A Friendly Guide to Wavelets by Gerald Kaiser

By Gerald Kaiser

I wholeheartedly suggest this ebook for a superb and pleasant advent to wavelets, for someone who's happy with the math required of undergraduate electric engineers. The book's allure is that it covers all of the primary techniques of wavelets in a chic, uncomplicated approach. It deals really relaxing (friendly!) mathematical exposition that's wealthy in intuitive motives, in addition to fresh, direct, and transparent in its theoretical advancements. i discovered Kaiser's straight forward end-of-chapter routines excellent...Kaiser has written a good creation to the elemental recommendations of wavelets. For a e-book of its size and goal, i feel it may be primarily unbeatable for an extended time.

—Proceedings of the IEEE

It is easily produced and definitely readable...This fabric should still current no hassle for fourth-year undergraduates...It will also be helpful to complicated staff in that it offers a unique method of wavelet conception from the standard one.

—Computing Reviews

I came upon this to be a superb e-book. it's eminently extra readable than the books...which can be thought of the important choices for textbooks on wavelets.

—Physics Today

This quantity is among the such a lot mild advent to wavelet concept out there. As such, it responds to an important want. The meant viewers will cash in on the incentive and commonsense causes within the textual content. eventually, it may possibly lead many readers, who won't in a different way were capable of achieve this, to head extra into wavelet concept, Fourier research, and sign processing.

—SIAM Review

The first 1/2 the e-book is thoroughly named. it's a well-written, properly prepared exposition...a welcome boost to the literature. the second one a part of the publication introduces the concept that of electromagnetic wavelets...This thought delivers to have many different functions and will good result in new methods of learning those subject matters. This publication has a couple of special gains which...makes it relatively precious for rookies to the field.

—Mathematical Reviews

The e-book is certainly what its identify grants: A pleasant consultant to wavelets...In brief, Kaiser's e-book is excellently written and will be regarded as the best textbooks in this subject shortly available...it will get pleasure from large distribution between mathematicians and physicists attracted to wavelet analysis.

—Internationale Mathematische Nachrichten

For extra evaluate samples and similar fabric, please stopover at the author's site at www.wavelets.com.

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Extra resources for A Friendly Guide to Wavelets

Example text

Its main advantage is its simplicity. In an expression otherwise loaded with symbols and difficult A Friendly Guide to Wavelets 18 concepts, it is very important to keep the clutter to a minimum so that the mathematical message can get through. The significance of the reciprocal basis is that it allows us to compute the coefficients of u with respect to a (not necessarily orthogonal) basis by taking inner products - just as in the orthogonal case, but using the reciprocal vectors. For this to be of practical value, we must be able to actually find the reciprocal basis.

Given N > 1, all the points t e Q[a,b] get mapped into 1 € IN (since IN = [1, T ^ J ) )> and all the points £ € Q'[a, 6] get mapped into 0 6 / o = [0, -^). 102) r upper /, N 1 . n N' + 1 &~ a V p =^-°)-]v + ( ) -n^ = ^rHence both Lebesgue sums converge to zero as TV —> oo, and Ja dtq(t)=0. 103) The concept of a measure can be generalized considerably from the above. Let M be an arbitrary set. ) values fi(A) to certain subsets o f A c M , called measurable subsets. The choice of subsets considered to be measurable is also arbitrary, subject only to the following rules already encountered in the discussion of Lebesgue measure: (a) M itself must be measurable (although possibly fi(M) = oo); (b) If A is measurable, then so is its complement M — A) (c) A countable union of measurable sets is measurable.

We now state, without proof, two important properties shared by all inner products and their associated norms. Both follow directly from the general properties (P), (H), and (L) and have obvious geometric interpretations. Triangle inequality: ||u + v|| < ||u|| + ||v|| for all u, v G CN. Schwarz inequality: |(u, v ) | < ||u|| ||v|| for all u, v G CN. T The name "metric operator" is based on the similarity of b n and b n to "covariant" and "contravariant" vectors in differential geometry, and the fact that G mediates between them.

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