Work on "time domain optimized filters" by M. Moffat

[arbenede]

In his book "Schiit Happened: The Story of the World's Most Improbable Start-Up" Jason Stoddard mentions work done by Mike Moffat on "First true time domain optimized digital filters, based on math perfected with a U of Iowa Professor Emeritus of Mathematics and a RAND Corp mathematician". In a different section of the book a certain John Lediaev math professor at the University of Iowa is mentioned, so I assume that he is the author of the aforementioned math. I have looked for papers by Lediaev on DSP math but did not find anything. I was wondering if anyone on this forum has any pointers to these works, if they were ever published.

 

[Wombat]

Give him a call: http://homepage.divms.uiowa.edu/~jlediaev/

 

[mansr]

Smells like BS. First off, what does "time domain optimized" even mean?

 

[arbenede]

When they say "time-optimized" it seems that they mean that the reconstruction filter retains the original time samples, i.e. it simply interpolates. Another term that they use is "closed-form digital filtering" where closed-form is related to the fact that the filter coefficients are computed in closed form, not iteratively. I searched in the DSP literature and found only one paper [1] mentioning "closed-form filter". If I find Mr. Moffat's email I'll ask him directly.

[1] Huang, Xiangdong, et al. "Closed-form FIR filter design with accurately controllable cut-off frequency." Circuits, Systems, and Signal Processing 36.2 (2017): 721-741.

 

[dc655321]

Is this interest simply for the sake of curiosity, or because you believe there may be something novel in what you've read?

BTW - what is your level of expertise with DSP?

 

[Mnyb]

Did not Theta DAC’s from the early years before they made HT processors hade some ridiculous novel filters . That did trigger your BS meter. As far as I can remeber did not Mr Moffat founded Theta ? Where they not pioneers in the separate DAC biz ?

I can’t say what I thought was wrong . I reckon you can be wrong on a “higher level” . For some reasons you can find people with absurd amounts of theoretical knowledge that still basically don’t get it ?

 

[arbenede]

Is this interest simply for the sake of curiosity, or because you believe there may be something novel in what you've read?

BTW - what is your level of expertise with DSP?

I am a EE with a pretty good knowledge of DSP theory (my main field is computer vision/image processing). So I am not a pure DSP guy (I have never designed a digital filter, for example) but I have a good understanding of FFT theory, sampling theory, statistical signal processing etc). My interest in this topic is for the sake of curiosity, as you suggested. I would just like to understand the theory behind Moffat's statements.

 

[mansr]

When they say "time-optimized" it seems that they mean that the reconstruction filter retains the original time samples

Why is that supposed to be desirable?

 

[dc655321]

I am a EE with a pretty good knowledge of DSP theory (my main field is computer vision/image processing). So I am not a pure DSP guy (I have never designed a digital filter, for example) but I have a good understanding of FFT theory, sampling theory, statistical signal processing etc). My interest in this topic is for the sake of curiosity, as you suggested. I would just like to understand the theory behind Moffat's statements.

Cool.
Welcome to ASR. Let us know if you find out what exactly was meant by those vague Schitt statements.

Maybe I'm somewhat jaded, but almost anything claimed by that group as technologically novel sends my BS-O-meter into the red...

 

[arbenede]

Why is that supposed to be desirable?

I think I see what you are getting at... since the samples stored on the CD or the audio file have been acquired with a physical transducer they are affected by noise, so from a statistical signal processing point of view interpolation does not seem to be a good idea. Right?

 

[Matias]

Smells like BS. First off, what does "time domain optimized" even mean?

I suppose the typical step response is well behaved without pre and post ringing.

http://archimago.blogspot.com/2016/07/musings-digital-interpolation-filters.html

http://archimago.blogspot.com/2018/01/audiophile-myth-260-detestable-digital.html

https://www.ayre.com/wp-content/uploads/2020/08/Ayre_MP_White_Paper.pdf

 

[MusicNBeer]

Why is pre/post ringing a problem exactly? Use minimum phase if you're really worried about pre-ringing. Our own hearing is filtered so our eardrum response creates the ringing anyway before it gets to the brain. Different ringing response, but same idea. I think this is another case of audiophile myths taken as fact.

 

[briskly]

From Stereophile, originally published in 1992.

Harley: All your designs—even the $1250 DS Pro Prime—use computer-based DSP chips running custom filtering software. Do you think DSP-based digital filters are a requirement for state-of-the-art digital playback?
Moffat: I believe so, yes. That's because there are no digital filters you can buy that optimize for time-domain performance. They are designed for best frequency-domain performance—minimum ripple in the passband and maximum attenuation in the stopband. They are frequency-domain devices only.
One of the purposes of an oversampling system, where you add dots [samples] between the existing dots, is to add more information. In the captive filter design [an off-the-shelf filter chip], that translates to improvements you see on spectrum analyzers—lower ripple and better stopband characteristics. But there is no optimization or enhancement of the time domain. So you're constrained to whatever information is in the original recording. Whereas in a time-domain–optimized filter, you can improve [the time-domain characteristics] the way you would improve the frequency-domain characteristics of a captive filter. With DSP filters you get the best of both worlds.
Harley: How much of your processors' spatial qualities are a result of DSP-based filters and custom software?
Moffat: Almost all of it. Having done a number of experiments with captive filters—the NPC, Philips, Sony, etc.—the variations of the algorithm they all run doesn't do anything to optimize the time-domain performance. The algorithm we run is a specific time-domain enhancer. That's why I build processors that are Motorola-based [the Motorola 56001 DSP chip] as opposed to captive filter–based; there is a substantial difference in imaging and sense of space.

The "time-optimization" performed is not clarified. The system response of Moffat's more recent DACs is clearly linear-phase.

closed-form is related to the fact that the filter coefficients are computed in closed form, not iteratively

Try applying a window (Hann, Kaiser, etc.) to a sinc/rect function.
I don't understand the problem with using an iterative method to determine coefficients, although I would think there is a more useful optimization method than the Remez/Parks-McClellan algorithm out there.

 

[Matias]

Still for all the optimization, the step response and roll off of their flagship Yggdrasil DAC looks pretty conventional brickwall fast filter to me.

https://www.stereophile.com/content/schiit-audio-yggdrasil-da-processor-measurements#

 

[ElNino]

I am a EE with a pretty good knowledge of DSP theory (my main field is computer vision/image processing). So I am not a pure DSP guy (I have never designed a digital filter, for example) but I have a good understanding of FFT theory, sampling theory, statistical signal processing etc). My interest in this topic is for the sake of curiosity, as you suggested. I would just like to understand the theory behind Moffat's statements.

I'm somewhat of a DSP nerd too. For the most part, Moffat's statements statements in the last 10 years or so regarding filtering don't make a lot of sense and are often incoherent (in the sense that there's no way to parse them in a way where all of his claims are mutually consistent).

He seems to have done work in two areas at different times: (i) closed form filtering and (ii) non-linear phase filtering. The "comboburrito" filter Schiit currently uses is just a regular linear phase filter, perhaps implemented as a closed form. Moffat also claims that this filter allows integer ratio oversampling to be done without affecting existing sample values, but that's impossible in the general case.

 

[MusicNBeer]

Moffat also claims that this filter allows integer ratio oversampling to be done without affecting existing sample values, but that's impossible in the general case.

It would have to have infinitely flat passband out to pre-interpolation Fs/2 and gain of 1. Yes, impossible theoretically, but maybe possible to get within quantization rounding. What's the point though? None.

 

[KSTR]

Pulse response and FR look pretty exactly like "full sinc upscaling" á la Rob Watts (Chord M-Scaler) or, to even higher precision, via software as proposed by Keith Howard and realized to extreme precision here. I've compiled his SoX branch to try it out but first tests so far to no avail (no difference in ABX). I probably need to reduce apparent sampling frequency so that it is in my audible range (15kHz tops) to see if I can reliably detect a difference between any kind of reconstruction filter from (droop-corrected) NOS with min-phase post filter to 16x uspcaling with full sinc function to 24bit+ precisions...