Prove the formulas in Proposition 9.60 for the norms of the mother and daughter wavelets. Proposition 9.60.
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Prove the formulas in Proposition 9.60 for the norms of the mother and daughter wavelets.
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Proposition 9.60. All integer translates (x - k), for k € Z of the Daubechies scaling function, and all wavelets wj,k(x) = w(2¹ x − k), j ≥ 0, are mutually orthogonal functions with respect to the L² inner product. Moreover, ||||² = 1, while || wj,k ||² = 2−³.
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To prove the formulas in Proposition 960 we will use the following properties of the Daubechies wave...View the full answer
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