MATLAB: Why values of multiwavlet transform have larger values of input

Question

Hello,

I would like to be clarified on this.

why values of multiwavlet transform output larger values of input and can have negetave one?

Thank you

Answer 1

The simplest wavelet predicts +1 for the first half and -1 for the second half.

Suppose you had an input that was [64 64 64 64]. You apply the wavelet to it, breaking it up into two halves, [64 64] and [64 64]. The coefficient for +1 to match the first half, [64 64] is +64. The coefficient for the -1 of the second half to match the second [64 64] is -64 . This leads to the coefficient pair [+64 -64] . Therefore you can get negative values.

Now suppose you had [64 64 -64 64] . Two halves, first half gives coefficient 64. Second half, the analyzer might say the coefficient for the -1 is +64 so that the -1*+64 matches the -64. Now for the second half of the [-64 64] you subract off the modeled -64 from the existing 64, and you get a difference of +128 . Therefor in the second output array that deals with the differences between modeled and actual you would have a +128 coefficient, which is larger than any of the input values. Generally speaking the +1 or -1 half can predict up to the negative of the actual value, leading to a potential output coefficient twice as large as the inputs.