I already gave this address: http://iesk.et.uni-magdeburg.de/~blumsche/ Just add M275 after ~blumsche/ and find again my result. I did never promise to make my Matlab code here public. I merely tried to link a wave file in order to provide the opportunity of a comparison between my result and what any traditional spectrogram gets from the same stimulus. Be sure, any such available software does not even come a little bit close. Stephan M. Bernsee wrote:> What is this M275/4 and where can we get it? I think you promised some > Matlab code to see what you're talking about... > > > Eckard Blumschein wrote>>I tried to link a pertaining wav file to M275. >>Maybe someone is also interested in M274.
simultaneous frequence and phase estimation
Started by ●April 21, 2004
Reply by ●June 23, 20042004-06-23
Reply by ●June 23, 20042004-06-23
Eckard Blumschein wrote:> I already gave this address: > > http://iesk.et.uni-magdeburg.de/~blumsche/ > > Just add M275 after ~blumsche/ and find again my result.http://iesk.et.uni-magdeburg.de/~blumsche/M275 gives me "Not Found - The requested object does not exist on this server. The link you followed is either outdated, inaccurate, or the server has been instructed not to let you have it." What now?> I did never promise to make my Matlab code here public.Well, I asked for Matlab code to back up your claims, and you said you'll get back to us later because you're too busy now. Although I cannot imagine a reason why someone working at a German university could be too busy to reply (sorry, couldn't resist), I do honor that you did reply. I honestly wasn't expecting this! So, no Matlab code. That's sad. You indeed claim you've found the holy grail but won't let us see it? You're really not giving us much to discuss this with you, don't you. Let's recount what we know so far: we have your postings that you're on to something. We're still lacking a description of that "something" but we have your assertion that it is "better" in some way than "everything else", that it evades the Heisenberg restriction, that you call it a "natural spectrogram", and we know it has something to do with the FCT. Oh, and not forgetting that and we've seen a nice picture that explains not a thing. I am very sorry, but the only conclusion I can reach here is that you're either a fraud or indeed so clever that the motive behind your behaviour eludes me (self-promotion maybe?). Even though I enjoy the argument, I don't see how it can be productive if you don't provide an additional incentive to tease us with...> I merely tried to link a wave file in order to provide the opportunity > of a comparison between my result and what any traditional spectrogram > gets from the same stimulus. Be sure, any such available software does > not even come a little bit close.I'd be curious to see that file once you've sorted out the link problem. I cannot really imagine how a wave file could clarify anything (at least not without some explanation), but I can't wait to see/hear it. Bear in mind that a "spectrogram", as the word suggests, is usually something to see, not hear. --smb
Reply by ●June 23, 20042004-06-23
After a little detective work, I found this works: http://iesk.et.uni-magdeburg.de/~blumsche/M275.html Richard Dobson There is a link to a soundfile "stimulus.wav", but it fails; either it's not there, or access permissions aren't set. Richard Dobson Stephan M. Bernsee wrote:> Eckard Blumschein wrote: > >>I already gave this address: >> >>http://iesk.et.uni-magdeburg.de/~blumsche/ >> >>Just add M275 after ~blumsche/ and find again my result. > > > http://iesk.et.uni-magdeburg.de/~blumsche/M275 gives me "Not Found - > The requested object does not exist on this server. The link you > followed is either outdated, inaccurate, or the server has been > instructed not to let you have it." > > What now? > > >
Reply by ●June 23, 20042004-06-23
"Stephan M. Bernsee" <stephan.bernsee@web.de> wrote in message news:38ab652c.0406230211.5e0df94c@posting.google.com...> Eckard Blumschein wrote: > > I already gave this address: > > > > http://iesk.et.uni-magdeburg.de/~blumsche/ > > > > Just add M275 after ~blumsche/ and find again my result. > > http://iesk.et.uni-magdeburg.de/~blumsche/M275 gives me "Not Found - > The requested object does not exist on this server. The link you > followed is either outdated, inaccurate, or the server has been > instructed not to let you have it." > > What now?Perhaps he intended http://iesk.et.uni-magdeburg.de/~blumsche/M275.html ? -- David Biddulph
Reply by ●June 23, 20042004-06-23
I would like to apologize for not yet fulfilling your demands.
Those who will have trouble to get, analyze, and interpret the wav file,
might look at the following equivalent sketch of the stimulus:
ooooo ooooo
ooooooooooooooo oooooooooooooo axis of elapsed time
ooooo ooooo
At the left margin, elapsed time equals zero. For the last 5
milliseconds the stimulus equals +one. Between 5 and 10 ms of past time,
it equalled -one. You may see three further steps which happend earlier.
Of course, do not try to listen to that file. It would merely be quite
simple to use e.g. CoolEdit or one out of many many other Programs
available as to get a spectrogram. I did so in CoolEdit and other
programs, tried also the specgram command of Matlab, and I asked those
who offer spectrogram software to do the same with their presumably ever
more powerful tools. The result was disappointing. Not a single
traditional tool delivered a spectrogram that was nearly as similar to
measurement and simulation of cochlear function as is my "natural"
spectrogram for the same above sketched stimulus.
Admittedly, the traditional spectrogram shows magnitude vs. time and
omits phase because of Ohm's law of acoustics.
_The_ natural spectrogram does not omit phase. It conveys all
information and would correspondingly be reversible.
Because it is not subject to the notorious trade-off between temporal
and spectral resolution, I concluded that it might not be subject to the
uncertainty principle either. This was wrong. Actually the natural
spectrogram shows output before on could expect it according to the
uncertainty principle. However, this output is not yet the finally
correct one. In other words: Frequency chirps up. The same was found to
happen in the cochlea. Sometimes it is alternatively called frequency
glide. Cochlea also apparently ignores the uncertainty principle. This
might be reasonable because animals do not intend to accurately measure
frequency but they simply have to survive. Some insects have their ears
close at their wings as to tive down as soon as they get aware of the
call of a bat. So rapid response is crucial.
> What now?
I will send the file by email attachment to you.
>>I did never promise to make my Matlab code here public.
And I will not do so here. I gave the code (about 100 lines) to a few
people, and nobody found an error so far.
> I cannot really imagine how a wave file could clarify
> anything (at least not without some explanation), but I can't wait to
> see/hear it. Bear in mind that a "spectrogram", as the word suggests,
> is usually something to see, not hear.
Yes. We do not hear what is to be seen. Even the natural spectrogram
does not yet show what we hear. But it is a more correct basis for a
correct correlogram which will perhaps do the job.
Eckard Blumschein
Reply by ●June 23, 20042004-06-23
Hi Richard, yes I've been there too, but as you said, the link to the .wav doesn't work either ;-) --smb
Reply by ●June 24, 20042004-06-24
Hi Eckard, Eckard Blumschein wrote:> > I would like to apologize for not yet fulfilling your demands. > Those who will have trouble to get, analyze, and interpret the wav file, > might look at the following equivalent sketch of the stimulus: > > ooooo ooooo > > ooooooooooooooo oooooooooooooo axis of elapsed time > > ooooo ooooo > > [snipped]Ok. So if I understand correctly, you analyze the stimulus in your wave file with both your "natural spectrogram" and a "traditional spectrogram" (we postpone the exact definition of the two terms for now). Now, how are we supposed to reproduce these results if we don't have access to your "natural spectrogram" code? It must be clear to you that without the means of reproducing the object in question (your spectrogram plot) we don't have a means for a comparison or evaluation. You should at least provide the visual output for both your "natural spectrogram" and a "traditional spectrogram" for us to see what you're talking about.> Admittedly, the traditional spectrogram shows magnitude vs. time and > omits phase because of Ohm's law of acoustics.If your definition of "traditional" is equivalent to "STFT-based", Ohm has nothing to do with it *). Phase is discarded simply because you're interested in the magnitude of the partial frequencies - that's practically the definition of a spectrogram. Displaying the phase, too, would only clutter the readout. Bear in mind that the spectrogram does not make the claim to be in any way related to something our auditory system does, it is primarily a means for measuring frequency, strength and, to some degree, onset of periodic signals. As such, discarding phase in this context is perfectly justified, because it has no bearing on magnitude. It also makes your comparison sortof futile, because you're comparing apples with oranges: a device intended for frequency measurement to a device that is supposed to model the human auditory process at its first stage. I think noone claims that human hearing uses a spectrogram like the one you have in Cooledit!> _The_ natural spectrogram does not omit phase. It conveys all > information and would correspondingly be reversible.Yes and no. If you're using the FCT (Fourier Cosine Transform), this is only true for even signals.> Because it is not subject to the notorious trade-off between temporal > and spectral resolution, I concluded that it might not be subject to the > uncertainty principle either. This was wrong.It sure was. And you're wrong about another thing, too: it is the uncertainty principle that imposes a lower limit on the time and frequency localization tradeoff. The FCT (Fourier Cosine Transform), like it's "parent" the full Fourier transform, maximizes the frequency localization at the expense of losing time localization. Think about that for a moment, and how it fits your above conclusion!> Actually the natural > spectrogram shows output before on could expect it according to the > uncertainty principle.Yes of course it does. If you're using the FCT (Fourier Cosine Transform), it is still very much subject to the Heisenberg restriction. As I said above, the basis functions of the FCT are cosines, which have perfect frequency localization but no time localization. This fact does not change depending on whether or not you include phase in your plot. You may also realize that you have just indirectly admitted that your resolution is actually not superior to the traditional (STFT-based) spectrogram. If you're using the Fourier Cosine Transform (which is what you said) and create a spectrogram from it that you admit being subject to the Heisenberg uncertainty principle we must conclude that it cannot have superior resolution. It may present your data differently, but that doesn't change the fact that it cannot be beyond anything we have already seen.> However, this output is not yet the finally > correct one. In other words: Frequency chirps up. The same was found to > happen in the cochlea. Sometimes it is alternatively called frequency > glide.Now you're mixing up things. If you use the FCT, it is *you* who is correlating the cosine basis functions at increasing (or decreasing, as you wish) discrete frequencies with the signal in question. This is neither a "glide", nor has it anything to do with the frequency glide observed by Carney in cats when he was measuring impulse responses of auditory nerve fibres (which is what I assume you're alluding to). It is just part of the procedure - comparing it to chirp responses of a nerve cell is like correlating the 4-year election period of the German Bundeskanzler with the 4-year population period of the May beetle.> Cochlea also apparently ignores the uncertainty principle.You probably mean the "auditory system" here, not the cochlea (you sometimes use these terms interchangeably, which is incorrect!). And I wouldn't be so quick to make this judgement.> This > might be reasonable...I'd rather say "conceivable" here. I doubt nature is ever "reasonable" in anything that exists as part of evolution.> ...because animals do not intend to accurately measure > frequency but they simply have to survive. Some insects have their ears > close at their wings as to tive down as soon as they get aware of the > call of a bat. So rapid response is crucial.Yes it is. But that doesn't have to mean that their perceptual processes evade the Heisenberg restriction. Think about irregular sampling and its impact on time and frequency resolution, aliasing, etc. Biological systems don't have a crystal built in to guarantee a uniform sample rate! And while we're at it: what about precision? What may this tell us about your attempt to model it using a (in both precision and sampling) discrete Fourier cosine transform, and the restrictions that come with it?> > What now? > > I will send the file by email attachment to you.I'm still looking forward to receiving it, although what you write above leads me to believe that it will not help much.> And I will not do so here. I gave the code (about 100 lines) to a few > people, and nobody found an error so far.Good for you! But that still doesn't prove it correct or incorrect, nor does it say anything about the validity of your claims.> Yes. We do not hear what is to be seen. Even the natural spectrogram > does not yet show what we hear. But it is a more correct basis for a > correct correlogram which will perhaps do the job.I'm afraid I have insufficient data on which to base such a conclusion. --smb _____________ *) He had some funny ideas about our auditory perception anyway, as did Helmholtz. But let's not get into this now.
Reply by ●June 24, 20042004-06-24
Stephan M. Bernsee wrote:> You should at least provide the visual output for both > your "natural spectrogram" and a "traditional spectrogram" for us to > see what you're talking about.Once again, this link will guide you to the mentioned example of a natural spectrogram: http://iesk.et.uni-magdeburg.de/~blumsche/M275.html My sketch and or linked wav file show the input. You can easily either analyze the wav file or create a corresponding input file from my sketch and then perform a usual spectrogram. When I did so, I always received a rather boring pattern of either vertical or horizontal lines or at best a coarse combination of both. I am ashamed of perhaps not being able to choose the best settings of parameters. As soon as somebody found acceptable settings I will try and add the traditional output to M275 for comparison.>>Admittedly, the traditional spectrogram shows magnitude vs. time and >>omits phase because of Ohm's law of acoustics. > > > If your definition of "traditional" is equivalent to "STFT-based",Yes. > Ohm> has nothing to do with it *).*) He had some funny ideas about our auditory perception anyway, as > did Helmholtz. But let's not get into this now. I will wonder if you can tell me something new. I did not directly refer to Ohm but to Ohm's law and the fact that hearing is actually highly insensitive against phase, not entirely though. You may understand it from natural spectrogram.> Phase is discarded simply because <<people are>> > interested in the magnitude of the partial frequencies - that's > practically the definition of a spectrogram.When the spectrogaph was invented in the late fourties, there was no alternative as to restrict to magnitude.> Displaying the phase, too, would only clutter the readout.It was not imaginable at all.> Bear in mind that the spectrogram does not make the claim to be> in any way related to something our auditory system does, It has been in use as to mimic the cochlea or even the auditory system.> it is primarily a means for measuring frequency,No. It is not just a spectrum but a representation over time.> strength and, to some degree, onset of periodic signals. As such, > discarding phase in this context is perfectly justified, because it > has no bearing on magnitude.The spectrogram shows rather a misleading pattern.> It also makes your comparison sort of futile, because you're comparing > apples with oranges: a device intended for frequency measurement to a > device that is supposed to model the human auditory process at its > first stage.E.g. linguists, researcher who are dealing with animal sound, engineers, and many others try to read out the pattern of a spectrogram. Neither the natural spectrogram nor cochlea itself are designed just for the first stage.> I think no one claims that human hearing uses a > spectrogram like the one you have in Cooledit!On what input are automatic speech-recognizers based if not a current spectral analysis?>>_The_ natural spectrogram does not omit phase. It conveys all >>information and would correspondingly be reversible. > > > Yes and no. If you're using the FCT (Fourier Cosine Transform), this > is only true for even signals.I do not know you, and I have to be polite in any case. However, I feel deeply disappointed because you did not even understand the simplest basics of what I found out. Use of even and odd functions of time is only necessary iff you decide to tacitly accept Heaviside's trick and perform a complex-valued Fourier transform. In this case one has to have a time function that extends from minus infinite to plus infinite including past as well as future time. Windowing does not matter in that respect. Future sound is not available to the ear and also not to the spectrograph. Only the latter is using a zero-padded half-axis of time resulting in an even real and an odd imaginary function of frequency. With real-valued analysis - as it is performed in cochlea as well as with the natural spectrogram - there is neither negative time nor negative frequency at all. I do not use FCT as a special case of FT in IR but my ear and me restrict to reality, which can sufficiently be reflected in IR^+. Notice, redundancy only belongs to complex FT.>>Because it is not subject to the notorious trade-off between temporal >>and spectral resolution, I concluded that it might not be subject to the >>uncertainty principle either. This was wrong. > > > It sure was. > > And you're wrong about another thing, too: it is the uncertainty > principle that imposes a lower limit on the time and frequency > localization tradeoff. The FCT (Fourier Cosine Transform), like it's > "parent" the full Fourier transform, maximizes the frequency > localization at the expense of losing time localization. Think about > that for a moment, and how it fits your above conclusion!I am defintely correct in this point. Incidentally, FCT is not necessarily derived from a parent FT but it is a equivalent whil not redundant representation.>>Actually the natural >>spectrogram shows output before on could expect it according to the >>uncertainty principle. > > > Yes of course it does. If you're using the FCT (Fourier Cosine > Transform), it is still very much subject to the Heisenberg > restriction. As I said above, the basis functions of the FCT are > cosines, which have perfect frequency localization but no time > localization. This fact does not change depending on whether or not > you include phase in your plot.I should tell you that elapsed time does not share its zero with ordinary time.> You may also realize that you have just indirectly admitted that your > resolution is actually not superior to the traditional (STFT-based) > spectrogram. If you're using the Fourier Cosine Transform (which is > what you said) and create a spectrogram from it that you admit being > subject to the Heisenberg uncertainty principle we must conclude that > it cannot have superior resolution. It may present your data > differently, but that doesn't change the fact that it cannot be beyond > anything we have already seen.Your thinking is not precise in that case.>>However, this output is not yet the finally >>correct one. In other words: Frequency chirps up. The same was found to >>happen in the cochlea. Sometimes it is alternatively called frequency >>glide. > > > Now you're mixing up things. If you use the FCT, it is *you* who is > correlating the cosine basis functions at increasing (or decreasing, > as you wish) discrete frequencies with the signal in question. This is > neither a "glide", nor has it anything to do with the frequency glide > observed by Carney in cats when he was measuring impulse responses of > auditory nerve fibres (which is what I assume you're alluding to).I appreciate that you are a little bit familiar with Laurent Carney, http://www.ima.umn.edu/biology/wkshp_abstracts/carney1.html hopefully with Mario Ruggero, Roy Patterson and others, too. I do not correlate in the usual manner cosine basis functions as you imagine.>>Cochlea also apparently ignores the uncertainty principle. > > > You probably mean the "auditory system" here, not the cochlea (you > sometimes use these terms interchangeably, which is incorrect!). And I > wouldn't be so quick to make this judgement.I gave a partial answer in M275. Look at data by Lin and Guinan in JASA.>>This >>might be reasonable... > > > I'd rather say "conceivable" here. I doubt nature is ever "reasonable" > in anything that exists as part of evolution. > > >>...because animals do not intend to accurately measure >>frequency but they simply have to survive. Some insects have their ears >>close at their wings as to tive down as soon as they get aware of the >>call of a bat. So rapid response is crucial. > > > Yes it is. But that doesn't have to mean that their perceptual > processes evade the Heisenberg restriction.Do not conclude on a wrong basis. Think about irregular> sampling and its impact on time and frequency resolution, aliasing, > etc. Biological systems don't have a crystal built in to guarantee a > uniform sample rate!That is why they perform more robust. Sorry I have even to stop reading now. Eckard
Reply by ●June 25, 20042004-06-25
The problem is that the link to "stimulus.wav" doesn't work. It is actually there, or are permissions set incorrectly? Richard Dobson Eckard Blumschein wrote:> > Once again, this link will guide you to the mentioned example of a > natural spectrogram: > http://iesk.et.uni-magdeburg.de/~blumsche/M275.html> My sketch and or linked wav file show the input.
Reply by ●June 25, 20042004-06-25
Hi Eckard, Eckard Blumschein wrote:> Once again, this link will guide you to the mentioned example of a > natural spectrogram: > http://iesk.et.uni-magdeburg.de/~blumsche/M275.html > My sketch and or linked wav file show the input.Too bad the .wav file doesn't work. It's a dead link - we already told you that.> I will wonder if you can tell me something new.I was rather hoping you could tell me something new!> I did not directly refer to Ohm but to Ohm's law and the fact that > hearing is actually highly insensitive against phase, not entirely > though. You may understand it from natural spectrogram.How? Our hearing is *not* insensitive to phase. It is insensitive to *absolute* phase, but actually quite capable of perceiving relative phase. For example, the phase in dichotic stimuli is important for the perception of localization cues.> > Phase is discarded simply because <<people are>> > > interested in the magnitude of the partial frequencies - that's > > practically the definition of a spectrogram. > > When the spectrogaph was invented in the late fourties, there was no > alternative as to restrict to magnitude.I doubt it. I know for a fact that Henrik Bode was known to plot magnitude and phase in his frequency response plots of complex functions since 1938 and the sound spectrograph was invented by Potter a little later, so I highly doubt that they were unable to plot phase in a spectrogram if they had wanted to. Maybe Jerry has some additional information, IIRC he provided valuable information on Bode plots some time ago.> > Displaying the phase, too, would only clutter the readout. > > It was not imaginable at all.I'd rather think it was not necessary! Why would someone plot phase in a spectrogram? How would you be able to say anything meaningful about the magnitude at a certain point if your display keeps oscillating wildly?> > Bear in mind that the spectrogram does not make the claim to be > > in any way related to something our auditory system does, > > It has been in use as to mimic the cochlea or even the auditory system.It has been used to study harmonic signals, most importantly speech. Since it has been observed that the auditory system localizes stimuli in time and frequency it seemed obvious (but not equivalent!) to use the spectrogram as a means for comparison and study. In the beginning this choice was easy, because the spectrogram was more or less all there was for such a purpose But the analogy is crude, even though it helps understanding some of the principles wrt. frequency. Going so far as to claim that the spectrogram was used as a means to "mimic the cochlea or even the auditory system" is nonsense - it has been (and still is) a means for plotting frequency dependent magnitude of periodic signals over time, nothing more.> The spectrogram shows rather a misleading pattern.No. The spectrogram shows exactly the pattern it was designed to display: the frequency and time dependend magnitude of partial waves in a signal. This is not misleading, it is, in fact, highly relevant to what it was designed to do. The misleading part comes from you believing it should do otherwise.> Neither the natural spectrogram nor cochlea itself are designed just for > the first stage.The cochlea *is* the first stage of our auditory perception (if we leave aside peripheral factors like the pinnae that contribute to the perception, but are not actually involved in the "active process"). The cochlea is the place where sound waves are converted into information in the form of nerve pulses.> > I think no one claims that human hearing uses a > > spectrogram like the one you have in Cooledit! > > On what input are automatic speech-recognizers based if not a current > spectral analysis?I never questioned whether ASR software is using "spectral analysis" (btw. are we talking just about a spectrogram or the whole "spectral analysis" ballgame here with all its possible flavors?). I said I doubt that someone claims that the *human hearing* uses a spectrogram like the one in CoolEdit, therefore it is my belief that you're barking up the wrong tree with your rant about the (natural or not) spectrogram.> >>_The_ natural spectrogram does not omit phase. It conveys all > >>information and would correspondingly be reversible. > > > > Yes and no. If you're using the FCT (Fourier Cosine Transform), this > > is only true for even signals. > > I do not know you, and I have to be polite in any case.Well, you don't have to, but it would be nice. I also see no reason why you shouldn't. I just said that the Fourier Cosine Transform is the even part of the complete Fourier Transform. That is how it is defined, and I see nothing wrong with that definition (neither do I find that statement in any way objectionable). According to its definition, the Fourier Cosine Transform is only meaningful for even signals. Does that fact disturb you? And if so, why?> However, I feel > deeply disappointed because you did not even understand the simplest > basics of what I found out.I'm sorry if I disappoint you, but you must admit you don't give us much to understand this from. Maybe you can tell me what you've found out *exactly*, so I can provide a less disappointing response?> Use of even and odd functions of time is > only necessary iff you decide to tacitly accept Heaviside's trick and > perform a complex-valued Fourier Transform.You mean I should paint my fingernails in pink like he did? :-) The Fourier Transform is inherently complex, because that's how it is defined. Perhaps it is my limited knowledge but I have not seen any other definition called the "Fourier Transform" that omits the "i".> In this case one has to have > a time function that extends from minus infinite to plus infinite > including past as well as future time. Windowing does not matter in that > respect.It does, on the discrete side of things, if you want to get any meaningful representation of your signal. There are no true infinities in a discrete world. The basis functions of the DFT are complex exponentials. As I said in my last post, they have perfect frequency localization but do not have time localization. This boils down to the fact that for each of them, time has no global significance. You cannot tell if you're *right here*, or one period away. This is no different for the Fourier Cosine Transform, except for the added restriction that it assumes even symmetry of your sequence. And you don't have to do any interpretation of negative time and negative frequency - these are just "labels" for the axes that are somewhat arbitrary and, as you said, redundant in all cases but for complex signals. If that redundancy really bothers you, why not use the Hartley transform instead - it is purely real and contains the same information. Now that we got rid of negative time and frequency, what have we gained over the Fourier Transform? Nothing really. For both the DFT and the Fourier Cosine Transform, the basis functions are periodic, which means they extend indefinitely into the past and the future. If you limit the transform to a finite window, they will be spaced in a way that their periods are in integer relationship to the transform size, which defines the resolution of the analysis. But they will always have constant amplitude and frequency (ie. no time-dependent change, that is the definition of "lack of time localization"), so the time localization is actually a function of your transform size. And without some sort of window, there is no way the transform will produce any meaningful result in practice. So, with that in mind, what is it now your FCT-based "natural spectrogram" does differently that would it make it "superior" to a "traditional spectrogram"? [Btw. in your last post you wrote: "Actually the natural spectrogram shows output before one could expect it..." Since I don't have code to reproduce what you see, I can only infer from this statement and the fact you are using the Fourier Cosine Transform that your "natural spectrogram" is subject to the same time localization restrictions as all other STFT-based spectrograms. One more piece of evidence that it is not *superior*, just different!]> Future sound is not available to the ear and also not to the > spectrograph. Only the latter is using a zero-padded half-axis of time > resulting in an even real and an odd imaginary function of frequency. > With real-valued analysis - as it is performed in cochlea as well as > with the natural spectrogram - there is neither negative time nor > negative frequency at all. I do not use FCT as a special case of FT in > IR but my ear and me restrict to reality, which can sufficiently be > reflected in IR^+. Notice, redundancy only belongs to complex FT.I agree that for purely real signals the Fourier Transform has redundancy. I assert that this redundancy is not influencing the outcome and can be avoided from the result (sortof a truism, because that's how redundancy is defined). So why would you have a problem with that? I believe you assign a meaning to the Fourier Cosine Transform that it does not have. No matter how you think about it, the Fourier Cosine Transform, as per its definition, is the even half of the Fourier Transform. Either you're talking about something other than the Fourier Cosine Transform (please define then!), or you are simply mistaken.> > Yes of course it does. If you're using the FCT (Fourier Cosine > > Transform), it is still very much subject to the Heisenberg > > restriction. As I said above, the basis functions of the FCT are > > cosines, which have perfect frequency localization but no time > > localization. This fact does not change depending on whether or not > > you include phase in your plot. > > I should tell you that elapsed time does not share its zero with > ordinary time.I'm not sure what you mean by "elapsed time" (elapsed since when? The start of our measurement? The time I was born?) and "ordinary time" (= time since the Big Bang?). Please explain.> > You may also realize that you have just indirectly admitted that your > > resolution is actually not superior to the traditional (STFT-based) > > spectrogram. If you're using the Fourier Cosine Transform (which is > > what you said) and create a spectrogram from it that you admit being > > subject to the Heisenberg uncertainty principle we must conclude that > > it cannot have superior resolution. It may present your data > > differently, but that doesn't change the fact that it cannot be beyond > > anything we have already seen. > > Your thinking is not precise in that case.At what point?> I appreciate that you are a little bit familiar with Laurent Carney, > http://www.ima.umn.edu/biology/wkshp_abstracts/carney1.html > hopefully with Mario Ruggero, Roy Patterson and others, too. > I do not correlate in the usual manner cosine basis functions as you > imagine.In what manner do you correlate them instead? And yes, I am quite familiar with the work you mentioned. I am partly involved in research in that direction, although on a commercial basis so I can't publish.> > Yes it is. But that doesn't have to mean that their perceptual > > processes evade the Heisenberg restriction. > > Do not conclude on a wrong basis.Do you think that's what I do? Why?> I gave the code (about 100 lines) to a few > people, and nobody found an error so far.Well, try me for a change :-) I'm pretty sure I can sort out the discrepancies if I have a clue of what's actually going on. But I must assume from previous correspondence that you do not want to share solid evidence with us but instead have us believe you from the little information you provide. I agree with you that this is disappointing. Maybe it's time to inquire about a separate comp.dsp.religion NG? :-)> Sorry I have even to stop reading now.That's too bad! I thought we were finally getting somewhere... --smb
