There is a lot of reliance on FFTs in this forum as the final arbiter on comparisons between devices - I have seen statements made that if it's below the noise floor of -120dB then it isn't of importance!
The frequency characteristics seems to always get the focus of attention when analysing audio signals. I would like to draw attention to a paper that has been referenced before "The audibility of the temporal characteristics of audio systems" in which it analysis some aspects of the temporal characteristics of audio as opposed to the frequency characteristics.
There are examples given in that paper of different input signals which result in the same FFT spectrum plot. Forgive me if this has been discussed here before but in the threads I have participated in, in which FFT plots have been shown, I have not seen any phase spectrum plots shown only amplitude plots.
The frequency characteristics seems to always get the focus of attention when analysing audio signals. I would like to draw attention to a paper that has been referenced before "The audibility of the temporal characteristics of audio systems" in which it analysis some aspects of the temporal characteristics of audio as opposed to the frequency characteristics.
There are examples given in that paper of different input signals which result in the same FFT spectrum plot. Forgive me if this has been discussed here before but in the threads I have participated in, in which FFT plots have been shown, I have not seen any phase spectrum plots shown only amplitude plots.
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So, what is the question 
Based on your other threads perhaps it is a questioning of measurement vs. perception?
FFT's are a tool. Like a hammer, they may be used for good or ill.
Just because two signals have the same fft doesn't make them sound the same, I don't think anyone would make that claim. Does that mean that the measurement is useless? No.
Based on your other threads perhaps it is a questioning of measurement vs. perception?FFT's are a tool. Like a hammer, they may be used for good or ill.
Just because two signals have the same fft doesn't make them sound the same, I don't think anyone would make that claim. Does that mean that the measurement is useless? No.
My questions - why are the phase plots seldom shown when FFT plots are presented here? It seems like only the frequency domain is being focused on to the exclusion of the temporal domain. Is this half the picture then & can this half-picture be of any value?So, what is the question
FFT's are a tool. Like a hammer, they may be used for good or ill.
Just because two signals have the same fft doesn't make them sound the same, I don't think anyone would make that claim. Does that mean that the measurement is useless? No.
(log)magnitude Fourier display has been found exceedingly useful by engineers for a while now
it makes some properties of system measurements easily visible to "educated" human perception/interpretation
it is excellent for picking "simply" structured multitone frequencies out of noise - and for detecting correlated errors as "new" frequency components with amplitudes above the noise floor - both intermodulation and harmonic distortions
the (log)magnitude display also gives the experienced viewer information about the measurement “quality” – the level, shape of the noise floor, level, frequency of external interference “spurs, “noise skirts” showing source noise properties – all can be used to quickly diagnose test and equipment errors that wouldn’t be as accessible to human perception from a time series plot ( oscilloscope or ADC plot )
to make these judgements you need to know about sample rate, record lenght/bin size, ADC bit resolution but sometimes this inforamation isn't provideded in a graphic - often the point can be made/decerned just with the relative levels at the frequencies of interest even without all of the information
the phase information is available for calculation but is not directly "human readable" - because the “noise floor” has "full magnitude" bin-to-bin phase variations making it hard to visually separate "interesting" phase features
also the "useful" phase information with the test signals best suited to Fourier analysis is the relative phase between well defined "single bin" frequency components - many "FFT" display software will allow measures between cursor pairs so that you can "navigate" to the relevant measurement pairs where the phase difference is helpful
under easy to meet conditions on real world measurements the full “complex valued” magnitude and phase Fourier output is the mathematical “dual” of the
Time Series data and contains exactly the same “information” – just arranged differently and which makes some of the “information” easier for humans to “read”
it makes some properties of system measurements easily visible to "educated" human perception/interpretation
it is excellent for picking "simply" structured multitone frequencies out of noise - and for detecting correlated errors as "new" frequency components with amplitudes above the noise floor - both intermodulation and harmonic distortions
the (log)magnitude display also gives the experienced viewer information about the measurement “quality” – the level, shape of the noise floor, level, frequency of external interference “spurs, “noise skirts” showing source noise properties – all can be used to quickly diagnose test and equipment errors that wouldn’t be as accessible to human perception from a time series plot ( oscilloscope or ADC plot )
to make these judgements you need to know about sample rate, record lenght/bin size, ADC bit resolution but sometimes this inforamation isn't provideded in a graphic - often the point can be made/decerned just with the relative levels at the frequencies of interest even without all of the information
the phase information is available for calculation but is not directly "human readable" - because the “noise floor” has "full magnitude" bin-to-bin phase variations making it hard to visually separate "interesting" phase features
also the "useful" phase information with the test signals best suited to Fourier analysis is the relative phase between well defined "single bin" frequency components - many "FFT" display software will allow measures between cursor pairs so that you can "navigate" to the relevant measurement pairs where the phase difference is helpful
under easy to meet conditions on real world measurements the full “complex valued” magnitude and phase Fourier output is the mathematical “dual” of the
Time Series data and contains exactly the same “information” – just arranged differently and which makes some of the “information” easier for humans to “read”
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Thanks Jcx,
I'm not a user of FFT plots & as I find out more information about it's use as a tool, I tend to want to ask those who use them here, the questions that occur to me. It does make me wonder if these tools are being used appropriately when at least half of the information in a music signal is temporal - maybe even more as the ear seems to have a higher sensitivity in the temporal domain then in the frequency domain. Yet phase information tends to be ignored in most FFT plots posted here. Any idea why? Maybe those who use it as a tool would care also to answer this?
I'm not a user of FFT plots & as I find out more information about it's use as a tool, I tend to want to ask those who use them here, the questions that occur to me. It does make me wonder if these tools are being used appropriately when at least half of the information in a music signal is temporal - maybe even more as the ear seems to have a higher sensitivity in the temporal domain then in the frequency domain. Yet phase information tends to be ignored in most FFT plots posted here. Any idea why? Maybe those who use it as a tool would care also to answer this?
Because it makes it easier for us geeks to keep all you tweaks in the dark?
Seriously though, for the large part, the magnitude information is what we're interested in.
It's true that we tend to pay attention to what we can measure and understand, and the effects of phase changes are less obvious, but a change in phase that is not accompanied by a change in amplitude is difficult to contrive deliberately, never mind it occurring by some coincidence of circuit values, particularly across a range of frequencies.
The time for wondering this is when you have learned to use them yourself, not before. Why do you imagine you have the right to importune and accuse people who have made the effort which you have not?
No it's not. Phase at the ear changes all the time as you move around. You're just aware that you're moving around, or not, as the case may be... When you move your head, there's a differential change in phase from the lowest frequency to the highest, the high frequencies changing by a whole cycle or more, the low by only a fraction.
No, it doesn't. People still listen to mono. Only a tiny fraction of the experience is lost.
You're just allowing yourself to be overawed. Temporal doesn't mean 'The Enterprise went through a wormhole' It means 'the off-licence is shut'
Get yourself some education. I don't mean 'read up on it on the internet', I mean, 'go somewhere they have teachers you can argue with and you have to pass exams.'
w
Yes, they are. For non-minimum phase devices (e.g., the vast majority of electronics and components), a Hilbert transform will yield phase data. A complex FFT of the data will yield both real and imaginary parts, from which phase data are also trivially obtained. Phase data are commonly presented in speaker measurements, where non-minimum-phase is common.
FFT helps use spectrum analyzers or better say that spectrum analysis is based on Fourier transform imho.
So once somebody feeds 1KHz into amp input and checks spectrum plot of the output it is where all these French mathematicians magic is in use. Very useful to check if 100Hz-120Hz depending on a country bleeds into signal from a power supply for example.
So once somebody feeds 1KHz into amp input and checks spectrum plot of the output it is where all these French mathematicians magic is in use. Very useful to check if 100Hz-120Hz depending on a country bleeds into signal from a power supply for example.
Yes it is covered by ice but icebreaker crush it in the middle occasionally so people would not tempting cross the river by frozen surface (that what I heard the reason for it but not 100% sure - just a rumor) because it is very hazardous walking on ice especially spring time when it starts melting.
If you plotted the phase information from an FFT calculation it would not necessarily tell you anything useful. Much of the phase data will simply be due to a constant time delay, which can be subtracted off. Because of the way our ears detect frequency, they are not particularly sensitive to phase. By definition, FFT only applies to periodic signals so it tells you nothing directly about transients. However, most amps have sufficiently simple circuits that their transient behaviour will not be pathological. By 'transient' I mean what an engineer means by transient: the exponentially decaying reponse after a stimulus has been removed. Given the steady-state response you can find the transient response. The only issue then is overload response - I guess you could look at how the FFT changes with signal level. Or, as I suggested in another thread, take the frequency response, find the poles and zeroes, then plot their movement with signal level. My guess is that an amp with stable, or smoothly moving, poles/zeroes will sound OK but this would have to be checked against reliable double-blind listening tests.
All FFT give you phase (no need for two channels!), this naturally comes out of the algorithm.
If you want to know about temporal response, you probably need to use wavelet transforms rather than Fourier. You could design a pathological amp which delays all signals above 1kHz by 100ms (e.g. use digital filters). On FFT it would look fine, but it would sound very strange. Fortunately it is very difficult to do anything like this accidentally.
All FFT give you phase (no need for two channels!), this naturally comes out of the algorithm.
If you want to know about temporal response, you probably need to use wavelet transforms rather than Fourier. You could design a pathological amp which delays all signals above 1kHz by 100ms (e.g. use digital filters). On FFT it would look fine, but it would sound very strange. Fortunately it is very difficult to do anything like this accidentally.
I believe I read somewhere that we can detect phase at low frequencies, but only time of arrival at high frequencies. As far as absolute polarity is concerned, my understanding is that some people can detect this on some signals, but most people cannot detect it on any signal. Again, low frequencies might be different. We also detect direction from amplitude differences, and possibly frequency response differences (the 'far' ear hears less HF than the 'near' ear, because HF does not diffract around the head so well as LF).
As I understand it, our ears have a whole bank of narrow bandwidth resonators covering the audio range. They send nerve impulses when the relevant frequency is present. This type of system is not particularly sensitive to phase, hence we are not. However, detecting the timing differences between nerve impulses from two ears does enable us to determine relative phase. My conclusion is that the phase response of an amp does not matter too much but the two channels of a stereo amp have to be identical, and the easiest way for us to achieve that is by making both channels have flat frequency response. Assuming a non-pathological circuit, this ensures flat phase response too so we only need amplitude FFT plots.
As I understand it, our ears have a whole bank of narrow bandwidth resonators covering the audio range. They send nerve impulses when the relevant frequency is present. This type of system is not particularly sensitive to phase, hence we are not. However, detecting the timing differences between nerve impulses from two ears does enable us to determine relative phase. My conclusion is that the phase response of an amp does not matter too much but the two channels of a stereo amp have to be identical, and the easiest way for us to achieve that is by making both channels have flat frequency response. Assuming a non-pathological circuit, this ensures flat phase response too so we only need amplitude FFT plots.
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