MakeWavelets

MakeWavelets - Exercises for How to Make Wavelets 1. Let 1...

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Exercises for How to Make Wavelets 1. Let a ( γ ) := 1 if γ = 0 or 3 0 otherwise and ϕ := χ [0 , 3) . Show that a) X γ Z a ( γ ) = 2 b) X γ 0 Z a ( γ 0 ) a (2 γ + γ 0 ) = ( 2 , if γ = 0; 0 , otherwise c) ϕ ( x ) = X γ Z a ( γ ) ϕ (2 x - γ ) d) Show that the system of functions { ϕ ( x - γ ) } γ Z is not orthogonal in L 2 ( R ). 2. Let now ϕ := χ [0 , 1) . i) Show that the system of functions { ϕ ( x - γ ) } γ Z is orthogonal in L 2 ( R ). ii) Show that the system of functions
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This note was uploaded on 11/23/2011 for the course MATH 2025 taught by Professor Staff during the Spring '08 term at LSU.

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