Math 414-502 Spring 2012
Current Assignment
Assignment 8
- Read sections 5.1 and 5.2
- Problems.
- Chapter 5 exercises: 2, 5, 8(c,d,e,f)
- Let the pk's be the scaling coefficients in Example
5.8, p. 195. For these, the scaling and wavelet relations are
φ(x) = p0φ(2x) + p1φ(2x−1) +
p2φ(2x−2) + p3φ(2x−3),
ψ(x) = p3φ(2x+2) − p2φ(2x+1) +
p1φ(2x) − p0φ(2x−1).
- Show these pk's satisfy the four properties in Theorem
5.9, p. 196.
- Find all four filters corresponding to these coefficients: low
pass and high pass decomposition and reconstruction filters.
- Use Theorem 5.9 and the wavelet ψ(x) above to show that ∫
ψ(x)dx = 0.
- BONUS: Show that ∫ xψ(x)dx = 0.
Due Wednesday, 4/25/2012
Updated 4/17/2012