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 J0 should have a minus sign before it in
the left-hand limit of the interval (five lines under the displayed
equation).
- (p. 11) In the sentence beginning "This detail function ..." about
2/3 of the way down the page, the first J0 in the
superscript
of f should be J0-1.
- (p. 11) In equation (1.8), the limits of the integral should be
k2-j and (k+1)2-j.
- (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 Vj), the
second sentence should read "Each subspace Vj consists of functions
that are piecewise constant over intervals of exactly half the
length of those for Vj-1 (and twice the length of those for
Vj+1)."
- (p. 16) In the displayed equation in the middle of the page, the
argument of the function on the right hand side should be 2jx
-k.
- (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.
- (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.
- (p. 51) The cJ,k in the text after (3.3) should
have a hat (^) on it.
- (p. 51) In the expression for the histogram just over halfway down
the page, the j' should just be j.
- (p. 63) The first line in the last full paragraph on the page should
begin "The algorithms given in (4.8) and (4.9) share . . ."
- (pp. 64-65) The equations (4.12), (4.13), and (4.14) should have
parentheses around the entire summands to make it read more clearly.
- (p. 119) The first sentence in Section 7.1 should refer to Section
3.2.
- (p. 122) In the third line of the derivation of the expected value
of the wavelet coefficient, there should be a (1/n) term before the
summation sign.
- (p. 122) In the first line of the variance computation, there
should be parentheses around the n i the wavelet coefficient's superscript.
- (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. 131) The third line from the bottom should have ellipses:
k = 0, . . ., 2J-1 -1.
- (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, ji = i should
read instead ji = 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, Paul Komarek, Sungho Lee,
Ted Norminton, Fanis Sapatinas, James Surles,
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
Last modified: Wed Dec 13