Let φ(x) be any scaling function, w(x) the corresponding mother wavelet and wj, k(x) the wavelet

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Step 1: Understand the definitions and properties of scaling functions and wavelets.u000Au002D The scali

Let $\varphi(x)$ be any scaling function, $w(x)$ the corresponding mother wavelet and $w_{j, k}(x)$ the wavelet descendants. Prove that (a) $\|\varphi\|=\|w\|$. (b) $\left\|w_{j, k}\right\|=2^{-j}\|\varphi\|$.