True for linear filters, but I think you would find in practical cases, that the switching transient was repeatedly band limited and non-linearly slew rate limited before it gets to you amp. By then, it's quite unlikely that there is much or anything left to bother the amp.
Also, such signals don't occur naturally in music. Not sure where such a signal would come from in the first place except maybe for some one-time or very infrequent glitch. Between that and all smoothing that would be expected to occur before your amp, I am struggling to imagine how it might ever be a practical problem.
Agreed, but it's easier for people to visualize what would happen in the case I mentioned, that's all.
P.S. alternatively we may want to look at it not as a "disturbance" but an important part of the musical program. we know how important "attack" and "decay" are to guitar players when judging equipment.
"Way beyond the frequencies of the tones." Nonsense, now that you are actually talking concepts where a real example might be provided, please do. Turning a sine wave off and on with a square wave is a poor example it's no longer BW limited. Nothing you can do by linearly adding sine waves can create new frequencies. What does Gabor have to do with this?
Nothing Dick Heyser ever presented was outside of known signal processing knowledge, instantaneous frequency, the analytic signal, etc. far predated him. He wrote some entertaining non-peer reviewed stuff in a stir the pot devil's advocate tone.
True about guitar players. I know, being one myself. However, my amp and speaker band limit what comes out of the guitar, and any pedals. Also, string plucking physics and guitar cable capacitance interacting with the pickups both tend to place physical limits on transients that can be produced at the signal source. Nothing fast enough there to cause the problems we have been talking about.
The only way I can think to make a sine wave switch on abruptly enough to create the type of signal we have been discussing is through fairly fast electronic switching.
They do. DF96 is correct, you can't switch from the absence to the presence of a stationary signal other than through an infinite spectrum.
The question is how much of that spectrum is important for our perception.
This is a sticking point for me. I guess I need your help to understand how they do. I'm not seeing it at this point.
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Any non-periodic signal has a (theoretically) infinite, continuous spectrum.
The simplest example is the impulse delta(t), which has all frequencies equally present.
Even signals such as sines that are switched periodically have an infinite bandwidth,
but their spectrum is discrete rather than continuous.
Any non-periodic signal has a (theoretically) infinite, continuous spectrum.
The simplest example is the impulse delta(t), which has all frequencies equally present.
Even signals such as sines that are switched periodically have an infinite bandwidth,
but their spectrum is discrete rather than continuous.
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I don't have an intuitive example at hand. DF96 was close with his "square wave modulation" but that still implies quite some maths in order to derive the spectrum of the modulated signal.
I'll just state Gabor's limit in its simplest form: a function (signal) cannot be both time limited and band limited.
His credentials are impeccable (inventor of holography, Nobel prize etc) I'm going with him on this one.
But DF96 was talking about math, not about the natural frequencies produced by musical instruments. Mathematically, if I use a fast electronic switch, then its possible to produce something closer to what the math can predict for an idealized case. But musical instruments don't produce fast rise-time square waves or fast transient sine waves. Nothing like that. The fastest I can think of would be a synth producing an unfiltered square wave plugged directly into a recording console. That would probably occur very rarely in music, because it wouldn't sound very good, especially, not for long. But even if somebody did that, and even if the synth can produce a fast enough rise time (unlikely), still by the time it goes through the console, the bus compressor, mastering, conversion to CD and so on, there can't be much left. And so far I haven't talked about A/D conversion and aliasing, but that would further interfere with any fast edges making it to your amp. I still can't imagine how it could happen with music and CDs. And so I can't see how it would ever be a actual problem.
Fourier/Heisenberg said it first. Such irony you state a fundamental principle of Fourier analysis and claim we will call you a denier, welcome to the club of believers.
I'm afraid that whether what happens beyond 20kHz is relevant or not is a different discussion that will get both of us in hot waters here. As for whether it exists or not, here is an interesting material:
There's life above 20 kilohertz! A survey of musical instrument spectra to 102.4 kHz
As for the last part of your post, I don't have any comments other than it's a good summary of what happens to the signal until it reaches the amp. And it raises some questions about what, in the end, has the most significant contribution to your perception of the resulting musical program.
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Yes, actually I was aware of the ultrasonics, but I still wouldn't expect problems from them. Most mics won't pick up a lot of that. Some small diaphragm condensers can go up part of that way. And if instead of CD you used HD 24/192 audio, then you potentially could get up somewhere below 100 kHz, if you really worked at it.
However, many amps are fairly flat in frequency response up into a few hundred kHz. Therefore, some normal level ultrasonic musical instrument signals still oughten't cause an upset event or substantial nonlinearity in an amplifier rated for a few hundred kHz bandwidth, assuming of course the load doesn't cause some problem in the way it interacts with the amp at very high frequencies.
I'm not aware of anybody doing that though. Most people still listen to CDs and I still don't see how it's going to bother an amplifier in that case.
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Actually it isn't easy to find a good mike that goes substantially beyond 20kHz - I tried.
I also remember a thread here where they looked at the spectra on DVD and BlueRay and many of them just had nothing beyond 20kHz. Nothing at all. Some of the 'better' ones had a fractional octave more and then dropped like a stone.
Jan
I also remember a thread here where they looked at the spectra on DVD and BlueRay and many of them just had nothing beyond 20kHz. Nothing at all. Some of the 'better' ones had a fractional octave more and then dropped like a stone.
Jan
some arguments from pure Math limits/dualities/infinities are Sophomoric when they meet the real word even when the Math is quite useful
Shannon-Hartley Channel Capacity is useful for seeing when some "infinities" can be ignored practically, or in evaluating how by how much they affect a given measurement
Bandwidth and Noise limited signals only convey a finite amount of information per unit time
all transducers, channels are bandwidth and S/N limited, in Audio the limits of the Sound Sources, transduction mechanisms are well within those of the Electronics that can be applied
Shannon-Hartley Channel Capacity is useful for seeing when some "infinities" can be ignored practically, or in evaluating how by how much they affect a given measurement
Bandwidth and Noise limited signals only convey a finite amount of information per unit time
all transducers, channels are bandwidth and S/N limited, in Audio the limits of the Sound Sources, transduction mechanisms are well within those of the Electronics that can be applied
You are correct except in the literature it's known as the Gabor limit and calling it other names wouldn't help with anything but confusion.
And, in the context, the irony is exactly with those using the "Fourier denier" label, without being aware that Fourier himself was aware of the limitations.
Rumours has it that when the SACD was first introduced, it victimized quite a few high end amplifiers at high end shows. Overheating and/or downright permanent failures due to considerable presence of high frequency content from the ultrasonic noise inherently generated by the DSD codec. It later appeared that, altough they claimed 100kHz BW, it was for bragging rights only, as those poor amps were not capable of any sustained power in the upper side of their BW. Sony "fixed" it later by adding a 50kHz low pass filter at the SACD players output.
And, as a result, bats and the audio review chimps are bitterly complaining ever since.
That is of less concern. The lesson is that the current "standards" in audio are the results of a long history of band-aid fixes, devised by (financial) necessity by those who weren't creating the problems in the first place.
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