By Paul R. Haddad and Ali N. Akansu (Auth.)
ISBN-10: 012047140X
ISBN-13: 9780120471409
This e-book offers an in-depth, built-in, and updated exposition of the subject of sign decomposition concepts. software parts of those innovations contain speech and picture processing, laptop imaginative and prescient, details engineering, High-Definition tv, and telecommunications. The publication will function the most important reference for these coming into the sector, teachers educating a few or the entire issues in a complicated graduate direction and researchers wanting to refer to an authoritative resource.
n the 1st publication to provide a unified and coherent exposition of multiresolutional sign decomposition techniques
n lecture room established textbook basically describes the commonalities between 3 key methods-transform coding, and wavelet transforms
n offers comparative functionality reviews of many proposed concepts
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Additional info for Multiresolution Signal Decomposition. Transforms, Subbands, and Wavelets
Sample text
151) k=0 For our purposes, we outline the steps in the proof. 154) For m = r — s > 1, the integrand is of the form G ^ A Α - (ζ_λ)-+ι (-l)r+sArAs/Xr+s = and has an (m + l)th order pole inside the unit circle at z — X, and an (m — l)th order zero at z = A - 1 . Then, for m > 1 1 /· 1 r/ro — φ G(z)dz = — - - — (1 - λ ζ ) ™ - 1 ! ^ = 0 For m < — 1, the integrand is G(z) = Ä"(2 - λ ) Η - ι (1 - λ ζ ) Η + ι with an (m + l ) t / l order pole at z = A - 1 outside the unit circle, and only zeros inside at z — A.
109) This definition is consistent with the interpretation that the DFT is the Z transform of {x(n)} evaluated at TV equally-spaced points on the unit circle. The set of coefficients {X(k)} constitutes the frequency spectrum of the samples. 108) we see that both X(k) and x(n) are periodic in their arguments with period 36 CHAPTER 2. ORTHOGONAL TRANSFORMS N. 108) is recognized as the discrete Fourier series expansion of the periodic sequence {x(n)}, and {X(k)} are just the discrete Fourier series coefficients scaled by N.
But the DCT is a strong competitor to the KLT for highly correlated signal sources. The important practical features of the DCT are that it is signal independent,(that is, a fixed transform) and there exist fast computational algorithms for the calculation of the spectral coefficient vector. In this section we define, list, and describe the salient features of the most popular fixed transforms. These are grouped into three categories: sinusoidal, polynomial, and rectangular transforms. 1 Sinusoidal Transforms The discrete Fourier transform (DFT) and its linear derivatives the discrete cosine transform (DCT) and the discrete sine transform (DST) are the main members of the class described here.