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Old 19th November 2012, 08:04 PM   #21
SY is offline SY  United States
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I's this simple- the Fourier transform allows you to go back and forth from the time to the frequency domain with no loss of information. One completely specifies the other. But since it's a mathematical technique, you can't understand the mechanics of it without doing math. If integrals and series expansions are familiar, then you'll pick it up quickly. If not, you'll have to treat it as a black box.

Joe d'Appolito's book on loudspeaker measurement gives a fine introduction.
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Old 19th November 2012, 08:35 PM   #22
cvjoint is offline cvjoint  United States
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Quote:
Originally Posted by jcx View Post
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

in the FR graph neither frequency or amplitude uses complex numbers. From this, should I gather that while the impulse response has 3 dimensions the FR graph that is derived from it virtually ignores the phase (time) properties?

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

My understanding here is that some assumptions are made about the bandwidth, assumptions that may be feasible

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

in-band, aka hearing range? 20-20k

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

What is the burst signal like, frequency, amplitude? Is this just a showcase of the assumption outlined above?

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

Ahh the test signal is 6khz. It is not a showcase of the assumption. If I get this now, we are talking about -100db and as being outside of the audible range by output level not frequency. Ok, so now we are introducing a time shift, a delay that can be represented in us or degree units.

no "100 kHz" info used in the calculation - no evidence any gets to our our brain via our ears

There is a conclusion drawn here, but not sure what to make of it. The 6khz test signal and the secondly, the same 6khz test signal delayed by 10 us sounds the same to us?
I'll start with this first attempt and point some areas of clarification.
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Old 19th November 2012, 08:41 PM   #23
SY is offline SY  United States
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If a system is minimum phase, the frequency response and the phase response uniquely determine each other. If it is not, then you need to see a phase plot. The Fourier transform is a complex operation and yields complex data. The Energy-Time curve is a whole 'nother thing.

Seriously, grab the d'Appolito book, that will do better for you than trying to pick up hundreds of pages of information in a random, piecemeal manner. You need to get concepts like phase unwrapping and windowing.
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Old 19th November 2012, 09:35 PM   #24
jcx is online now jcx  United States
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Default and you may be tripping over "loaded phrases" in the ongoing EE/Audiophile debate

there is a major recurring argument from a part of the Audiophile/subjectivist side that “conventional engineering” applied to audio is "missing something critical" - that our measurements must be "incomplete" because they "don't explain how this sounds"

a subtheme is that engineers deliberately ignore time domain issues because they are so focused on frequency response, misuse theory that only applies to “infinite” sine waves, only make “steady state” measurements

magnitude, frequency response graphs don't show all of the information a engineer uses, expects in designing/testing, working “in the frequency domain” Bode plots are the more common engineering “frequency response” graphs – they have a added phase vs frequency plot – Nyquist plots are another perspective
yes the point is to display a “3-d” curve showing magnitude and phase vs time - and as Sy points out there are situations where the phase information is redundant

this magnitude, phase information is typically encoded in a Fourier Transform as complex number – as in the standard plots in the Ltspice simulation


the psychoacoustically established interaural time displacement resolution is often pointed to or referenced with the implication that sub 10 us resolution “must” mean silly engineers, Scientists calling ~20 kHz the upper limit of audio are just plain stupid
the faulty inference being that detecting a few us difference in the time delay between sounds presented to each ear “must” mean that we can “hear” ~ 1/t_delay in frequency, 100 kHz or more

my sim shows test signal similar to those used in the psychoacoustic interaural time delay listening tests – and that such signals don't have audible level above 20 kHz – the magnitude falls way below the noise floor
(nowdays I understand that you need special permission from your safety board to present sounds above ~ 80 dB SPL in a human listening test at a University)

I created the sim to show the time diference information is encoded in the fft - used by standard EE tools
the standard Ltspice fft plot result default only shows the magnitude, but the phase info can be inspected with the cursors, results in the grey box

the fft phase plotting can be turned on – but the plot isn't handily human readable because of large random numeric variation in frequency bins at the noise/numeric resolution floor – the phase really only is meaningful where the magnitude of the signal is large

by reading the values in the grey box for the cursors @ 6kHz, one on each of the delayed signal – you can see the fft contains the information on their relative time delay – you can calculate it from 21.6 degrees phase difference and the period of 6 kHz if you don't know how “group delay” is being calculated by the sw


so the 2 points I was trying to make were that interaural time delay discrimination of few us doesn't use signals above 20 kHz, doesn't imply we hear anything above 20 kHz

and the Fourier frequency domain tools do have the ability to detect small time differences between signals – completely in the frequency domain

Last edited by jcx; 19th November 2012 at 09:58 PM.
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Old 20th November 2012, 05:46 AM   #25
fas42 is offline fas42  Australia
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Sometimes there's nothing like "A Dummy's Guide to ...", just to get into the front door with a concept. Here's such an effort, talking about the visual or optics field in fact, but it's pretty easy to translate the concepts across to the auditory side of things, with a little thought: An Intuitive Explanation of Fourier Theory

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Old 20th November 2012, 10:53 AM   #26
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Visual representation of Fourier is helpful. Thanks for the link. Slight complication is that it is 3D, while audio signals are (a pair of) 2D.

Quote:
Originally Posted by cvjoint
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.
If in order to understand something you need to fully understand the precursors, but you don't, then it is not the other person's fault. It may be possible to get a general superficial grasp of something, but then the danger is that people misunderstand this for true understanding. In the case of Fourier you need to be aware of the possibility of an information-preserving transform (which some folk find hard to grasp), and for the detail you need to know about inner product spaces and orthogonal basis sets (which many EEs are never taught).

A recurring feature on DIYaudio is people who think they understand Fourier but actually do not; a little bit of knowledge can be a dangerous thing. These people flatly deny things which are true, and confidently assert things which are false.
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Old 21st November 2012, 03:39 PM   #27
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Quote:
Originally Posted by DF96 View Post
If in order to understand something you need to fully understand the precursors, but you don't, then it is not the other person's fault. It may be possible to get a general superficial grasp of something, but then the danger is that people misunderstand this for true understanding. In the case of Fourier you need to be aware of the possibility of an information-preserving transform (which some folk find hard to grasp), and for the detail you need to know about inner product spaces and orthogonal basis sets (which many EEs are never taught).

A recurring feature on DIYaudio is people who think they understand Fourier but actually do not; a little bit of knowledge can be a dangerous thing. These people flatly deny things which are true, and confidently assert things which are false.
maybe this is pointless philosophy but...
I think every new user here should be forced to read the post above prior to registration. and here's why.
I'm a computer engineering graduate. we are taught control theory during the first year. unfortunately, the part focusing on non-linear systems (which is the most interesting wrt audio) is only a few pages long and optional for the exam.
chance has had it that in 10 years I've never applied this in my field of work. engineering nowadays has to do with division of labor, making the customer happy and meeting deadlines no matter what but not so much with actual understanding or intellectual growth. but I digress...

I checked if I still have the control theory book that we used at the university and found it. browsed it a bit and imagine my surprise when I learned that I was first taught what a minimum-phase system is when I was 18. that's 15 years ago. needless to say, I forgot almost everything except the basics.

what's the point of all this? I can't recall the times when I read utter nonsense here and I believed it. and I'm not referring to the age-old subjectivist/objectivist debate, the "hearing is oh so complex that we won't ever understand it" mantra and all that. I'm speaking about things that are downright illogical and deny math. somehow I was many times dazzled by a few very vocal and self-confident users that keep posting things that would give a math teacher a heart attack.
I am sure it happens to many people, otherwise I can't explain some of the things I keep reading here. almost 10 years on diyaudio taught me that each and every post here must be taken with a grain of salt. sometimes this forum does a very good job at attempting to kill critical thinking. there are exceptions and I applaud those people who are able to see the common fallacies and try to point them out. some of them even manage to do it with great concision and simplicity.

what should people make out of this rant? the knowledge is out there. it was printed long before Internet even existed. I can bet a good book written 30 years ago would settle many of the recurring debates here once and for all. given it is read and understood, of course.

maybe it's time I read that control theory book one more time I'll finish the beer first, though. who needs critical thinking anyway?
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Old 22nd November 2012, 07:56 AM   #28
cvjoint is offline cvjoint  United States
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My prior is also that some folks that claim to understand linear distortion fully misrepresent the implications of some of the testing. For example, I never understood how the FR contains all the information the CSD has. If that were true, every FR that looked the same would also have the same corresponding CSD. Often times FR look very much alike, but there is severe ringing at some frequency in the CSD.

Some things I find fascinating in the responses:

Minimum phase, sounds like an assumption that could potentially determine the final result. Is the empirical evidence actual speaker performance, or a result of the assumptions the researcher makes? Does the minimum phase assumption hold in every listening environment, like a car?

If the phase content is sometimes redundant, then shouldn't we always have a 3d rendition in case it isn't? Basically, if you can display the full 3d in one graph, why collapse it to 2d because in "some" cases there is no need for the third dimension?

If the Fourier frequency domain tools are limited to small differences, is it large enough to pick up say... 2 standard deviations increase in decay performance? What is the magnitude of what it can and can't capture as a function of typical time domain distortion that speakers or environments are capable of?

In regards to: "An Intuitive Explanation of Fourier Theory" I'm just hoping there are ways to learn the limitations as well as the potential of tools in the Dayton Omnimic setup without having to have a strong background in Fourier type material. The President has a counsel, or two, he doesn't go out and read every book there is. It must be there are ways to acquire information that is faster than learning everything from scratch. Besides, it's more fun to learn from conversations. I read enough published work for work. I have seen applications of the FT in economics, optics, and acoustics now. I get some general workings, but I'm sure I'm far from understanding the specific application to audio.

I think some of the members here can educate others with regards to time domain distortion. This is a much more knowledgeable bunch than almost anywhere else (other audio forums).
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Old 22nd November 2012, 09:23 AM   #29
SY is offline SY  United States
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It is an unfortunate thing, but to really understand a mathematical technique, you have to get in there and do the math. Hand waving explanations will only mislead you further.

I'll recommend once again Joe d'Appolito's book, which has very nice qualitative explanations of things like phase unwrapping, minimum vs, nonminimum phase, windowing, and the other basic concepts which will allow you to at least have a surface understanding of this powerful tool.
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Old 22nd November 2012, 10:07 AM   #30
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Is this it? I suppose I could engage in some self-gifting this Christmas. Oh wait, I'm also buying 4 BG Neo10s, and two Airbone AMTs...
Testing Loudspeakers: Joseph D'Appolito: 9781882580170: Amazon.com: Books

Mr_push_pull, do you think I can read this cind stau pe tron?
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