f(t) -> F(w) -> f(t)
If you do the complex transform properly and appropriately for that sort of signal, then yes, the fundamental mathematics forces that to be true. There's an interesting application of that remarkable property of the Fourier transform- you can completely phase-correct a CD (or whatever digital source), compensating for the anti-aliasing and anti-imaging filter phase shifts.
If you do the complex transform properly and appropriately for that sort of signal, then yes, the fundamental mathematics forces that to be true. There's an interesting application of that remarkable property of the Fourier transform- you can completely phase-correct a CD (or whatever digital source), compensating for the anti-aliasing and anti-imaging filter phase shifts.
No comments to CB + CC ? :'-(
I think also, that nowadays the real distortions cant
be showed with THD or with other similar numbers.
We have the suffice power, and can roughly follow the
input level at the output, but thats only the vertical dimension.
Maybe the secret to the next generation audio-quality is in the
tiny little details, specially in the horizontal (time) dimension,
in the phase. Why we optimize our amps to 0.0000...% THD
when our ear is senitive to quite different problems ?
Maybe something completely different kind of distortion is hurtful for our ear.
I think also, that nowadays the real distortions cant
be showed with THD or with other similar numbers.
We have the suffice power, and can roughly follow the
input level at the output, but thats only the vertical dimension.
Maybe the secret to the next generation audio-quality is in the
tiny little details, specially in the horizontal (time) dimension,
in the phase. Why we optimize our amps to 0.0000...% THD
when our ear is senitive to quite different problems ?
Maybe something completely different kind of distortion is hurtful for our ear.
Hi Francis
What you write is pretty interesting, but in audio we should always end up in psychoacoustics. Windowing and time-finite analysis isn't that bad, because our ering system does more or less the same.
You can easily imagine joint time and frequency accuracy. Time signal gives you 100% time accuracy and 0% freq. accurancy, Fourier transform shows 100% frequency accuracy and 0% time accuracy.
Anything inbetween gives you partial accuracy of time and freq. , borderlined by Heisenberg uncertainty principle (no joking here). What you describe is when accuracy of freq. is pretty well known and accuracy of time is blured (but you know when you've measured). Back to psychoacoustics- what our ears do is joint time-freq. analysis, same as musical notes together eith these italian words are joint time-frequency notation. Our ear is sensitive to time windows of a small fraction of a second. MPEG layer3 makes 1024 sample windows for 44.1kHz sampling for example. So THD-FFT measurements of longer that 1/10 of a second should be considered enough for audio, if something is masked by these time-multiplection--freq.-convolution issues than it's irrelevant. Sorry for long and boring answer, the end.
regards
What you write is pretty interesting, but in audio we should always end up in psychoacoustics. Windowing and time-finite analysis isn't that bad, because our ering system does more or less the same.
You can easily imagine joint time and frequency accuracy. Time signal gives you 100% time accuracy and 0% freq. accurancy, Fourier transform shows 100% frequency accuracy and 0% time accuracy.
Anything inbetween gives you partial accuracy of time and freq. , borderlined by Heisenberg uncertainty principle (no joking here). What you describe is when accuracy of freq. is pretty well known and accuracy of time is blured (but you know when you've measured). Back to psychoacoustics- what our ears do is joint time-freq. analysis, same as musical notes together eith these italian words are joint time-frequency notation. Our ear is sensitive to time windows of a small fraction of a second. MPEG layer3 makes 1024 sample windows for 44.1kHz sampling for example. So THD-FFT measurements of longer that 1/10 of a second should be considered enough for audio, if something is masked by these time-multiplection--freq.-convolution issues than it's irrelevant. Sorry for long and boring answer, the end.
regards
Cutting-edge research
>A little-known fact that affects sound quality more than previously recognised is >that a schematic drawn on a Windows system has markedly poorer performance >than the same one drawn on a Linux system. This only applies to solid-state >circuits. Valve circuits perform best when drawn with a pencil and paper. It's >true...
Valve circuits perform best when drawn on OpenBSD because they are
secured. ;-)
Rintek
>A little-known fact that affects sound quality more than previously recognised is >that a schematic drawn on a Windows system has markedly poorer performance >than the same one drawn on a Linux system. This only applies to solid-state >circuits. Valve circuits perform best when drawn with a pencil and paper. It's >true...
Valve circuits perform best when drawn on OpenBSD because they are
secured. ;-)
Rintek
Yes, but that is just a test, in general an amp is just viewed withSY said:
square wave or impulse, but not designed with that. I'am not saying
that we must optimize just for square wave, but maybe a little more
like now. Its not a good sign, when the amp has a resonance on the
square (of course not on 100MHz) or on complex load, etc...
In my view on other real and important problem is the complex load.
Not just modelled as capacitance or inductance, cause a dynamic speaker is
much more complex, it has its own life, can store energy, and can give it back...
Like in the discussions Back EMF, etc. Feedback can be correct things
needlessly, cause not everything is his problem, then why to correct them ?
(The PS' weakness is also not his problem, even so is tried to correct.)
And that just adds more trouble cause due to eager-correction.
Ideal it wouldnt be a problem, but a wrong correction or controll is a very wrong thing.
Ultima Thule said:
Ok Michael, never mind !
Most designers I know- scratch that, EVERY designer I know- test the hell out of their designs- square waves, transients, complex loads...
I don't know where the idea originated that in some dank basement sit Big Bad Engineers measuring 1kHz sine waves into resistive loads and laughing hysterically, knowing that their job is done.
I don't know where the idea originated that in some dank basement sit Big Bad Engineers measuring 1kHz sine waves into resistive loads and laughing hysterically, knowing that their job is done.
One needs to be careful. Yes the ear does something similar, but not exactly the same. Thus, in principle the error appears in a different place. Each is information limited, but Fourier throws away different information to the ear.
I think I see what you're trying to say, but again, be careful. Each contains the same information. It is simply expressed in a different space. Perhaps a better way to express the difference is to look at where we must place limits on each representation when sampling in the real world.
In both cases we are implicitly talking about a discretised representation for audio. That is sampled digital information. Earlier I wrote of the need to window the FFT - creating a window of samples in time. The dual of that in temporal space is the need to bandwidth limit the signal when we sample it - that is with an anti-alias filter - and to use the same language - to create a window in frequency. (Aside - the window does not have the start at 0Hz, it is its width that is limited, not its maxima.) So rather than say 0% time or frequency information, it is perhaps more accurate to think about where there must be limitations placed upon the measurement to reach our information bandwidth. This of course brings us neatly to Shannon and (via Fourier again) the duality of information content in a bandwidth limited noisy channel.
The Heisenberg uncertainty principle is derived directly using Fourier analysis, but other than that I don't really think it applies here. The limitations of thermal noise far outweigh any other issue as a limitation. If you want to invoke famous physicists the right one is Einstein, and his work on statistical mechanics, eventually linking thermal noise back to Shannon Entropy.
Yes, absolutely. And again yes, it is an intermediate spread of the information between resolution of temporal and frequency resolution. It is all about where we put the information in our limited channel.
I think this is on the right track - but I still don't believe that pushing the measurement purely into the frequency domain is the right answer. It still places inappropriate emphasis on the spread of information in the channel.
The manner in which the ear works is far closer to a maximum entropy method using resonators of arbitrary frequency. So the transform is done using poles in the z plane. It is interesting to notice that such a method provides vastly better frequency resolution than a traditional FFT can manage. Something our ear is also very good at. Many musicians can resolve a single cent of pitch. This is very fine resolution indeed. So from a very hand-waving point of view the model is a better match in terms of the physical realisation of the ear, and even predicts some performance artefacts. This is probably not a bad start
Folks, the last few posts bring me back to a question I had a while ago about frequency resolution of MP3's. Say I want to make 30min MP3's of a 60Hz sine wave to drive a TT motor from a power amp. How much frequency resolution can I achieve? At the time none of our DSP experts could answer definatively. I still think the frequency resolution issue an interesting one.
scott wurcer said:
You need to separate the MP3 part from the intrinsic resolution of the sampled stream. In principle the frequency resolution you can achieve is unlimited. An encoded stream can be made to have exactly the correct number of sine wave cycles as would be predicted by theory - accurate to better than the nearest sample. So the longer the recording the more accurate the frequency. Similarly the jitter inherent in any one sine wave is of the order of one sample period divided by the quantisation resolution (i.e. 65k for 16 bits.) So very very small.
Now the issue of compression in the MP3 is really complex. It depends. Depends upon the exact codec you use. In principle the amount of information in your stream is very low indeed - so a good codec could devote a very large amount of space in each frame to your paltry needs. Easily encoding the full information without loss. In principle. However there are encoding engines and there are encoding engines. Since most are designed to code music you run the risk that the one you use will have internal assumptions about how much space should be devoted to low frequency information - and since the perceptual coding is done early in the piece the encoder's built in rules probably only devote a very small amount of space to very low frequencies - on the assumption that there really is more important information about to arrive.
The MP3 spec is very loose. You could conceivably take an existing encoder program, gut it, and use it to create a synthetic encoding that is totally loss-less with your mooted 60Hz sine wave.
SY said:
That was sort of the answer I got. I think I'll do the experiment by compressing two 30min. wav files generated in Matlab and find out.
The equvalent didn't work in JPEG BTW. I saved a huge image of just one color at low quality mode and got a uniform image but at a slightly different color back. I use the term equivalent loosely this was just a quick experiment in Photoshop.
Ah, good, for a while I thought this thread would drift off into pure tit for tat dismissals and jokes...
SY, I'm really more interested in new questions, or rather, questions posed differently, than in current standard answers. That's how you get progress in science. I admit so much that I am not always aware of the exact derivations of the standard mathematical models. But I know that the most common errors made in "applied science" come from either ignoring the limits of the method, calling the error "insignificant", or from taking a soecific model for a complete and accurate representation of reality. The first leads to obvious mistakes that have a scientifically correct look to them, the latter leads to miss the forest for the trees. That's what makes me so sensitive to statements of certainty, truth, objectivity etc
Francis, good points about the limitations dues to the discrete nature of DFT/FFT, and the idea of discrete resonators. Makes me think of a series of Helmholtz resonators of old... Plus of course the nature of the firing patterns of the nerve cells htemselves which we discussed earlier in this thread .
Darkfenriz, the ear most certainly has shorter time windows of audibility for certain acoustic phenomena, than 1/10 second. See this article (Physics Today).
SY, I'm really more interested in new questions, or rather, questions posed differently, than in current standard answers. That's how you get progress in science. I admit so much that I am not always aware of the exact derivations of the standard mathematical models. But I know that the most common errors made in "applied science" come from either ignoring the limits of the method, calling the error "insignificant", or from taking a soecific model for a complete and accurate representation of reality. The first leads to obvious mistakes that have a scientifically correct look to them, the latter leads to miss the forest for the trees. That's what makes me so sensitive to statements of certainty, truth, objectivity etc
Francis, good points about the limitations dues to the discrete nature of DFT/FFT, and the idea of discrete resonators. Makes me think of a series of Helmholtz resonators of old... Plus of course the nature of the firing patterns of the nerve cells htemselves which we discussed earlier in this thread .
Darkfenriz, the ear most certainly has shorter time windows of audibility for certain acoustic phenomena, than 1/10 second. See this article (Physics Today).
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