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Wavelet Problem

  1. Jan 12, 2010 #1
    I am new to wavelet, and found this thing interesting, and had been studying for couple of days.

    I have few questions that i couldn't find any good answers to them :

    1. From the materials i had read, they all saying that the multiresolutional levels are of 2^j, where j is the levels number. Is it necessary to construct a structure like this? i mean, why could not it be more level to get more precise resolutions in analysis? what is the principle underlying the theorem saying it has to be 2^j ?

    2. Again regarding the question above, it implicitly indicates that the sample must be of M-by-M matrices (for 2D image case for example OR a voice signals with N times interval where N = M x M ), in order to get the level to serve as a base for power of TWO, where N = M x M, and N must be of multiple of 2. Is there any essence of this ? what if my input signals are not a multiple of 2 ? let's say for image with a dimension of 533 * 311 ?

    3. For the wavelet bases functions, how did one comes out with such bases functions? what i am referring is the inspiration and idea behind these bases functions, i have seen couple of bases functions using cosine-sine to serve as orthogonal bases, so is there any other than this? can eigenvectors play a role in this wavelet theory? Or is there any other concrete orthogonal bases? what are the major difference between these bases?


    A Big Big Thanks to whoever read and concern about my questions above.
    Due to the lacking of information regarding this newly amazing topics,
    hereby appreciate whoever is willing to lend a hand onto this cutting edge mathematical tools.


    Have a nice day,
    God Bless.


    Regards,
    Daniel.
     
  2. jcsd
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