Math 414-501 — Spring 2024

Assignment 11

• Read sections 5.3.3, 6.2, 6.3
• Problems.
  1. Chapter 5 exercise: 13
  2. Chapter 6 exercise; 3
  3. Show that, for a db4 wavelet $\psi_4$, the wavelet coefficients for a cubic polynomial will be zero.
  4. Consider the samples of a function f(x) taken at the resolution 2⁻³ (j = 3) listed below. Suppose that you are using the db2 scaling function and wavelet, and that
     a³ = [2, −2, 0, 4, 5, 1, 2, 3],  k = −1 to 6. (I.e., a³₋₁ = 2, etc.)
     For each type of padding listed in section 6.3 find the padded signal required to obtain a²_k and b²_k for all possible k using at least one genuine sample