New PDF release: Computational Signal Processing with Wavelets

By Anthony Teolis

ISBN-10: 1461241421

ISBN-13: 9781461241423

ISBN-10: 1461286727

ISBN-13: 9781461286721

This designated source examines the conceptual, computational, and sensible facets of utilized sign processing utilizing wavelets. With this ebook, readers will comprehend and be capable of use the facility and software of latest wavelet tools in technological know-how and engineering difficulties and research.

The textual content is written in a transparent, available kind warding off pointless abstractions and info. From a computational standpoint, wavelet sign processing algorithms are provided and utilized to sign compression, noise suppression, and sign identity. Numerical illustrations of those computational concepts are additional supplied with interactive software program (MATLAB code) that's to be had at the world-wide-web.

Topics and Features:

* non-stop wavelet and Gabor transforms
* Frame-based conception of discretization and reconstruction of analog signs is developed
* New and effective "overcomplete" wavelet rework is brought and applied
* Numerical illustrations with an object-oriented computational standpoint utilizing the Wavelet sign Processing laptop (MATLAB code) available

This publication is a wonderful source for info and computational instruments had to use wavelets in lots of forms of sign processing difficulties. Graduates, execs, and practitioners in engineering, computing device technological know-how, geophysics, and utilized arithmetic will make the most of utilizing the booklet and software program instruments.

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Additional info for Computational Signal Processing with Wavelets

Example text

1. The mappings Land L' . A characterization of frame representation operators is given in the following theorem. 2} is a well-defined topological isomorphism onto a closed subspace of £2 (~). 14 has certain significant consequences worthy of mention. Namely, if L is a frame representation operator then (a) L is injective (one-to-one), (b) L(H) is closed, and (c) L' is surjective (onto). To see the injectivity of the map L suppose {¢n} is a frame for H with bounds A and B and that Lh = Lh. Then which implies that h = h.

Be Computed E:ractl:y? J In this section the question of computing the Fourier transform of an analog signal f on a finite precision digital machine is addressed. In all of its generality this task is an impossible one for arbitrary signals f E L2(JR) for the main reason that a digital machine is inherently constrained to operate on objects represented by a finite number of bits. Because of this, any signal to be digitally processed must first be representable by a finite number of bits. (tn)}:=l' where -'Xl < a <::: tn < tn+l <::: b < 00 and Q is a quantization g function.

Lf f E H}. 2 =L (I, ¢n) (g, L* L = IH, where IH is the identity operator on H. In particular, L is invertible and L -1 = L *. In other words f may be recovered from its orthonormal representation Lf through the application of the operator L*.

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Computational Signal Processing with Wavelets by Anthony Teolis


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