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Old 17th November 2012, 09:55 PM   #11
SY is offline SY  United States
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If that's what you want, start with the impulse response in the time domain, not the ETC.
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Old 17th November 2012, 11:30 PM   #12
jcx is offline jcx  United States
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the Fourier domain is fine too – the “amplitude only” restriction is a strawman tactic for use in Sophmoric arguments

“The Fourier Transform” of a time series contains both amplitude and phase info – using single complex number values for each frequency bin

the intra aural uS time domain resolution results say nothing about hearing beyond 20 kHz

the test signals are all “in band” - enveloped sine bursts of << 20 kHz

the sim below show the spectrum of such a burst signal, its frequency content falls over 100 dB by 20 kHz – practically no “information” is conveyed above 20 kHz


I delayed the raised sine enveloped 6 kHz by 10 us – you can read the delay from the fft plot cursors (both @ 6 kHz) calculate it yourself from the 6 kHz, 21.6 degree phase difference

no "100 kHz" info used in the calculation - no evidence any gets to our our brain via our ears
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Last edited by jcx; 17th November 2012 at 11:45 PM.
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Old 19th November 2012, 12:24 AM   #13
cvjoint is offline cvjoint  United States
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Shucks, that went right over my head. Is there a 5th grade level explanation for the above?
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Old 19th November 2012, 12:15 PM   #14
DF96 is offline DF96  England
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I may be wrong, but my guess is that the OP does not have sufficient foundation in maths and physics to understand his own questions. 'Time domain' and 'frequency domain' have meanings, connected via Fourier theory. I am not familiar with the American school system but I would guess that 5th grade does not cover orthonormal basis functions on inner product spaces, which is the foundation of Fourier?
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Old 19th November 2012, 01:56 PM   #15
SY is offline SY  United States
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Ours did. By sixth grade, we were deriving closed form solutions to the three body problem.
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Old 19th November 2012, 02:55 PM   #16
DF96 is offline DF96  England
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OK. Educate me: at roughly what age do you come across this stuff?

In the UK it would probably be 1st or 2nd year undergraduate (i.e. 18 or 19 years old) - perhaps slightly earlier for physicists, slightly later for EEs, but with wide variations.
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Old 19th November 2012, 03:40 PM   #17
SY is offline SY  United States
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1st year undergrad for physics and physical chemistry majors. The concept of complete orthonormal basis sets was covered in Chem 101, then Math 102 was where we first saw Fourier expansions and decompositions.

I didn't finish high school so perhaps some of this was covered earlier as well.
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Old 19th November 2012, 04:11 PM   #18
DF96 is offline DF96  England
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Nice to know that US and UK teenagers are at roughly the same educational level. One minor caveat: I was reporting when I did it (nearly 40 years ago) so it could be done a bit later these days as our school system has degraded since then.
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Old 19th November 2012, 04:38 PM   #19
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Schools are never as good as they used to be. More's the pity.
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Old 19th November 2012, 07:51 PM   #20
cvjoint is offline cvjoint  United States
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I'm not an engineer or a physicist...this is a hobby for me. Nonetheless, I regularly have to explain my research to specialists in other industries. Presenting to a wider audience is basic requirement in many fields is it not?

I've studied in both European and American (U.S.) institutions. In the E.U. the general consensus seems to be that everyone must have a rather elevated general knowledge tool set. In the U.S. the contribution to society comes first, general know-how far second. I find the U.S. model is a key ingredient to U.S.'s success. Snookie may not know how to read but she certainly has a show with global appeal. If she did take the time to learn Fourier theory I doubt she would be the movie star, and therefore the massive GDP contributing export that she is.

1. at least some of you should be able to explain the Fourier mapping in a different way. To some degree the ability to teach reflects your own grasp of the subject matter.

2. If I took a simple random sample of the population (U.S., E.U., or the world), or even the undergraduate, or graduate subsamples the share of those who know the Fourier transform would be negligible. I know this because the majority cannot take a derivative. However, I don't see this as a failure of the education system. Specialization is key.

If I get 5 explanations of the Fourier transform, they are all alike, and equally incomprehensible to someone that does not know it already, I might be considering it a failure on your part. :P
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