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.
Joe d'Appolito's book on loudspeaker measurement gives a fine introduction.
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.
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.
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
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
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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
Frank
Frank
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.
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.
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).cvjoint said:
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?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).
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).
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.
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.
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?
Testing Loudspeakers: Joseph D'Appolito: 9781882580170: Amazon.com: Books
Mr_push_pull, do you think I can read this cind stau pe tron?
nu cred, e genul de carte care trebuie parcursa cu atentie. doctorii spun ca sederea prelungita pe tron e nesanatoasa.
(he asked if it's the type of book that can be read while satisfying certain physiological needs, I responded that I don't thinks so, it requires sustained attention and doctors say that prolonged sitting on that specific device is unhealthy).
Yes, you pay someone else to think for you. That is what presidents and managers do. The result is that they sometimes make bad decisions based on their misunderstanding of what they have been told.cvjoint said:
It is a characteristic of people who lack knowledge of a field that they often do not understand their own questions, let alone the answers. That is fine provided they realise that. The fundamental difference between a wise person and a fool is not how much they know, but how well they recognise the boundaries of their knowledge.
You can get so far with Fourier-type tools by just knowing that they tell you how much of a particular frequency is present. You can get further by knowing that phase information matters too, even though many tools hide this. Then you need to understand that FFT involves sampling, which then brings in issues about Shannon sampling theory and windowing. Eventually a wise person accepts that there are only two choices: learn the maths, or remain somewhat in the dark.
tell me about it. it may seem a naive look on things but it's true, sometimes (as in not always) they simply have no idea.
I remember when, at an ex employer, the engineering team was surprised to find that one of the managers didn't know that there were 2 MCU's in the project we were developing. movie like moment with the guy shrugging and going "well, somehow I get by without knowing it" LOL
I left them but somehow I'm not surprised to find that meanwhile the department is not doing so great and quality issues are constantly reported by customers. I find it funny how they always blame it on the engineers, exactly what W. Edwards Deming thought was not the thing to do.
another story. mr push pull is at work, stands and says to himself "ok, I really don't get it, I have to ask X". he goes to X's office and starts phrasing the question. stops in the middle of the sentence and goes "oh, now that I really think about it...". X tries to comfort mr push pull by saying "happens a lot to me too". moral? sometimes we think we try our hardest but we don't, really. the right question may contain 90% of the answer.
and on the subject... a concise, hands-on kind of book that, while not at all focused on audio, deals with part of the issues discussed here is "The DSP Guide". I read it when I was a student and as far as I remember it does the job. it is free for download here: The Scientist and Engineer's Guide to Digital Signal Processing's Table of Content printed version also available.
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I used to work in software development. We discovered something we called 'the cardboard cutout effect'. When someone had a nasty bug in his newly-written software he would describe the code in detail to a colleague and hope the colleague could spot the problem. We found that the act of explaining the code often resulted in the author finding his own bug. Thus the colleague could be replaced by a life-size picture.mr_push_pull said:
Some questions contain 90% of the answer. Other questions include assumptions which mean that the right answer may be rejected by the questioner.
and now you say? I used to keep a (3 years old) calendar with two barely dressed girls hanging on the wall near me at work...
(somehow no-one really noticed until a manager from US visited. I got to learn a few things about political correctness and how the slightest sexual implication while at work is not well regarded in US. don't mind me, I'm really tired.)
When you study speakers I'm sure all this can work the way you mean it too, and the best and brightest should lead the pack. When you have to deal with social issues, there is always a stochastic component to human behavior, an irrational part, etc. In social sciences decisions must be made and lines have to be drawn and different advisers perfectly capable of applying science to social behavior often get conflicting results and it's not because of an adding up error.
There are only 24 hours in the day and we spend a huge chunck sleeping, but more importantly we each only have 24hr. One that spends his work hours learning how to manage may have to forgo the benefit of learning Fourier theory. I'm not saying skills are accurately priced in the market but I do support the division of labor.
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