Please answer all questions. f^ implies Fourier transform of f. Please write explanation of steps wherever necessary

Wavelets I Y E LORRI satisfies the following admissibility Condition 2 * ( w ) - X ) them in Called a basic wavelet .4 . Let y (x ) = 0 x e , X E IR. Them ( i] Show that 7 ce R ( TR ) ( it ) Find i ( ili ) show that YELL RR ) ( iv ) show that if is a wavelet d. Let y EL (R ) be defined by ple ) = ceRonEd . Them ( is SIT YER( R ) (ii) Find y (ili ) show that HE L( (R ) ( in ] show that y is a wavelet