Find Filters for Wavelets Analysis Homework: p_k Coefficients & Relations

[eemath_tamu]

Homework Statement

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.

Homework Equations

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

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.

 

[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?