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Discovering Wavelets: Errata and Comments
maintained by Edward Aboufadel and Steven Schlicker
Listed below are typos that have been found in the book, along with new comments and questions that may inspire further learning. Corrections to typos were sent to Wiley on July 21, 2000. If you discover other errors, please contact the authors.
Last Update of this list: June 10, 2003

Note: TeX codes have been used for math symbols, where appropriate.

page 5:
For the definition of the father wavelet, \phi should equal 0 at t=1, not 1.
(not sent to Wiley yet)

page 6:
The definition of the Haar mother wavelet is mangled. It should read that the value of $\psi$ is -1 if $\frac{1}{2} \le t < 1$.

page 25:
In problem 7, in the "show that" sentence, the square root should be of the whole fraction, not just the numerator.

page 26:
In the first sentence, that should read $w_{\perp} = v - w$, not w - v. At the beginning of section 2.2, the first sentence should end with m=2^n, not n=2^m.
(not sent to Wiley yet)

page 36:
In problem 39, f(t) is the projection of h onto V_2.
(not sent to Wiley yet)

page 42:
Something to think about: how does $M_4$ compare to the $A_2^T$?

page 44:
Fifth line, replace $V_2$ with $V_1$. (The dimension of $V_1$ is 2.)
(not sent to Wiley yet)

page 53:
For the nested sequence for the MRA, the subset relations can be replaced with proper subset.

page 54:
In the third criterion for the MRA, the latter half of that line should read: if and only if $f(2^{-n} t) \in V_0$.

page 56:
Something to think about: is $F$ a linear transformation?

page 56:
In the last sentence before problem 24, $f_0$ is defined to be 1+t from -1 to 0, not 1 to 0.
(not sent to Wiley yet)

page 58:
It is a little confusing to tell which lines are to be entered into Maple and which are not. Any line beginning with a > is a Maple code line. There is one line in the middle of the page that is centered, beginning f[i+1](t) =, that should probably not be in the Maple font.

page 61:
Along with problem 37, something to think about: create a dilation equation so that the cascade algorithm settles into a period two oscillation.

page 62:
Middle of page ... in the orthonormal basis generated by /psi, the scale factor 2^{-k/2} should be 2^{n/2}.
(not sent to Wiley yet)

page 63:
Problem 38 is a consequence as problem 16.
In problem 39, the wording is a little confusing. Basically, V is an inner product space with an orthogonal set of vectors. None of the vectors in the set is the zero vector. Show that the set is linearly independent.
(not sent to Wiley yet)

page 65:
On the top half of the page, the same summation appears twice. The subscript on the second g, which says $i-2(k-m)$, should read $i-2(m-k)$.
(not sent to Wiley yet)

page 66:
In problem 44, the ambitious reader should also consider the special cases where $\phi(1) = 0$ or $\phi(2) = 0$.

page 67:
The moment conditions can also be thought of this way: since $\psi$ is in $V_0^{\perp}$, it is orthogonal to anything in the span of $\phi$ and its translates. Both 1 and t are in the span, by assumption, so <1, \psi> = 0 and = 0.
The regularity condition is something referred to as the polynomial accuracy condition.

Equation (3.15) is incorrect. The right hand side should read $-c_0 \phi(2t - 1) + c_1 \phi(2t) - c_2 \phi(2t + 1) + c_3 \phi(2t + 2 )$.
(not sent to Wiley yet)

page 68:
In problem 48, you want to use conditions (3.13), (3.14), (3.16) and (3.17). Also, think about how one could solve this system either algebraically or by Newton's method.
In problem 49, as a third part of the problem, determine the exact values of $\D_4(1)$ and $\D_4(2)$.

page 70:
Something to think about: why does it make sense to say that $\{ \psi_{n,k} | n \in Z, k \in Z \}$ is a basis for $L^2(R)$?

page 81:
In the paragraph that begins "Accordingly", you should sample the sound every $2^{-15}$ seconds. Duh.

page 95:
In problem 1, instead of "quadratic polynomials", that should read, "polynomials of degree two or less."
(not sent to Wiley yet)

page 108:
In the first line of that page, that line should end with "end):" and not "end:"
In the last line of that page, replace "matrix A8" with "matrix A8inv"

page 109:
In the first line of that page, replace "A8" after "multiply" with "A8inv".
In the middle of the page, in the sentence that begins "To deprocess", replace "A8inv" with "A8". Do the same in the line of Maple code immediately following.

page 109-112:
The code in both sections B.3 and B.5 have errors in it. Correctly working code can be downloaded here. (Use proj_vn.mws for B.3 and images.mws for B.5)

page 121:
In reference 37, the correct spelling of the city with the Golden Gate is "San Francisco".