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From: Robert Hodge[SMTP:r-hodge@xxxxxxxxxxxxxxx]
>>I can use a wavelet transform to encode say X daily closes in Y wavelet
coefficients each representing the relative strength of a particular wavelet
"size" (ie length in time) at the point where the input ends...Each
coefficient in turn only represents fluctuation in the input at a higher
frequency than the last - ie the same frequency information is not presented
as output by more than one of the coefficients (??)<<
Yes
>>Whereas, if I used Y streams of the same daily closes sampled at Y different
rates (to notionally achieve the same effect) I would in practice be
presenting similar frequency information but getting some overlap in the
process...In other words its not "wrong" it just presents redundant
frequency information when compression and independence of each input is at
a premium (ie input to a neural net).<<
Yes, but proper temporal compression does not merely sample Y parallel streams
at different rates. You need to prefilter at different rates for each stream to satisfy
the Nyquist sampling theorem ( otherwise you would be missing a lot of important
information ) as well as time shift the streams to avoid redundancy at any one
moment. When properly executed, the samplings produce no redundant frequency
information.
- Mark Jurik
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