

WAVELETS AND SUBBAND CODING 













Errata Manuscript ·
first through fourth printing, Errata 1,2,3
lists apply, ·
fifth and sixth printings, Errata 2,3 lists apply, ·
seventh printing and above, Errata 3 list applies. Errata 1
Dedication
page
It should read "zvezdici" instead
of "zvedzdici". Chapter
3
Page 110: Equation (3.2.9) should
have "h_i[L3]" instead of "[L4]". Page 126: In part (b) of Theorem
3.8: The last "K" should be capital. Page 134: Under P(z) equation it
should read "odd roots of +1" instead of "at +1". Page 169: Equation (3.4.23): Take
out "B_0 B_0^T = " in both equations. Page 199: In Problem 3.25 (b) The
second "[1 1]" should be "[1 1]". Chapter
4
Page 233: Under (4.3.20) it should
say "Fourier transform OF g(t)". Page 234: 5th formula from top: The
$\omega/2$ in the middle in the formula should be $\omega$. Page 253: Second equation of the
proof: the whole sinc is at the power of N. Second line from the bottom
should read: 2^{J1} \leq \omega < 2^J. Page 254: Expression for "B_l
= sup ...." should have an absolute value sign. Page 291: In the sentence starting
with "Finally, orthogonality..." add "for $k \neq m$"
after "\varphi_{j,m}$". Page 295: In Problem 4.6 (a) should
read: "Verify that 4.3.11 is the DTFT of 4.3.12". Chapter
7
Page 372: Equation (7.1.1) should
read: $\frac{1}{N} \sum_{i=0}^{N1} E(x_i  \hat{x}_i^2)$. Page 395: At the end of table
caption add "[146]". Page 438: Part (a) has a double
point at the end. Page 457: In Problem 7.3, in both
equations, $\omega$ should be with absolute value. Page 458: In Problem 7.5(a),
$\omega$ should be with absolute value. References
[100] After GauthiersVillars remove the
colon. [141] N.S. Jayant. [142] N.S. Jayant, J.D. Johnston, R.J.
Safranek. [143] N.S. Jayant. Errata 2
Chapter 2
Page 19 [JK]: In Definition 2.2, should
be "complexvalued". Page 24 [JK]: Last equation should have
under the sum: "x_i \in S". Page 25 [JK]: 5th line from top:
"..for x in S, is attained..." Page 25 [JK]: In Figure 2.2,
"\hat(y) = Page 28 [AO]: The topright index of
the matrix at the bottom of the page should be A_{1n}. Page 30 [JM]: (adjugate(A))_ji =
cofactor of A_ij, not A_ji. Page 31 [AO]: 2nd paragraph in 2.3.2:
When there are m equations and n unknowns, the matrix has m rows and n
columns, in which Page 33 [JK]: 8th line from top:
"...allowed on the right..." Page 41 [JRT]: 15th line: "nw_0"
should be "kw_0". Page 43 [JRT]: Eq. (2.4.17): there
should be a "+" on the RHS (that is, in (2.4.17) f(tt_0) >
f(t+t_0)). Page 46 [JM2]: Eq. (2.4.28) should have
\exp(+j(\omega)t) instead of \exp(j(\omega)t). Page 47 [JRT]: Eq. below (2.4.29) should
have "=" sign instead of "<>". Page 60 [UCB, AO]: line 3: \rho^n >
\rho^{n}. Page 61 [AO]: Eq. at the bottom of the
page: replace z^{1} by z^{k} both in numerator and in denominator. Page 69 [AO]: The two equations on up/downsampling
should be switched, Page 75 [JK]: Figure 2.11. In part (b)
should be "scale doubled". In part (c) should be "scale
halved". Page 76: [UCB]: In T 2.7: "If f(t)
is differentiable and vanishes faster than 1/sqrt{t} ..." Page 90 [UCB]: Prob. 2.17, "<\alpha_i,\beta_i> > <\alpha_i,\beta_j>". Chapter 3
Page 92 [JK]: 4th line from top:
"Thus, given an arbitrary sequence.." should be "Thus, given
an arbitrary sequence from l_2(Z)...". Page 104 [GH]: Equation (3.1.23) should
have [pi/2,pi/2], not [pi/2,pi/2]. Page 104 [JK]: Add +/ in front of
g_1[n]. Page 104 [HL]: Sentence before (3.1.24):
"... choose a modulated version of g_0[n] with a time reversal and a
shift by one". After (3.1.24) substitute the paragraph "While the
time ... squaresummable sequences" with the following: "While the
time reversal and odd shift are necessary when the filter is FIR (see Proposition
3.20), in this particular case, both are immaterial (that is, g_1[n] +/
(1)^n g_o[n] will work as well). Page 105 [JM]: Figure 3.2: Caption
should state "using ideal halfband filters". Page 106 [JK]: After Proposition 3.3:
"Therefore,..." add "if certain frequency locality is
desired" at the end of that sentence. Page 108,109 [JK]: Matrices T_a and T_s
should be extended to infinity on the right and left as well. Page 125 [JK]: Add +/ in front of both
G_1(z) and g_1[n]. Page 126 [JK]: Add +/ in front of
G_1(z) in Theorem 3.8(b). Page 127 [ED]: In (c) of Corollary 3.9:
+/ z^{2K+1} G_0(z^{1}). Page 131 [JK]: Add +/ in front of
G_1(z) before (3.2.60). Page 135 [JK]: In the proof:
"..filters are of even length." Add at the end of this sentence
"by Corollary 3.9". Page 137 [UCB]: Eq. below (3.2.72) should
read "P(z) = 1/256 (1 + 9z^{2} + 16..)". Page 137 [JK]: "that is, the same
P(z) as in Example 3.2". Add "within sign and multiplication by
z^3". Page 139 [AO]: Top line, "z^2"
should be "z^{2}". Page 140 [UCB]: In eq. above (3.2.79),
denominator is "10z^4 + 120z^2 + ..." (not "z^3"). Page 149 [JK]: In the proof of
Proposition 3.14, the last equation (and the one before that) should have
"+" instead of "" in front of m. Page 152 [JK]: Fourth line from top
should have "g_1[n] in V_0". Page 155 [AO]: In (3.3.24),
"G_2^(2)(z)" should be "G_1(z)G_1(z^2)", and "G_3^(2)(z)"
should be "G_1(z)G_0(z^2)". Page 156 [AO]: Figure 3.12(c): Assuming
the lower branch is the lowpass filter, the top two bands in the figure
should be switched Page 162 [AO]: Last equation, the vector
should be "(1 z^{1} z^{2} ...)". Page 163 [ED]: Before (3.4.10), K's
should be k's. Add also, k \in Z. Page 172 [UCB]: (3.5.3) "x = 1/2
( y_0^2 + ...)" (instead of 2 times). Page 197 [HL]: Problem 3.2 is not correct.
The shift by one is not necessary. In the solutions, the limit function does
not exist. Substitute current Problem 3.2 with: "With the aid of
downsampling and upsampling formulas (2.5.13) and (2.5.17), reconstruct
Figure 3.2. What happens is the filters have support larger than allowed by
the sampling theorem? Draw and example." Page 198 [DP]: In Problem 3.16 (a), G_i0
should be only G_i. Chapter
4
Page 217 [JM]: Equation near bottom:
should be "G0(1)=sqrt(2)", i.e. no absolute values. Page 224 [JM]: Line 8 from end: ideal
sinc case (not ideal  sinc case). Page 227 [JM]: We use two different
conjugation signs. One is * and the other one is bar. Then, in the sentence
"Then, for any k..." Page 227 [UCB]: In the last equation,
remove "1/Sqrt(2)", and "(4k+1)" should read
"(4k+2)". Page 233 [ED]: LHS of (4.3.23) is
missing "[n]". Page 236 [UCB]: Factor "1/120"
in (4.3.27). Page 251,252 [AO]: "g_0^{i}[2n] =
g_0^{i1}[n]" and it tends to "\varphi(t)" as i tends to
"\infty". Change all "\varphi(2t)" into
"\varphi(t)" in the proof of Prop. 4.6. Page 254 [W], [NKB]: The first line in the
paragraph following the proof "(1 + e^jw)", should not be squared. Page 258 [UCB]: Table 4.2, list is for
R(z)R(z^{1}) (not R(z)). Page 269 [W]: Third line in paragraph
below (4.5.10). It should read "l=2n+k" not "l=2nk". Page 270 [UCB]: The last line of the
threeline equation should read "g1[2nl]" instead of
"g1(2nl)". Page 274 [ED]: In (4.6.8) it should be
uppercase "Psi". Page 276 [ED]: It should be uppercase
"Psi". Page 295 [CW]: Problem 4.1(a): The range
for t should be [0,1). Problem 4.2(b):
"g_0[n] = sqrt(2) Problem 4.3(a): Limit of
summation should be lowercase "n". Problem 4.6(b): Lower
limit of integral should be "infinity". Chapter
6
Page 345 [JK]: Caption of Figure 6.4(b)
should have "H_e". Page 347 [UCB]: In the second equation,
matrices should be "[(1,1),(1,1)]" twice, instead of
"[(1,1),(1,1)]". Chapter
7
Page 425 [EL]: The LH2 coefficient 9 in
Table 7.9 is a positive 9 in table 7.8. Page 454 [W]: (7.A.9) on bottom of
page: It should read: S_{XY}(e^{jw}) = H(e^{jw}) S_X(e^{jw}). References
[151] A.A.C.M. Kalker. [157] M.R.K. Khansari. [160] There should be accents on JK's name. [211] Should be Schaffer. [294] [MU] It should be: M. Unser, "On
the Approximation of the Discrete KarhunenLoeve Transform for Stationary
Processes," Signal Processing, vol. 7, no. 3, pp. 231249, December
1984. Errata 3
Chapter
2
Page 43 [NKB]: Equation (2.4.17) should
end with "= f(t_0).". Page 70 [NKB]: Equation should have
"1/N" on both sides. Page 89: Problem 2.14 should be as
follows: Page 90: Problem 2.15(d), typo,
should be "pulses". Chapter
3
Page 119 [NKB]: In the proof of
Proposition 3.5, G_p(z) should be "adjugate(H_p(z))" not
"cofactor(H_p(z))". Page 120 [NKB]: In the proof of
Proposition 3.6: Page 131 [NKB]: In (3.2.60), square
brackets should open after the product sign, not before. Page 133: Both (3.2.65) and
(3.2.66) should have a "+/" on the righthand side of the
equations. Page 134 [NKB]: The expression for P(z)
should read as follows: Page 135: Proof of Proposition
3.12: The polyphase decomposition of H(z) should be in reverse as in the
equation after (3.2.22). Page 136 [NKB]: In (3.2.70), square
brackets should open after the product sign, not before. Page 168: 8th line below (3.4.18)
should have a minus sign in front of h_k[3N/2+l]. Page 181: First equation should
have determinant in front (det H_p). Page 195: In the second equation:
(D^t)^{i}) >(D^t)^{1}) . Page 198: Problem 3.14: Page 199: Problem 3.23: Page 199: Problem 3.24: Page 199: Problem 3.27: It should
be "(3.6.4)(3.6.5)". Page 198: Problem 3.16: Add the
following at the end of (c): Chapter
4
Page 212: 5th line below (4.1.13)
should have: "(f_0^(m_1)2^{m_1/2})". Page 219: Number second equation
above (4.2.18) as (eq1). Then, right before the sentence "We can choose
.." that starts (4.2.18) add the following: Page 219: Right before "To
prove that this wavelet...", insert the following: Page 221 [NKB]: 4th equation from the top
should have G^*_0. Page 243: (4.4.10) and (4.4.11)
should have "n/2^i" in fraction mode. Page 246: Assumption (d) should
have "g_1[n] = (1)^n g_0[L1n]". Page 247: Second equation should
have "g_0[m2l]" instead of "g_0[2l+m]" twice. Page 251: After (4.4.27), add the
following: Page 254 [W], [NKB]: The first line in the
paragraph following the proof "(1 + e^jw)", should not be squared. Page 296: Problem 4.12(b): It
should have "G_0(e^j\omega)" twice. Chapter
7
Page 373: Line below (7.1.8) should
have: "\Lambda_{ii} = \lambda_i = E(y_i^2) = \sigma_i^2, i=0, \ldots,
N1$, where $\sigma_i^2$ is the variance of the $i$th transform coefficient. Comments from:
ZC : Zoran Cvetkovic NKB: Nirmal K. Bose ED: Eric Dubois GH: Garrick Harmon JK : Jelena Kovacevic EL : Edouard Lamboray HL : Henri Landau JM : Jim Mazo JM2: Jarno Mielikainen TTN: Thao Nguyen AO : Antonio Ortega DP: Dragan Petrovic SS : Shep Siegel UCB: Students at UC
Berkeley KR : Kannan Ramchandran JRT: JaanRong Tsay MU : Michael Unser W : Walter CW : Chip Webb 





