It is quite instructibe to draw the 2-d vector representing the
amplitude and then the error vector when you assume certain things...
Change the magnitude by 50% and see the error vector, then change the
phase by a random shift - say 90 degrees and draw the error vector. In
general it is much more severe for case 2 than case 1..
eleanor
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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