# Wavelets Analysis

1. Apr 26, 2010

### eemath_tamu

1. The problem statement, all variables and given/known data
Given the following $$p_k$$ scaling coefficients and the following wavelet relations, find all four filters corresponding to these coefficients: low-pass decomposition, high-pass decomposition, low-pass reconstruction, and high-pass reconstruction.

2. Relevant equations
$$\phi (x)= p_0\phi (2x) + p_1\phi (2x-1) + p_2\phi (2x-2) + p_3\phi (2x-3)$$
$$\psi (x)=p_3\phi (2x+2) - p_2\phi (2x+1) + p_1\phi (2x) - p_0\phi (2x-1)$$

3. The attempt at a solution
I just need help knowing how to start this problem. I've been looking throughout my book for the equations of the filters. I don't really understand how to design the filters from the wavelet relations.

2. Nov 15, 2011

### mike21

Does anyone know if i can construct-compose time-series consist of wavlets? e.g. if i have as data a characteristic wave height and a wave length i can produce time-series with Fourier transform which equals of a superposition of sinus waves. i want to do the same but with wavelets. possible?