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.