 and 192 kHz), and it would become synchronous. Since there is a more-direct signal correlation with synchronous conversion, such a conversion would be less "lossy" than with asynchronous conversion. (Unless the conversion is actually the 320/147 method.)

"This is what gives rise to all the effects Doug specifies in his paper"

Asynchronous conversion is *not* preferable to synchronous conversion, since in the case the 320/147 method is not utilized, the signal at the new rate will have to be calculated off an *interpolated* (filtered) signal, not the actual data on the CD. (It's analogous to putting an extra gain stage in an amplifier.)

"> 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.

How is this synchronous? Explain this in more detail."

44.1 * 320 / 147 = 96. This is an *exact* calculation. (For conversion to 192 kHz, it would be "640/147".) The problem is every upsampler data sheet I have seen indicates the conversion is *not* done by this particular method.

"The brickwall term describes the analog post-filter, not the behavior of the digital filter."

You have this backwards... Otherwise the digital filter would be doing a useless function, and the analog post filter would be acting like those old Sony analog brickwall filters.

"It's called brickwall because it has to be steep enough to wipe out the first image starting at about 24KHz."

Actually 22.05 kHz...

"If you use the FIR without the gradual post-filter, there is flat response to 22KHz, then nothing, then stuff starting at x*fs, where x=the oversampling coefficient. This is not brickwall behavior, this is just oversampling."

It is oversampling *and* the brickwall filter... Provided the oversampled signal is convolved with the windowed "sinc" FIR function.

"Sinc rolloff is *not* the FIR impulse curve. The FIR impulse curve is described by a sinc function which arises due to the finite number of fourier components. Again, this is not the sinc rolloff."

"Sinc rolloff" is the sharp cutoff of the "brickwall" response. The Fourier *transform* of the sinc function in the time domain is the "brickwall" response in the frequency domain. The Fourier transform is the frequency domain/time domain relationship.

"> 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.

Not true with an upsampler. Due to asynchronicity, the ringing frequencies are not half the sample rate."

The filter response in the upsampler is totally dependent on its **input** sample rate. Just like with an oversampling DAC. It has nothing to do with the sample conversion, be it synchronous or asynchronous.

"The fourier coefficients in the upsampler's reconstructed impulse are different from those in the FIR's reconstructed impulse."

The upsampler first filters the signal like an oversampling DAC, and *then* does the conversion. If this was not the case, you would end up with "frequency-modulated" distortion due to the asynchronous conversion. (Which output sample gets tied to the input sample?) Or maybe a broken signal.

"My point was that you are associating time smear only with impulse response."

Because the only way it can be seen is with impulse response!! You know, those "bumpy" square wave plots and impulse plots that used be shown in reviews of CD players and DACs. The vast majority of players and DACs exhibited similar behavior, since all were made for a flat response to beyone 20 kHz, and such behavior requires convolving the signal with the windowed "sinc" function. Hence the impulse response has the ringing induced by that "sinc" function.

"Impulse response contains information about the phase error,"

The average phase error can be seen in the symmetry of the impulse response, which correlates to the symmetry of the FIR function.

"but it doesn't explicitly tell you anything about real world musical transient response."

It sure does!! If it rings, the transient response is "smeared." That is where the "time smear" manifests itself!

"You need to see the behavior of the phase response across the audible band to understand the effect on time smear (as per my definition of time smear above)."

Phase error, once again, is dependent on the symmetry of the FIR function. The time smear is induced by the FIR function, if the function of choice is the "sinc" function. A symmetrical function is not necessarily a "sinc" function, hence it does not necessarily induce "time smear." And the "sinc" function can be assigned "asymmetrically" in the FIR kernel, which would increase phase error, but leave "time smear" roughly the same.

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

Defined by whom? Ringing components are supposedly inaudible."

Defined by the ringing in the impulse response. And *only* that. And I personally *can* hear the difference between a "sinc" function DAC and a "time resolute" (less ringing) DAC. A "time resolute" DAC uses a function that induces *less* ringing than classic "sinc," and reduces "time smear".

"Like I said in the previous message, transients in real music are not anything like the impulse function (or the FIR-filtered approximation), they are spectrally complex."

But which DAC would you rather listen to- one that rings from transients, or one that does not? I think the impulse response is the best indicator of how one perceives the music from a time-resolution standpoint.

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

My point above (The brickwall term describes the analog post-filter..., etc.). "

Once again, the "brickwall filter" is the digital filter in the upsampler or DAC, not the post filter...

"Which is the brickwall to you, the post-filter or the oversampler?"

In the oversampler!

"You're inconsistent about this"

Where did I say otherwise?

"Here, you say that brickwall filter takes place in the digital filter itself."

Yes.

"Prior to this, you said that all DACs are using brickwall filters nowadays (except non-OS)."

Also yes. More like "95 percent" in my recollections.

"Any way you think about it, there is a contradiction."

No, since almost every DAC uses oversampling or upsampling (a few have no oversampling), and almost all such DACs use the "brickwall" filter (a few use alternative filter functions).

"And saying that an upsampler is a brickwall filter is patently wrong."

You can choose to believe the one posting the wrong information- I won't stop you. This is why I have such a big problem with misleading technical papers. People believe the misleading stuff, and end up purchasing suspect equipment as a result. But, this is a free country.

"> Conversely, a gradual filter does *not* completely reject the first image.

Yes it does! The gradual rolloff filter does reject the first image of the FIR filter."

If the "gradual" refers to the **slope** of the filter. If the slope is "gradual," some of the image will pass through!! The FIR filter does not produce the image, it rejects the image that would exist if the digital signal was *not* filtered.

"About interpolation, that is obvious and has nothing to do with how to obtain differential linearity with 'frequency-dependent high-frequency image' dither, which you still aren't understanding."

Once again, dither is applied in the A/D stage. You are believing someone who has no clue what dither actually does. (I'd be happy to correct this guy directly, if given the opportunity.)

"I know that you understand classic dither, which I termed noise floor dither in my previous post, same thing as 'hiding the LSB in noise' "

Dither does not hide anything. In fact it "unhides" information below the LSB, when applied properly in the A/D process. Information that would remain "hidden" had dither *not* been applied.

"Noise floor is a DC phenomenon, and you put a random LSB signal on top of it to "linearize" the LSB error. Now extrapolate this to a high frequency tone, say a constant zero order hold at X volts. Now during each ZOH timeslice, the upsampler modulates this with a series of dither levels, made up of frequencies that are non-integer multiples of the sample output frequency. This is what I termed "plateau dither" previously."

I have no clue here... Except the fact noise floor has nothing to do with DC...

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

Yes it does have use in the D/A process, because it linearizes the noise floor. With an upsampler and also with 1x sampler, it also linearizes the D/A conversion."

Try to find an audio upsampler chip or DAC data sheet that mentions "dither" in it... http://www.cirrus.com/en/pubs/proDatasheet/cs4932am-3.pdf

For your convenience, the link below is a Google Search...

http://www.google.com/search?hl=en&lr=&ie=UTF-8&oe=UTF-8&q="data+sheet"+Upsampler+Dither+-Video+&btnG=Google+Search (Open in New Window)