I have been politely reminded offline that by definition amplitudes
cannot be negative. We could call them coefficients, but:
1. I definitely am not recommending any change in the way we represent phases-
I just thought it might explain part of the dominance of phases,
that they are taking over what might plausibly be considered part
of the domain of the coefficients.
2. With completely random phases, I guess the maps would be equally
garbage either way. I withdraw my suggestion.
Edward A. Berry wrote:
This bias is exacerbated by the convention that phases go from 0 to 360*
while amplitudes go from zero to Plus.
Thus the phase decides where to put it, and whether to add or take away,
while the amplitude only decides how much.
If phase was 0 to 180* and amplitude was Minus to Plus, then
amplitude would decide whether to add or take away as well as how much.
Lijun Liu wrote:
Does anybody have a good way to understand this?
=========
There are a lot of good ways to understand this. The amplitudes
determines how much
to put, while the phases tell you where to/how to correctly put. For
example, treating San
Francisco as a cell, the heights of buildings and lines of streets
determine the landscape.
Moving all buildings along some streets separately will change more the
landscape than
just changing some buildings' height along the street. Another example,
taken at different
lighting/darkness conditions, the photos from the same face could be
easily recognized
and compared. However, with the same light condition, when the position
of nose, eyes,
mouth, etc., are dislocated from their original positions, the face will
be very different.
One possible answer is "it is the nature of the Fourier Synthesis to
emphasize phases." (Which is a pretty unsatisfying answer). But, could
there
be an alternative summation which emphasizes amplitudes? If so, that
might
be handy in our field, where we measure amplitudes...
==========
It does have. For example, Patterson function.
Lijun
Regards,
Jacob Keller
*******************************************
Jacob Pearson Keller
Northwestern University
Medical Scientist Training Program
Dallos Laboratory
F. Searle 1-240
2240 Campus Drive
Evanston IL 60208
lab: 847.491.2438
cel: 773.608.9185
email: [email protected] <mailto:[email protected]>
*******************************************
Lijun Liu
Cardiovascular Research Institute
University of California, San Francisco
1700 4th Street, Box 2532
San Francisco, CA 94158
Phone: (415)514-2836
