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Errata for ``Wavelets and Subband Coding'', 4th printing, 1997.

  • Copyright page

    "three dimensional" should be "three-dimensional".

  • Chapter 2

    Page 19 [JK]:
    In Definition 2.2, should be "complex-valued"
    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..." In Figure 2.2, \hat(y) = x_i
    Page 28 [AO]:
    the top-right index of the matrix at the bottom of the page should be A_{1n}
    Page 30 [JM]:
    Isn't (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 case, rank(A) + Null = n, not m as is stated.
    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(t-t_0) -> f(t+t_0) )
    Page 47 [JRT]:
    Eq. below (2.4.29) should have "=" sign instead of "<-->"
    Page 60 [UCB]:
    line 3: \rho^n -> \rho^{-n}
    Page 60 [AO]:
    3rd par. f'[n] = \ro^{-n} f[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]:
    In p. 69 you describe the conditions for up and downsampling to commute. The two equations should be switched, i.e. the first one corresponds to downsampling, followed by upsampling. Also, they are both missing 1/N factors in fron of summations.
    Page 75 [JK]:
    Figure 2.11. In part (b) should be "scale doubled". In part (c) should be "scale halved".
    Page 76: [UCB]:
    Thm 2.7: f(t) is assumed to be differentiable (not mentioned), and it vanishes faster then 1/Sqrt(ABS(t)) (the ABS was missing).
    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 105 [JM]:
    Figure 3.2: Assume that the caption states "using ideal half-band filters".
    Page 106 [JK]:
    After Proposition 3.3: "Therefore,..." add "if certain frequency locality is desired" at the end of that sentence.
    Page 108 [JK]:
    Matrices T_a and T_s should be extended to infinity on the right and left as well.
    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]:
    Equation 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 140 [UCB]:
    In equation 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". In the paragraph beginning with "In Figure 3.7(b)... W_j, j=1,...,J". put j instead of i to be consistent.
    Page 162 [AO]:
    Last equation, the vector should be (1 z^{-1} z^{-2} ...).
    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.

  • 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..." say first "Then, for any $k \neq 0$ EQUATION, because $\Phi(\omega + 2k\pi) = 0$, while for $k = 0$, EQUATION."
    Page 227 [UCB]:
    In the last equation, remove "1/Sqrt(2)", and "(4k+1)" should read "(4k+2)".
    Page 236 [UCB]:
    Factor "1/120" in (4.3.27)/
    Page 253 [JK]:
    Remark on the case N=1. Criterion is not useful since R(0)=1, B < 2^0 is never satisfied. Moreover, it would be better to make the remark that there exists an $\epsilon > 0$ such that $B < 2^{N-1-\epsilon}$, otherwise the derivation of the one but last sequence of inequalities is hard to follow.
    Page 254 [W]:
    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=2n-k".
    Page 270 [UCB]:
    The last line of the three-line equation should read "g1[2n-l]" instead of "g1(2n-l)".
    Page 295 [CW]:
    Problem 4.2(b): "g_0[n] = sqrt(2) ".
    Problem 4.3(a): Llimit of summation should be lowercase "n".
    Problem 4.6(b): Llower limit of integral should be "-infinity".
    Problem 4.1(a): The range for t should be [0,1).

  • Chapter 6

    Page 345 [JK]:
    Caption of Figure 6.4(b) should have H_e.
    Page 347 [UCB]:
    In the econd 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]:
    Top paragraph: Incorrectly describes Nth order stationarity. Nth order stationarity refers to all distributions involving N or fewer samples to being time-invariant. This implies ALL order moments involving N samples is time invariant. The equations describing wide-sense-stationarity (WSS) are correct for WSS but not 2nd order stationarity. 2nd order stationarity implies WSS, but the other direction does not hold in general. (7.A.9) on bottom of page: It should read as either: S_{XY}(e^{jw}) = H(e^{-jw}) S_X(e^{jw}) or S_{YX}(e^{jw}) = H(e^{jw}) S_X(e^{jw}), ie., either the subscripts of S need to be transposed or the 'w' needs to be negated in H(ejw). This can be used to find H(ejw) whether or not X[n] is uncorrelated with other time samples of X so long as Sx(ejw) is nowhere 0.

  • References

    [100] After Gauthiers-Villars remove the colon.
    [141] N.S. Jayant.
    [142] N.S. Jayant, J.D. Johnston, R.J. Safranek.
    [143] N.S. Jayant.
    [151] A.A.C.M. Kalker.
    [157] M.R.K. Khansari.
    [160] There should be accents on JK's name.
    The title of the paper should read: "Perfect reconstruction filter banks with rational sampling factors".
    [211] Should be Schaffer.
    [294] [MU] It should be: M. Unser, "On the Approximation of the Discrete Karhunen-Loeve Transform for Stationary Processes," Signal Processing, vol. 7, no. 3, pp. 231-249, December 1984.

  • Comments from:

    JK : Jelena Kovacevic
    JM : Jim Mazo
    TTN: Thao Nguyen
    KR : Kannan Ramchandran
    HL : Henri Landau
    W : Walter
    AO : Antonio Ortega
    MU : Michael Unser
    CW : Chip Webb
    EL : Edouard Lamboray
    JRT: Jaan-Rong Tsay
    UCB: Students at UC Berkeley
    		•