Exercise 1.5.8

Answers

We have

W^{T} W = [\begin{matrix} 4 & 0 & 0 & 0 \\ 0 & 4 & 0 & 0 \\ 0 & 0 & 2 & 0 \\ 0 & 0 & 0 & 2 \end{matrix}]

and

W^{- 1} = [\begin{matrix} \frac{1}{4} & \frac{1}{4} & \frac{1}{4} & \frac{1}{4} \\ \frac{1}{4} & \frac{1}{4} & - \frac{1}{4} & - \frac{1}{4} \\ \frac{1}{2} & - \frac{1}{2} & 0 & 0 \\ 0 & 0 & \frac{1}{2} & - \frac{1}{2} \end{matrix}] .

The $n = 8$ Harr wavelets are: (TODO)

W_{8} = [\begin{matrix} W_{4} & 0 \\ 0 & W_{4} \end{matrix}] .

niuers

2020-03-20 00:00