Course Solutions Uncategorized (Answered) : Theorem 829 Let Wavelets Let F Ge L2 K Wy Af G B Wyf B W 8 B C B Wy Tcf B Wyf B C T Trans Q28866016

(Answered) : Theorem 829 Let Wavelets Let F Ge L2 K Wy Af G B Wyf B W 8 B C B Wy Tcf B Wyf B C T Trans Q28866016

June 27, 2024June 27, 2024| adminadmin| 0 Comment| 6:52 pm
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Please solve parts g,h

Theorem 8.2.9. Let ? and ? be wavelets and let f, ge L2(K). (a) (Wy(af+ßg))(a, b)-?(Wyf)(a, b)+ ?(W+8)(a, b) for any ?, ?? C, (b) (Wy(Tcf))(a, b) = (Wyf)(a, b-c), where T. is the translation operator defined by Tt)-ft-c), (c) (W,Dfa.bW. (, 2), where c is a positive number and Dc c c is the dilation operator defined by Dft) f) (e) (????+p,f)(a, b)-?(W,f)(a, b) + ?(w,f)(a, b) for any ?, ? ? C, (f) (Wpy Pf(a, b)- (W^f)(a, -b, where P is the parity operator defined by Pf), (g) (Wyyf)(a, b) = (Wef)(a, b + ca), (h) (WpcM(a, b)= (Wwf)(ac, b), c > 0. DcV

Theorem

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