Re: A new paradigm?(On pitch and periodicity (was "correction to post")) ("Richard F. Lyon" )


Subject: Re: A new paradigm?(On pitch and periodicity (was "correction to post"))
From:    "Richard F. Lyon"  <DickLyon@xxxxxxxx>
Date:    Tue, 6 Sep 2011 19:29:10 -0700
List-Archive:<http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>

Ranjit, I commend you on your bravery. Dick At 12:53 PM -0400 9/6/11, Ranjit Randhawa wrote: >Dick, >I felt that it would not only be negligent on my part but also >cowardice, to end this thread without at least offering a possible >approach to a new "paradigm", even if I am not capable of describing >it in excruciating detail at the moment. So, with the greatest >trepidation, here goes. >If one were to consider a pure sinusoid in the phase domain (one >where the axis are x(t) and dx(t)/dt), the locus would be a circle. >The area of this circle would give us the magnitude, though how to >determine this requires a different approach as the integration over >2pi would be zero. >If we consider the product x(t)*dx(t)/dt as the rate of change of >energy it would have a sign associated with it, then it is possible >to determine this area, though the resulting algorithm would be too >simple and fall apart for more complex signals since we don't know >the period. To get a more general approach, it would be better to >consider the circle in sectors of harmonically increasing sizes, >thereby converting the sinusoid signal to a harmonic series, the >area of each sector becomes the magnitude of a related tonal >harmonic with the smaller sectors associated with magnitudes of >higher frequencies. >We see then that we start with a single sinusoid being considered >not as a single valued entity but as a harmonic series and this >therefore immediately answers two questions, the first being the >reported psycho-acoustical behavior whereby some people have >indicated an ability to recognize harmonics of a pure tone and shown >by others to be possible by using beats. The second being that the >extent of the traveling wave can have an explanation in that the >stiffness of the BM would limit activity for higher frequencies as >these frequencies would have smaller areas for lower strength >signals and the TW would grow as this strength increases. >More importantly, since we are directly using energy to determine >magnitudes, the missing fundamental would show a magnitude and this >magnitude would vary depending upon the relative phases of the >components. This approach also provides for a much reduced >computational method to determine the period, an alternative form of >auto-correlation. These two assertions are based on the method >chosen for determining the harmonic series and the one chosen by me >was picked from the field of psychology and called "evaluative >bivalence", whereby one makes use of sign associated with the rate >of change of energy in the summation process. >The modified auto-correlation does work rather well for >quasi-periodic signals and would welcome any suggestions for >practical use, since I don't believe it is used by the auditory >system. I believe it would fail in the "party room" environment. >Other options are possible based on the summation process. >There are many consequences of this approach as it now becomes >possible to provide a more exact method to explain source location >capabilities, pitch explanations, and I would like to say cochlear >functions but have to admit my knowledge at that level is focused >only on what has been reported on the behavior of the Traveling >Wave. The rest of it is a mystery to me. >I would like to apologize if this blurb causes some kind of angst >among some in this LIST. It was not the intent. I simply wanted to >show that sticking with existing mathematics has not made much >progress in being to explain our original discussion and that was >"The Case of the MIssing Fundamental". Thanks for your understanding >and kindness and sorry for this delay, >Randy Randhawa > > > > >On 8/4/2011 1:42 PM, Richard F. Lyon wrote: >>Randy, >> >>I'll be the first to agree that linear systems theory is sometimes >>stretched beyond where it makes sense, and that you need to use >>nonlinear descriptions to describe pitch perception and most other >>aspects of hearing, and more so when you get up to cognitive levels. >> >>I'm sorry to hear that you "gave up on linear systems", because I >>don't think it's possible to do much sensible with nonlinear >>systems when you don't have linear systems as a solid base to build >>on. Certainly at the level of HRFTs, cochlear function, and pitch >>perception models, a solid understanding of linear systems theory >>is in indispensible prerequisite. Then, the nonlinear >>modifications needed to make better models will seem less >>"tortured". >> >>Dick >> >>At 10:33 AM -0400 8/4/11, Ranjit Randhawa wrote: >>>Dear Dick, >>>While linear system theories seem to work reasonably well with >>>mechanical systems, I believe they fail when applied to Biological >>>systems. Consider that even Helmoholtz had to appeal to non-linear >>>processes (never really described) in the auditory system to >>>account for the "missing fundamental" and "combination tones". >>>Both of these psycho-acoustical phenomenon have been well >>>established and explanations for pitch perception are either >>>spectral based or time based with some throwing in learning and >>>cognition to avoid having to make the harder decision that maybe >>>this field needs a new paradigm. This new paradigm should be able >>>to provide a better model that explains frequency (sound!) >>>analysis in a fashion such that the nothing is missing and >>>parameter values can be calculated to explain pitch salience, a >>>subject that seems to be never discussed in pitch perception >>>models. >>>Furthermore, such a new approach should also be able to explain >>>why the cochlear is the shape it is, which as far as I can see has >>>never been touched upon by existing signal processing methods. >>>Finally, are these missing components "illusions" that are filled >>>in so to speak by our higher level cognitive capabilities? It is >>>remarkable that this so called filling in process is as robust as >>>it is, to be more or less common to everyone, and therefore one >>>wonders if all the other illusions are really not illusions but >>>may have a perfectly good basis for their existence. If they were >>>"illusions" one would expect a fair amount of variation in the >>>psycho-acoustic experimental results I would think. >>>I myself gave up on linear systems early in my study of this field >>>and have felt that other systems, e.g. switching, may offer a >>>better future explanatory capability, especially when it comes to >>>showing some commonality of signal processing between the visual >>>and the auditory system. To this end, I am quite happy to accept >>>that I do not consider myself an expert in linear system theory. >>>Regards, >>>Randy Randhawa >>> >>> >>>On 8/2/2011 1:49 PM, Richard F. Lyon wrote: >>>>At 5:55 PM +0300 8/2/11, ita katz wrote: >>>>>The periodicity is determined by the least-common-multiple of >>>>>the periodicities of the present harmonics, so if (for example) >>>>>a sound is composed of sines of frequencies 200Hz, 300Hz, and >>>>>400Hz, the periods are 5msec, 3 1/3msec, and 2.5msec, so the >>>>>least-common-multiple is 10msec (2 periods of 5msec, 3 periods >>>>>of 3.33msec, and 4 periods of 2.5msec), which is of course the >>>>>periodicity of the sum of the sines, or in other words 100Hz. >>>>>(actually it is the same as the greatest-common-divisor of the >>>>>frequencies). >>>> >>>>Ita, that explanation is sort of OK, but as written implies that >>>>the auditory system has the ability to do number-theory >>>>operations on periods (or frequencies), and depends on there >>>>being harmonics present and separately measureable. >>>> >>>>It would be much more robust to say that "The pitch is determined >>>>based on an approximately common periodicity of outputs of the >>>>cochlea," which I believe is consistent with your intent. >>>> >>>>Why is this better? First, it doesn't say the periodicity is >>>>determined; what is determined is the pitch (even that is a bit >>>>of stretch, but let's go with it). Second, it doesn't depend on >>>>whether the signal is periodic, that is, whether harmonics exist. >>>>Third, it doesn't depend on being able to isolate and separately >>>>characterize components, harmonic or otherwise. Fourth, it >>>>doesn't need "multiples" (or divisors), but relies on the >>>>property of periodicity that a signal with a given period is also >>>>periodic at multiples of that period, so it only needs to look >>>>for "common" periodicities--which doesn't require any arithmetic, >>>>just simple neural circuits. Fifth, it admits approximation, so >>>>that things like "the strike note of a chime" and noise-based >>>>pitch can be accommodated. Sixth, it recognizes that the cochlea >>>>has a role in pitch perception. It's still not complete or >>>>perfect, but I think presents a better picture of how it actually >>>>works, in a form that can be realistically modeled. >>>> >>>>Is this "tortured use of existing signal processing techniques" >>>>as Randy puts it? I don't think so. Is it "a unique way to do >>>>frequency analysis and to meet the dictum in biology that 'form >>>>follows function'"? Sure, why not? But why call it "frequency >>>>analysis"? How about "a unique way to do sound analysis" (if by >>>>"unique" we mean common to many animals)? >>>> >>>>I do have some sympathy for Randy's concern that we are far from >>>>a complete understanding, and that hearing aids are not as good >>>>as they would be if we understood better, but yes, he sounds way >>>>too harsh in overblowing it so. I'm wondering what's behind >>>>that, and whether it's just confusion about all the confusing >>>>literature on pitch perception, which I agree is a complicated >>>>mess -- or is the problem, indicated by Randy's previous posts, >>>>just that he doesn't understand basic linear systems and signal >>>>processing, and that's why it all seems "tortured"? >>>> >>>>Dick


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