MQA: Aliasing, B-Splines, Centers of Gravity Page 2

Austin: What about upward imaging during reconstruction?

Stuart: If properly managed, upward imaging need have no negative impact on the sound, especially if the images are beyond the frequency range of associated electronics or transducers. Nevertheless, MQA applies quite specific constraints, not just to replicate what was heard in the studio but to maintain envelope and slew rate.

Austin: MQA's main claim is that it improves temporal response—hence, sound quality—by removing digital-conversion–induced "timing artifacts." There's less "ringing," and no "pre-echo." Impulse response is shorter. Critics, though, have pointed out that aliasing, which MQA seems to accept by design (while attempting to minimize), manifests itself not just in the frequency domain but also in the time domain—as acknowledged in an MQA-related article written by you and Peter Craven (footnote 4). Is this a real issue? Is it significant?

Stuart: In MQA, the first moment (center of gravity) of the reproduced impulse is always at exactly the right place.

For a number of reasons based on the auditory science of object detection, it seems very plausible that the first moment is of prime importance to the ear and that higher moments are less important and (importantly) can be shown not to contribute errors such as jitter. The possible timing error caused by the variation of the leading-edge shape of MQA impulse response pales into insignificance compared with the error that results from triggering on the wrong peak; we are considering differences of more than an order of magnitude.

Austin: How can a system with finite aliasing have the center of gravity always in exactly the right place? How is this possible if, as suggested in the previous question, aliasing can induce timing errors?

Stuart: We need to answer your question in three ways: in general theory, theoretically relating to MQA, and in actual practice.

In fact, generalizations of sampling theory help us solve the practical situation we face.

A minimum-phase filter's impulse response has certain attributes: it has a risetime from zero to the first peak (which is not necessarily coincident with the center of gravity); it has a decaying portion; it has a total "area" (the 0th moment) that expresses the "energy" in the response; it has a total response duration from start to finish (infinite in an analog or IIR filter but finite in some digital systems; this duration we call the "support" of the filter); it has a 1st-moment (and a center of gravity = 1st/0th moments) that occurs after an impulsive input by an amount equal to the group delay at 0Hz; etc.

How is it possible that the center of gravity is always in exactly the right place? The simple answer is that this is a property of B-splines. The more complete answer is that the B-spline (and sinc) sampling kernels satisfy the so-called "Strang-Fix conditions."[footnote 5] MQA is designed to ensure that the center of gravity of a reproduced pulse is at exactly the correct place. Although the kernels in MQA are not simple B-splines—they comprise the convolution of a B-spline with another filter—this property of the B-spline remains after the convolution.

You may have realized by now that the comparatively recent theoretical advances in sampling theory attempt to deal with non-band-limited signals, or more exactly, to reconcile the fact that bandwidth and information content are not synonymous.

It is important to re-emphasize that whereas we commonly use the terms system end-to-end impulse response, characteristic response, and average kernel response, these provide convenient ways to express important ideas. However, in the real world we do not have impulses in air. We do not listen to impulses. In fact, the power spectrum of all the signals to which we listen are radically different from these test signals. In music, speech, and environmental sounds, the spectral energy decays as frequency rises, and normally that energy spectrum has decayed below the system noise floor before the "Nyquist frequency" of our "Encapsulation" (which includes a resampler when the signal sample rate is higher than the kernel rate). Aliasing cannot be a problem if there are no signals to alias. [Stuart's emphasis]

So, MQA is designed to ensure that the center of gravity of a reproduced pulse is at exactly the correct place. Hence, to the extent that the ear determines the "timing" of a pulse by estimating the center of gravity, MQA has no timing error at all. It would be strange if the ear used a measure radically different from the center of gravity, but an alternative measure such as the start of the leading edge leads to a result that differs only slightly—for example, by 2.6µs— compared with an error of about 13µs if a 192kHz stream has been sinc-filtered to a Nyquist of 96kHz and the ear mistakenly latches on to the first positive pre-pulse 13µs away. Or with an error of approximately 26µs if the stream is sinc-filtered to 48kHz in preparation for transmission at 96kHz.

Even this small error is with a highly unrealistic test signal. With actual music, in the application for which MQA was designed, this effect is either simply not present, or exists at such a low level that it is considered, by us, to be immaterial to the human listener.

Austin: Above, you said, "Aliasing cannot be a problem if there are no signals to alias." Is it not similarly true that time smear itself does not occur if there are no signals to alias?

Stuart: Any deviations that aliasing brings to the "impulse response" (when analog is being uniformly sampled) are quite different from the impact of the filters controlling (and contributing to) end-to-end system response. The latter is there whether or not filtering is adequate to control or eliminate aliasing. Time smear relates to the fact that the "filter" spreads every sample out in time, irrespective of frequency—particularly in the "real world," where we take into account quantization (and sometimes aliasing) effects in A/D, workstations, and DACs.

This smear, we believe, can be material for the human listener who is extracting multiple cross correlations, as well as envelope and nonlinear measures of the audio.



Footnote 4: This is the paper referenced in footnote 2. The relevant text: "Aliasing in the frequency domain is equivalent to the time-domain phenomenon of an impulse response that depends on where, relative to the sampling instants, the original stimulus was presented: see footnote 8." Footnote 8 reads: "The complication is that because of the sampling, the total system is not time-translation invariant and so does not have a unique 'impulse response'—the response is slightly different according to the position of an original impulse relative to the sampling points."

Footnote 5: Note that parenthetical "(and sinc)," which implies that this property of MQA is shared by the usual Shannon approach to sampling—that is, by old-fashioned PCM. For more on the Strang-Fix conditions and their implications, see Stereophile's "MQA: Questions and Answers."—Jim Austin

COMMENTS
dalethorn's picture

Adding to the above, a good tube/valve amp needs more power than the solid state types, so extra accomodation is required there. Sometimes the sound makes it very beneficial.

Bogolu Haranath's picture

You can use external power conditioners for cleaning up electricity ........ AQ makes several of these power conditioners ........ Also PS audio makes them ....... At least dozen other companies make these power conditioners .......... Many of these including AQ and PS audio are very favorably reviewed in Stereophile ....... RH-5 can put out a lot of "juice" ....... RH-5 has 3 different gain settings ......... It can drive any 'phone ....... I use Hugo2 which is battery powered (internal supply) ........ It can easily drive a lot of high efficiency low impedance 'phones including my Lcd-x and Lcd-MX4 ....... It has problem driving low efficiency high impedance 'phones like my Lcd-4 ...... Hugo2 sounds great with my high efficiency low impedance 'phones ....... Hugo2 is very favorably reviewed by many (and many "golden ear") audio reviewers ........

dalethorn's picture

I like AudioQuest products a lot, so I wouldn't hesitate to buy their power solution for a small amp that puts out maybe 5-10 watts of power. If you do have the power, chances are you'll like the lower efficiency headphones best. A lot of people read headphone specs and get "just enough" power, then they find out that a lot of the amps do a kind of "soft" clipping where the sound isn't too harsh, but some of the dynamics get squished.

Bogolu Haranath's picture

Agreed ......... RH-5 puts out enough power, it can drive any 'phone ......... Like I mentioned, it has 3 gain level settings as well ........... Check out AQ Niagara power conditioners .......... They have several of them ......... They are very favorably reviewed by many audio reviewers ..........

Bogolu Haranath's picture

Speaking about EQ, are you familiar with Sonarworks? ........Are you already using their EQ? ......... If not, check them out .......... They have several different EQs for several different 'phones ........ I saw Elear in the list but not Clear (yet) ........... Regarding Rogue RH-5, there are many reviews listed on Rogue Audio website including Stereophile review ........... R.A website also has all the specifications of RH-5 ........

dalethorn's picture

On this page you'll see Audioforge pages 1-10, with thumbnails and full photos of the curves I've created for nearly 200 headphones.

http://dalethorn.com/Photos.html

On this page, among other things, you'll see item 3 Headphone EQ with Audioforge Equalizer, which has the intro and precise settings for the images as noted above. Frequency, 'Q', and amplitude. Below that is item 4, Headphone EQ with Audioforge Tutorial. The tutorial is very brief, but helps a person understand what's involved and what's the goal (i.e. natural sound, NOT correction for individual hearing.)

http://dalethorn.com/Hifi2.html

Bogolu Haranath's picture

Thanks for your info ......... I will check those websites as you recommended ............ The poor impulse response of any transducer (mics, headphones, loudspeakers) can cause IMD and TDD (time domain distortion) ......... None of these transducers (so far) have perfect impulse response ...... Ehrlund says their triangular diaphragm (in the mics) has the best impulse response, hence the least amount of IMD and TDD ........... The MQA description of "blurring" could be IMD ...... Of course they also talk about TDD ....... My thinking is ...... are these distortions originating from the microphone? They may not be originating from the digital recording ......... The old computer saying "garbage in garbage out" may apply here ........ THD is different, although the origin of THD could be from the microphone ........ People measure THD+N ......... Is the "noise" originating from the microphone? ......... As I said before, I was trying to connect all the dots ........ Poor impulse response could also cause high Q factor .......... This could be the "ringing" Ehrlund describes ..........

dalethorn's picture

This is such a huge topic it will have multiple answers. First, the ehrlund mic reviews make it pretty clear that they are less a factor in distortions than most anything else. If you have time, check out the IsoMike site and maybe follow its logic to see how the left-right isolation reduces phase and other similar problems. Note that this is NOT specific to a particular microphone - it's a technique, and the Chopin Last Waltz recording is a great example.

http://isomike.com/he2004.html

One of the reasons a parametric equalizer is vital is because of strong narrow peaks and dips in the response, and you need a good continuous tone sweep to be sure where such narrow deviations occur. So even if you have a ringing problem, you may be able to suppress a particular peak in the response where the ringing is worst, enough to make your music listenable and enjoyable without losing that frequency entirely.

I can't guess exactly what MQA is doing, but as long as I have a good parametric equalizer I can make partial corrections for nearly anything, at least until a problem is so bad that a loss of detail in the area of that problem or distortion becomes so obvious that it can't be ignored - and then it's time to replace some hardware.

I like to find good gear at a reasonable price, but I respect the fact that the higher priced gear usually sounds better - not because it's always more neutral and detailed, but because it usually fixes a lot of the issues that cheaper gear can't.

Bogolu Haranath's picture

You can use external power conditioners for cleaning up electricity ........ AQ makes several of these power conditioners ........ Also PS audio makes them ....... At least dozen other companies make these power conditioners .......... Many of these including AQ and PS audio are very favorably reviewed in Stereophile ....... RH-5 can put out a lot of "juice" ........ It can drive any 'phone ....... I use Hugo2 which is battery powered (internal supply) ........ It can easily drive a lot of high efficiency low impedance 'phones including my Lcd-x and Lcd-MX4 ....... It has problem driving low efficiency high impedance 'phones like my Lcd-4 ...... Hugo2 sounds great with my high efficiency low impedance 'phones ....... Hugo2 is very favorably reviewed by many (and many "golden ear") audio reviewers ........

Bogolu Haranath's picture

Visit the website before you make up your mind, please ....... It is free ....... There are several videos, reviews and comments by several artists and recoding engineers, you can find on Google search ....... You can ask dalethorn above for further information ......... He posted some comments above about these microphones as well .........

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