Re: Non-linear additions to linear models. (was On pitch and periodicity (was "correction to post")) (Ranjit Randhawa )


Subject: Re: Non-linear additions to linear models. (was On pitch and periodicity (was "correction to post"))
From:    Ranjit Randhawa  <rsran@xxxxxxxx>
Date:    Sun, 7 Aug 2011 11:50:21 -0400
List-Archive:<http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>

Hi Dick, My last observation is on your suggestion of adding non-linearity to some linear model to cover what some people may call illusions. As an aside, I believe Helmholtz was forced to add in the quadratic function only because experimentalists (Seebeck I believe) were breathing down his neck proving the existence of the missing fundamental problem. I would have to strongly disagree with some of the conclusions reached from such quadratic and cubic expansions. In my opinion, I think when people say that a new paradigm was needed I assumed that it meant a totally new approach to signal analysis that did not necessarily adhere to any assumptions of linearity. Take for example a system based on rate of change of signal energy, it could right away explain some minor psycho-acoustic phenomenon associated with changes in static pressure or that tricky bias term that comes up when one is analyzing sounds like speech. But as I am sure you would point out, much more would be needed before such a statement could have any validity as the basis for a system theory. I agree. On that note, I believe that till some such system is offered for review, non-linear additions to linear models will have to do for rest of us who are appalled by the associated mathematics. Regards, 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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