<div>Monty Montgomery <<a href="mailto:xiphmont@gmail.com">xiphmont@gmail.com</a>>: </div><blockquote class="gmail_quote" style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0.8ex; border-left-width: 1px; border-left-color: rgb(204, 204, 204); border-left-style: solid; padding-left: 1ex; ">
Energy is preserved, even at the exact nyquist frequency, however</blockquote><blockquote class="gmail_quote" style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0.8ex; border-left-width: 1px; border-left-color: rgb(204, 204, 204); border-left-style: solid; padding-left: 1ex; ">
modulating the input signal against the sampling clock results in the</blockquote><blockquote class="gmail_quote" style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0.8ex; border-left-width: 1px; border-left-color: rgb(204, 204, 204); border-left-style: solid; padding-left: 1ex; ">
signal being partly shifted to DC. The signal energy is there... it</blockquote><blockquote class="gmail_quote" style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0.8ex; border-left-width: 1px; border-left-color: rgb(204, 204, 204); border-left-style: solid; padding-left: 1ex; ">
appears somewhere else.</blockquote><div><br></div><div>I bet a scientist could come up with a wacky experiment to disprove your assertion that nyquist is the only thing that mattered.<div><br></div><div>For example, assuming one had a way of "playing back" in real-time, echoes of what a bat would hear as it flew around a room of known geometry.... Consider an experiment:</div>
<div><br></div><div>Record/playback one using the "pure nyquist" hypothesis, and therefore containing only "energy" or real-plane information.</div><div><br></div><div>Record/playback another assuming "nyquist++" -- nyquist theory augmented by hypothesis that both real and imaginary plane information can be perceived by mammals with advanced hearing capabilities (dogs, bats, humans, dolphins).</div>
<div><br></div><div>Do the bats virtually "fly into walls" when presented with "pure nyquist" virtual audio world?</div><div>Or do they navigate correctly when presented with sampled/reconstructed representations that had concern over both real and imaginary plane info? (aka phase matters, esp at high frequencies, and therefore you need much higher sampling rates).</div>
<div><br></div><div>Note that the experimental subject, being a bat, is probably unbiased to the argument at hand. Further, no double-blinding is needed because, again, they're bats :-). </div><div><br></div><blockquote class="gmail_quote" style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0.8ex; border-left-width: 1px; border-left-color: rgb(204, 204, 204); border-left-style: solid; padding-left: 1ex; ">
This is utter hogwash. All the signal energy and resolution is</blockquote><blockquote class="gmail_quote" style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0.8ex; border-left-width: 1px; border-left-color: rgb(204, 204, 204); border-left-style: solid; padding-left: 1ex; ">
preserved to exactly the limits of the sampling rate at all lower</blockquote><blockquote class="gmail_quote" style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0.8ex; border-left-width: 1px; border-left-color: rgb(204, 204, 204); border-left-style: solid; padding-left: 1ex; ">
frequencies, even if your 'biggest dots' aren't landing at 0dB or</blockquote><blockquote class="gmail_quote" style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0.8ex; border-left-width: 1px; border-left-color: rgb(204, 204, 204); border-left-style: solid; padding-left: 1ex; ">
wherever. True of audio signals, true of images, true of video. The</blockquote><blockquote class="gmail_quote" style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0.8ex; border-left-width: 1px; border-left-color: rgb(204, 204, 204); border-left-style: solid; padding-left: 1ex; ">
same discrete sampling lessons apply to all three equally.</blockquote><div><br></div><div>Prove it! I don't need another paper telling me about nyquist or how compression works. Until you have a proper model of human perception, this kind of cocky blinded-pseudo-rationalism, or repeating the same old tired truisms -- is just a waste of everybody's time. Nyquist is at best a sophomoric model of the *human* perception of sound, the biological perception, of the "energies" you're talking about. It's like Marie Curie saying "well it only fogs the film"... yeah, and in biological organisms it causes cancer -- because it's not just the energy, it's also the frequency (and in this argument, phase).</div>
<div><br></div><div>Furthermore, your perspective totally ignores the fractal nature of reality -- of nature. And of sound. </div><div>Fractal image compression is resolution independent and works precisely because it better models real-plane and intra-dimensional aspects of reality that you've decided to rationalize away. You claim this is true for images and video too: How does it work in fractal compression? ( <a href="http://en.wikipedia.org/wiki/Fractal_compression">http://en.wikipedia.org/wiki/Fractal_compression</a> ).</div>
<div><br></div><div>And when you think about it fractals, and not "masking" is the correct way to compress sound, as it's most likely directly involved in our ability to perceive sound: Ultimately, the brain isn't masking anything, it's taking each instrument heard and "triggering" the fractal-equation that would generate it's sound. So if we perceive sound as a bunch of activated fractal recognizers -- the fractal that generates the "bass" sound... the fractal that generates the "drum" --- our brain reconstructs the missing pieces no matter what. Just like a broken hologram can still reconstruct the original image.</div>
<div><br></div><div>See also Michael Barnsley's "Fractals Everywhere" (it's on my nightstand now, alongside David Wright's "Mathematics and Music"). Or one of the most mind-blowing papers ever: <a href="http://www.ams.org/notices/201001/rtx100100010p.pdf">http://www.ams.org/notices/201001/rtx100100010p.pdf</a></div>
"The Life and Survival of Mathematical Ideas" Michael F. Barnsley. (and also in the same issue <a href="http://www.ams.org/notices/201001/rtx100100030p.pdf">http://www.ams.org/notices/201001/rtx100100030p.pdf</a> )<br>
<div><br></div><div>Niels<br><a href="http://nielsmayer.com">http://nielsmayer.com</a><br><br></div></div>