Essential Wavelets for Statistical Applications and Data Analysis
R.T. Ogden, University of South Carolina
0-8176-3864-4 * 1996 * $40.00 * Hardcover * 285 pages * 40 Illustrations
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Essential Wavelets for Statistical Applications and Data Analysis |
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Errata for
Essential Wavelets for Statistical Applications
and Data Analysis
- (p. 3) In Figure 1.1, the labels for the three sets of plots should be j=1, j=2, and j=3 rather than j=0, j=1, and j=2
- (p. 10) The J_0 should have a minus sign before it in the left-hand limit of the interval (five lines under the displayed equation).
- (p. 13) In the first equation, the second summation should be over k rather than over l.
- (p. 13) In the third displayed equation, there should be "(x)" just before the equals sign.
- (p. 13) In the last equation, neither norm should be squared.
- (p. 14) Just under the first displayed equation (for V_j), the second sentence should read "Each subspace V_j consists of functions that are piecewise constant over intervals of exactly half the length of those for V_{j-1} (and twice the length of those for V_{j+1})."
- (p. 20) The coefficient values for j=1, k=-4 and for j=1, k=3 should both be 0.9805. Here's the corrected table.
Table 1.2: Haar scaling function coefficients for the example function
|----------------------------| | k | j=-1 j=0 j=1 | |----+-----------------------| | -7 | 0 0 0.0142| | -6 | 0 0 0.2769| | -5 | 0 0 0.6305| | -4 | 0 0.0100 0.9805| | -3 | 0 0.6416 1.1107| | -2 | 0.4608 1.4787 1.1107| | -1 | 2.1563 1.5708 1.1107| | 0 | 2.1563 1.5708 1.1107| | 1 | 0.4608 1.4787 1.1107| | 2 | 0 0.6416 1.1107| | 3 | 0 0.0100 0.9805| | 4 | 0 0 0.6305| | 5 | 0 0 0.2769| | 6 | 0 0 0.0142| |----------------------------|- (p. 21) The coefficient value for j=0, k=-2 should be -0.9207 and that for j=0, k=1 should be 0.9207. Here's the corrected table.
Table 1.2: Haar wavelet coefficients for the example function
|-----------------------| | k | j=-1 j=0 | |----+------------------| | -4 | 0 -0.0100 | | -3 | 0 -0.2500 | | -2 | -0.4466 -0.9207 | | -1 | -0.0651 0 | | 0 | 0.0651 0 | | 1 | 0.4466 0.9207 | | 2 | 0 0.2500 | | -4 | 0 0.0100 | |-----------------------|- (p. 122) In the second-to-last line of the second set of equations, the wavelet function should be squared.
- (p. 131) In the last equation on the page, the right-hand side should be multiplied by n.
- (p. 148) In the first displayed formula on the page, there should be a (1/d) on the right hand side.
- (p. 159) In equation (8.8), the superscript on the second threshold value in the equation should be n/2 rather than n.
- (p. 162) In the first displayed formula on the page, the d should be a w.
- (p. 175) In the last sentence on the page, j_i = i should read instead j_i = i-1. Also, the limits on the union in Equation 9.4 should run from i=0 to infinity. For further reading on this topic, see "Entropy-based Algorithms for Best Basis Selection" by Coifman and Wickerhauser, IEEE Transactions on Information Theory, Vol. 38, Number 2, pp. 713-718 (1992).
- (p. 178) In Figure 9.6, the G's and the H's should be switched. To be consistent, the G's and H's should be switched in Figure 9.7 as well.
Many thanks to Harry Dwyer, Tom Early, Mario Figueiredo, Mark Fowler, Jae Keun Jo, Ted Norminton, Fanis Sapatinas, Dai Wei-Wen, and others for pointing out these errors. Of course, I take responsibility for them. Any other errors? Please e-mail me.
R. Todd Ogden
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