I literally wrote "most real-life music fragments are not just sums of long-running perfect sinusoids with unchanging amplitudes".
Except they are.
Enough of this nonsense.
I literally wrote "most real-life music fragments are not just sums of long-running perfect sinusoids with unchanging amplitudes".
In fact Linkwitz did a lot of testing of speaker distortion with impulse waveforms.
That argument pops up far too often, it's an old standby argument for the believers.
"We don't listen to sine waves, music signals are much more complex"
To be fair it is higher math and not generally taught in high school unless you are in advanced classes which let's be honest here, the folks that took these classes moved on to higher education anyway. Or some people really like math and learned it on their own, that's fine also it greatly helps understand complex concepts. It goes back to the age old question, is math something we discovered or is math a human construct to help better understand the world around us? It doesn't matter, math rules
I literally wrote "most real-life music fragments are not just sums of long-running perfect sinusoids with unchanging amplitudes".
I was in the top 5%, per finals results, in both university classes I took that dealt, among other things, with Linear Time-Invariant Systems Theory (LTS), of which Fourier transform is a part. Not to mention other university math education needed to get a graduate degree in Physics.
Compared to Quantum Electrodynamics, LTS Theory is simple. I believe I know where my mathematical understanding limits are. I believe that the basic math underlying LTS is well within my limits, even though some highly specialized topics within that theory are quite sophisticated, and I didn't study them all.
The real-life problem I encounter over and over again is that some audio practitioners take LTS Theory as a gospel, literally treating it as a sacrosanct religion. In reality, it is a beautiful set of theoretical abstractions, describing some real-life systems with sufficient precision, under specific circumstances.
This theory has its limitations. It fails to explain, for instance, why professional studios prefer 192/24 representation for their masters, whereas 48/16 shall be seemingly sufficient per LTS Theory. Of why large enough number of listeners are attracted to vinyl media, despite it being "inferior" per LTS Theory.
Those limitations were constraining for the work I do, so I had to go beyond LTS Theory. I got answers to lots of questions that are not resolvable if one stays within the LTS paradigm. The set of questions around the distortions audibility thresholds being one of them.
Well professional studios overwhelmingly use 44.1 khz /24 bit or 48 khz/24 bit for recording, mixing, mastering everything.This theory has its limitations. It fails to explain, for instance, why professional studios prefer 192/24 representation for their masters, whereas 48/16 shall be seemingly sufficient per LTS Theory. Of why large enough number of listeners are attracted to vinyl media, despite it being "inferior" per LTS Theory.
Those limitations were constraining for the work I do, so I had to go beyond LTS Theory. I got answers to lots of questions that are not resolvable if one stays within the LTS paradigm. The set of questions around the distortions audibility thresholds being one of them.
Fourier transform and the Sampling theorem apply everywhere, including in mammalian cochlea and to any and all music and to every sound that was ever created. There's nothing in human anatomy that violates a mathematical truth.
If you're saying that cochlea doesn't use FT/FFT for processing, then sure, we can all agree to that. But this doesn't excuse it from obeying reality, and having to deal only with signals that can be equivalently represented as a sum of perfect sine waves. Every one of them. No exceptions. That's because all finite bandwidth signals are. This is proven beyond any shadow of a doubt; this is not one of those "maybe we don't know something yet” cases.
If you're saying that cochlea doesn't use FT/FFT for processing, then sure, we can all agree to that. But this doesn't excuse it from obeying reality, and having to deal only with signals that can be equivalently represented as a sum of perfect sine waves. Every one of them. No exceptions. That's because all finite bandwidth signals are. This is proven beyond any shadow of a doubt; this is not one of those "maybe we don't know something yet” cases.
Yikes!!
I try and stress this point often when people get really hung up on the electronics aspect, the transducer is by far the weak link in the chain on so many regards. Just awful compared to the accuracy we can get with the electronics side, yet it still sounds amazing to me. So ya I joke at the minuscule changes people make like swapping fuses and hear a difference, their speakers must be the most accurate speakers we have never seen before.
....
There is, however, one other major loss of information, that being in the reduction to 2, 4, 5, 7, whatever channels. That's insurmountable in current reproduction technologies. 2 channel, in particular, ignores work from the 1930's.
Crank, not troll.Gentlemen, do not feed the Trolls, please.
I don't know, it's pretty surmountable according to dr. Griesinger, and he doesn't ignore that work from the 30s.There is, however, one other major loss of information, that being in the reduction to 2, 4, 5, 7, whatever channels. That's insurmountable in current reproduction technologies. 2 channel, in particular, ignores work from the 1930's.
Why?I am trying to make sense of his argument that Fourier doesn't explain all things we hear...
Why?
The latter is a good start toward the former.I have no idea. I suppose I'm trying to get where he is coming from.
I did injure my head so I'm probably just not thinking correctly.
I am not a native speaker, Sir. Can’t see a tiny difference.Crank, not troll.
You are completely lost and off topic.
The topic is the audibility thresholds of defects in amplifiers and DAC.
Math is a set of tools, not the topic.
You make me want to go pick up a Double Jack.