Digital Drive: Re: Erroneous Stuff... by Todd Krieger

"If you oversample at a large integer multiple, the amplitude response is basically unity across the audible band. However, with upsampling (non-integer oversampling), you will get a damping envelope that begins to manifest itself in the audible band."

The amplitude response is totally dependent on the digital filter function. It is unity if classic windowed "sinc" interpolation is utilized. A more-time-resolute Redbook filter will have a more-gradual rolloff, beginning at roughly 10 kHz. This is because a time-resolute filter allows more "modulation" of HF signals, hence the *average* amplitude in the HF range is somewhat lower than unity.

I do not know what you mean by "damping envelope" in the event of asynchronous sample conversion, but upsampling does not "damp" anything.

"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.

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.)

"And with this particular type of digital filter, the phase error is not terribly bad. In this sense, it is a 'gradual filter that reduces time smear'."

The average phase error on a symmetrical-window FIR filter has nothing to do with "time-smear." If the coefficients of the FIR "taps" are symmetrical along the window, the average phase error will be zero. The "time smear" has to do with the "attack" and "decay" mode of the function itself. The "ringing" is induced into the signal to cut down HF modulation and improve rejection of frequencies above half the sample rate frequency.

"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.)

"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.

"Which type of Redbook playback are you talking about? Are you referring to redbook playback as a whole?"

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.

"I recall (correct me if I'm wrong on this) that one of the strengths of FIR filters is pure phase response."

If the coefficient window is symmetric (almost all of them are), that is correct.

"This type of filter is quite common in oversampling DACs."

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

"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.

"For non-oversampling DACs such as my dAck"

I will be getting one of these things shortly!!

"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.

"The ZOH operation in non-oversampling DACs results in total phase error of 90 degrees across the band; in practice it is not quite this bad."

True, if you are talking maximum *instantaneous* phase error. There is no way to get around this on *any* DAC.

"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.

"That's part of why the imaging with the dAck! is so good; most digital designers are so concerned about flat frequency response that by ensuring it, they compromise imaging performance."

Well, as I said, I'll be trying one these out!! (The DACK is the opposite extreme to upsampling, which is *no* oversampling or upsampling.)

I realize this is not exactly the easiest concept to grasp, but I hope you find this a neat learning experience!

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.