[Arny Krueger]

"M0she_" wrote in message


Playing devil's advocate, because I agree with Ethan for
the most part as well, what if there is a measurement, or
parameter that we as humans have not discovered yet?

The devil is in the details. I'll answer the question with another
question.

How many orthogonal (perpendicular or non-interacting) parameters are
required to uniquely describe a point in 3 dimensional space?

The answer is of course 3. However, if you remove the requirements that the
parameters be orthogonal, then there can be any number of parameters that
you like greater than 3. However, then there will be many different sets of
parameters that describe the same point. If you pick other orthogonal
parameter systems, then they are like coordinate systems that are rotated
from the first one you picked. There is nothing new under the sun.

If we move on to audio, we observe that any single audio signal is
completely described by pairs of (again orthogonal) numbers, being a time
and the amplitude that corresponds to that time. Since we are interested in
characterizing errors in audio signals, the question becomes how many unique
different ways can an audio signal be in error? There are any number of
orthogonal or non-interacting sets of three ways that the signal can be in
error: The most common sets of non-interacting errors is that an
interfering signal can be added, the signal can have the wrong amplitude,
and/or the signal can have the wrong shape.

Each of these can be thought of as being orthogonal and non-interferring
with each other in the sense that you can add or subtract any one of these
kinds of error without changing the signal in any other way. IOW, you can
add an interferring signal without changing the size or shape of the basic
signal, you can change the shape of the signal without changing its size,
and you can change its size without changing its shape. There are no other
non-interacting ways that a signal can be in error once you pick these
particular three kinds of error. There are other ways to characterize
errors in the signal, but they are in some sense equivalent, or other
combinations of these three. These three seem to be natural and intuitive to
us. If we picked some other orthogonal ways to characterize the signal, all
we would do is have something that is less intuitive for us. There would be
no actual new information about errors in the signal.

The three kinds of signal error that I described can also be characterized
by measurements. The addition of an interferring signal can be measured as
SNR or dynamic range. Incorrect amplitude is characterized as frequency and
phase distortion. Incorrect shapes can be characterized by nonlinear
distortion, which includes harmonic distortion, intermodulation distortion,
and phase or frequency modulation distortion. That's it. There is nothing
new under the sun.

The basic math of signal analysis says that once you have nailed down these
three basic error parameters relating to interferring signals, amplitude
error, and shape error, there can be no others that aren't somehow already
covered by these three. So there can't be a parameter that hasn't been
discovered yet, given that you are dealing with audio signals that are
described by time and amplitude.