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: [log in to unmask] <mailto:[log in to unmask]>
>>> *******************************************
>>
>> Lijun Liu
>> Cardiovascular Research Institute
>> University of California, San Francisco
>> 1700 4th Street, Box 2532
>> San Francisco, CA 94158
>> Phone: (415)514-2836
>>
>>
>>
>
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