By Jaideva C. Goswami
ISBN-10: 0470484136
ISBN-13: 9780470484135
Such a lot current books on wavelets are both too mathematical or they concentrate on too slender a distinctiveness. This publication presents a radical therapy of the topic from an engineering viewpoint. it's a one-stop resource of conception, algorithms, purposes, and computing device codes regarding wavelets. This moment version has been up-to-date by means of the addition of:
- a part on "Other Wavelets" that describes curvelets, ridgelets, lifting wavelets, and so on
- a part on lifting algorithms
- Sections on area Detection and Geophysical purposes
- Section on Multiresolution Time area technique (MRTD) and on Inverse difficulties
Read Online or Download Fundamentals of Wavelets: Theory, Algorithms, and Applications (Wiley Series in Microwave and Optical Engineering) PDF
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Additional resources for Fundamentals of Wavelets: Theory, Algorithms, and Applications (Wiley Series in Microwave and Optical Engineering)
Example text
There are a variety of norms one may choose as a measure for a particular linear space. 3) which we shall call the L2-norm. This norm has also been used to measure the overall difference (or error) between 36 two finite energy functions. 4) where fa(x) is an approximating function to f(x). 4) is the approximation error in the L2 sense. 2 VECTORS AND VECTOR SPACES Based on the basic concepts of functional spaces discussed in the previous section, we now present some fundamentals of vector spaces.
Definition: A matrix A = [Aij] is a rectangular array of elements. The elements may be real numbers, complex numbers, or polynomials. The first integer index i is the row indicator, and the second integer index j is the column indicator. A matrix is infinite if i, j → ∞. 54) 57 If m = n, A is a square matrix. An N × 1 column matrix (only one column) represents an N-dimensional vector. 2. Transposition: The transpose of A is At whose element is Aji. If the dimension of A is m × n, the dimension of At is n × m.
The time-domain and polyphase-domain equivalent of the algorithms are discussed. Examples of biorthogonal wavelet construction are given at the end of the chapter. In Chapter 8, limitations of the discrete wavelet algorithms, including time-variant property of DWT and sparsity of the data distribution are pointed out. To circumvent the difficulties, the fast integral wavelet transform (FIWT) algorithm is developed for the semiorthogonal spline wavelet. Starting with an increase in time resolution and ending with an increase in scale resolution, a step-by-step development of the algorithm is presented in this chapter.
Fundamentals of Wavelets: Theory, Algorithms, and Applications (Wiley Series in Microwave and Optical Engineering) by Jaideva C. Goswami
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