By Gerald Kaiser

ISBN-10: 0817681108

ISBN-13: 9780817681104

ISBN-10: 0817681116

ISBN-13: 9780817681111

I wholeheartedly suggest this booklet for a superior and pleasant advent to wavelets, for someone who's pleased with the math required of undergraduate electric engineers. The book's attraction is that it covers all of the primary innovations of wavelets in a chic, trouble-free manner. It deals actually stress-free (friendly!) mathematical exposition that's wealthy in intuitive factors, in addition to fresh, direct, and transparent in its theoretical advancements. i discovered Kaiser's basic end-of-chapter routines excellent...Kaiser has written an outstanding advent to the elemental innovations of wavelets. For a ebook of its size and objective, i believe it's going to be primarily unbeatable for an extended time.

—Proceedings of the IEEE

It is definitely produced and definitely readable...This fabric may still current no hassle for fourth-year undergraduates...It will also be necessary to complicated staff in that it provides a distinct method of wavelet concept from the standard one.

—Computing Reviews

I stumbled on this to be a great booklet. it's eminently extra readable than the books...which should be thought of the relevant choices for textbooks on wavelets.

—Physics Today

This quantity is likely one of the so much mild advent to wavelet thought out there. As such, it responds to an important desire. The meant viewers will benefit from the inducement and commonsense reasons within the textual content. finally, it may well lead many readers, who would possibly not differently were capable of accomplish that, to move additional into wavelet thought, Fourier research, and sign processing.

—SIAM Review

The first half the ebook is adequately named. it's a well-written, properly prepared exposition...a welcome boost to the literature. the second one a part of the booklet introduces the concept that of electromagnetic wavelets...This thought gives you to have many different functions and will good result in new methods of learning those subject matters. This publication has a couple of targeted good points which...makes it quite invaluable for beginners to the field.

—Mathematical Reviews

The booklet is certainly what its identify delivers: A pleasant consultant to wavelets...In brief, Kaiser's booklet is excellently written and will be regarded as the best textbooks in this subject almost immediately available...it will take pleasure in broad distribution between mathematicians and physicists drawn to wavelet analysis.

—Internationale Mathematische Nachrichten

For extra assessment samples and comparable fabric, please stopover at the author's web site at www.wavelets.com.

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Additional resources for A Friendly Guide to Wavelets

Example text

We will call { b 1 , b 2 , A Friendly Guide to Wavelets 16 . ^ b ^ } the reciprocal basis^ of { b i , D 2 , . . , b^v}. 38), which characterizes the reciprocal basis, implies ( b n , bk ) = 6k. The biorthogonality relation generalizes the idea of an orthonormal basis: { b n } is orthonormal if and only if (bfc, b n ) = 6k, which means t h a t ( b k — bfc , b n ) = 0 for fc, n = 1, 2 , . . , A/", hence bk = b ^ . 17) to yield N £> n (bT = / . (1-39) n=l This gives an expansion of any vector in terms of b n : N u = J]bnun, un = ( b n ) * u = ( b n , u ) .

Bn} does not depend on any choice of inner product, since no such choice was made in its construction. Now choose an inner product in CN. Then each Bk G C^v determines a unique vector b fc = (Bk)* E CN. 12) gives < b f c , b n ) = (b f c )*b n = Bkbn = 8kn. 38) T h e vectors { b 1 , b 2 , . . , bN} can be shown to form another basis for C ^ . 1. We will call { b 1 , b 2 , A Friendly Guide to Wavelets 16 . ^ b ^ } the reciprocal basis^ of { b i , D 2 , . . , b^v}. 38), which characterizes the reciprocal basis, implies ( b n , bk ) = 6k.

Mathematically, the symmetry is based on the fact that R is self-dual as a locally compact Abelian group; see Katznelson (1976). 82) again a Riemann sum. 83) J — oo a relation between f(i) and f(uj) known as PlanchereVs theorem. The Fourier transform has a straightforward generalization to functions in L 2 ( R n ) for any n £ N . Given such a function /(£), where t = ( t 1 , ^ 2 , . . , tn) € R n , we transform it separately in each variable tk to obtain -oo A Friendly Guide to Wavelets 30 / ( a / i , • • • ,w„) = / • • • / dt1---dtn exp[-27rj(a; 1 t 1 + • • • + untn)) }{t\ ..

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A Friendly Guide to Wavelets by Gerald Kaiser


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