# Errata do livro "Discrete Fourier Analysis and Wavelets: Applications to Signal and Image Processing"

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English: This page contains a list of errors/typos found in the book Discrete Fourier Analysis and Wavelets: Applications to Signal and Image Processing, used in the course MAC5920 - Algorithms for Audio, Image and Video Processing in 2010 and 2013 at the Institute of Mathematics and Statistics of the University of São Paulo.

Português: Esta página mantém uma lista de erros encontrados no livro Discrete Fourier Analysis and Wavelets: Applications to Signal and Image Processing, utilizado no curso MAC5920 - Algoritmos de Processamento de Áudio, Imagem e Vídeo nos segundos semestres de 2010 e 2013 no IME/USP (Instituto de Matemática e Estatística da Universidade de São Paulo).

English: Errors found that are not in the official errata:

Português: Erros encontrados durante os cursos, que não constam da errata oficial:

• p. 21, figure 1.17: all p and q values are swaped; for instance, the upper-left figure corresponds to p=0, q=10.
• p. 25, section 1.6.5: "(...) displayed with -256 as black and 256 as white." (alternatively, redefine $f(x,y)=128+128\sin(2\pi (50x+70y))$ ).
• pg. 34, example 1.19, $dt$ missing from last integral.
• p. 104, Exercise 2.17, line 2 should read "Let ${\textbf {B}}$ be the matrix obtained by circularly shifting ${\textbf {A}}$ (...)".
• p. 104, Exercise 2.19, line 3 should read "(...) coefficients ${\hat {a}}_{k,l}$ , ${\hat {a}}_{m-k,l}$ , ${\hat {a}}_{k,n-l}$ , and ${\hat {a}}_{m-k,n-l}$ .".
• p. 117, right after Equation 3.15, should read "(...) or the transpose of the $k$ th row of ${\mathcal {C}}_{N}$ (...)"
• p. 126, Example 3.1, ${\hat {B}}$ and all numerical data derived from it ($q({\hat {B}})$ , ${\tilde {B}}$ , and error values) are wrong. For instance, ${\hat {B}}_{0,0}=157$ and not $148.9$ , which can be easily verified with the Octave/Matlab code 8*mean(mean(B-127));
• p. 146, 4th paragraph, 3rd line should read "(...) equation (2.6) in Chapter 2.".
• p. 160, right before Equation 4.18, the text in parentheses should read "(so $f=T{\tilde {f}}$ and $df=Td{\tilde {f}}$ )".
• p. 164, Example 4.5, should be $L^{2}(\mathbb {Z} )$ instead of $L^{2}(\mathbb {R} )$ .
• p. 165, the formula for $Y(z)$ should be expanded as $\cdots -8z^{3}-4z^{2}-2z$ .
• p. 169, Section 4.5.6, The first vector is written with brackets instead of parentheses.
• p. 184, 5th paragraph should read "(...) zeros out all components $x_{k}$ with $k and $k>m+M-1$ ".
• p. 186, last paragraph should read "Equation (5.6) (...) is not identical to $X$ but (...)".
• p. 207, 2nd paragraph, 2nd line, should read "The $k$ th component of $v_{h}$ is ${\frac {1}{2}}(x_{k}-x_{k-1})$ if $k$ is even (...)".
• p. 213, 2nd line after equation (6.9), the inline equations have double opening parentheses.
• p. 224, first paragraph of section 6.5.3 should read: "If all convolutions (...), then $X_{l}=DM_{la}x$ and $X_{h}=DM_{ha}x$ , where (...)"
• p. 240, equation 6.31, a factor of ${\frac {1}{2}}$ is missing in the last summand (the one ending in $X(-z)$ ).
• p. 270, Figure 7.3, figures seem to be mirrored. They are synthesized like this if we switch filters of analysis and synthesis. Compare the situation of figures 7.2 and 7.4 (mirrored) with figures 7.13 and 7.14.
• p. 274, Equation 7.6, there should be no $2^{k/2}$ there.
• p. 288, last line of Equation 7.30, missing $+\delta _{0}$ on the sum.