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Monty Montgomery :
> Energy is preserved, even at the exact nyquist frequency, however
modulating the input signal against the sampling clock results in the
signal being partly shifted to DC.  The signal energy is there... it
appears somewhere else.
I bet a scientist could come up with a wacky experiment to disprove your

assertion that nyquist is the only thing that mattered.
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:
Record/playback one using the "pure nyquist" hypothesis, and therefore

containing only "energy" or real-plane information.
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).
Do the bats virtually "fly into walls" when presented with "pure nyquist"

virtual audio world?

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).
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 :-).
This is utter hogwash.  All the signal energy and resolution is
preserved to exactly the limits of the sampling rate at all lower
frequencies, even if your 'biggest dots' aren't landing at 0dB or
wherever.  True of audio signals, true of  images, true of video.  The
same discrete sampling lessons apply to all three equally.
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).
Furthermore, your perspective totally ignores the fractal nature of reality

-- of nature. And of sound.

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? (

http://en.wikipedia.org/wiki/Fractal_compression ).
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.
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:

http://www.ams.org/notices/201001/rtx100100010p.pdf

"The Life and Survival of Mathematical Ideas" Michael F. Barnsley. (and also

in the same issue http://www.ams.org/notices/201001/rtx100100030p.pdf )
Niels

http://nielsmayer.com
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Monty Montgomery <xiphmont@gm=

ail.com>:=C2=A0

Energy is preserved, even at the exact nyquist frequency, however

modulating the input signal against the sampling clock results in the

signal being partly shifted to DC. =C2=A0The signal energy is there... it

appears somewhere else.I bet a scientist c=

ould come up with a wacky experiment to disprove your assertion that nyquis=

t is the only thing that mattered.For example, assuming=

 one had a way of "playing back" in real-time, echoes of what a b=

at would hear as it flew around a room of known geometry.... Consider an ex=

periment:

Record/playback one using the "pure nyquist" =

hypothesis, and therefore containing only "energy" or real-plane =

information.Record/playback another assuming &quo=

t;nyquist++" -- nyquist theory augmented by hypothesis that both real =

and imaginary plane information can be perceived by mammals with advanced h=

earing capabilities (dogs, bats, humans, dolphins).

Do the bats virtually "fly into walls" when p=

resented with "pure nyquist" virtual audio world?Or do=

 they navigate correctly when presented with sampled/reconstructed represen=

tations that had concern over both real and imaginary plane info? (aka phas=

e matters, esp at high frequencies, and therefore you need much higher samp=

ling rates).

Note that the=C2=A0experimental subject, being a bat, i=

s =C2=A0probably unbiased to the argument at hand. Further, no double-blind=

ing is needed because, again, they're bats :-).=C2=A0

This is utter hogwash. =C2=A0All the signal energy and resolution is

preserved to exactly the limits of the sampling rate at all lower

frequencies, even if your 'biggest dots' aren't landing at 0dB =

or

wherever. =C2=A0True of audio signals, true of =C2=A0images, true of video.=

 =C2=A0The

same discrete sampling lessons apply to all three equally.Prove it! I don't need another paper telling me about n=

yquist or how compression works. Until you have a proper model of human per=

ception, this kind of cocky blinded-pseudo-rationalism, or repeating the sa=

me old tired truisms -- is just a waste of everybody's time.=C2=A0Nyqui=

st is at best a sophomoric model of the *human* perception of sound, the bi=

ological 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).=
Furthermore, your perspective totally ignores the fract=

al nature of reality -- of nature. And of sound.=C2=A0Fractal im=

age compression is resolution independent and works precisely because it be=

tter models real-plane and intra-dimensional aspects of reality that you&#3=

9;ve decided to rationalize away. You claim this is true for=C2=A0images an=

d video too: How does it work in fractal compression? (=C2=A0http://en.wikipedia.org/wiki=

/Fractal_compression=C2=A0).

And when you think about it fractals, and not "mas=

king" is the correct way to compress sound, as it's most likely di=

rectly involved in our ability to perceive sound: Ultimately, the brain isn=

't masking anything, it's taking each instrument heard and "tr=

iggering" the fractal-equation that would generate it's sound. So =

if we perceive sound as a bunch of activated fractal recognizers -- the fra=

ctal that generates the "bass" sound... the fractal that generate=

s the "drum" --- our brain reconstructs the missing pieces no mat=

ter what. Just like a broken hologram can still reconstruct the original im=

age.

See also Michael Barnsley's "Fractals Everywhe=

re" (it's on my nightstand now, alongside David Wright's &quot=

;Mathematics and Music"). Or one of the most mind-blowing papers ever:=

=C2=A0http:=

//www.ams.org/notices/201001/rtx100100010p.pdf

"The Life and Survival of Mathematical Ideas"=C2=A0Michael F. Bar=

nsley. (and also in the same issue http://www.ams.org/notices/201001/rtx100100030p.pdf=

 )

Nielshttp://niels=

mayer.com
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