Correction to: Cosine-/Sine-Modulated Filter Banks

Correction to: V. Britanak, K.R. Rao, Cosine-/Sine-Modulated Filter Banks, https://doi.org/10.1007/978-3-319-61080-1

This book was inadvertently published without updating the following corrections:

Preface

On p. v, in the third line from top, “in” was inserted after comma to read “. . ., and vice versa, in many sub-band/transform-based schemes . . .”

Chapter 1

On p. 1, in the second paragraph, two occurrences of “pseudo-OMF” was replaced by “pseudo-QMF”

Chapter 3

On p. 50, in the sentence after equation (3.33): “. . . D_N = diag {1, −1, 1, …, −1} is the diagonal odd sign changing diagonal matrix, . . .”, the third word “diagonal” was removed.

On p. 54, in equation (3.52), replace “cos” transform kernel by “sin” transform kernel.

On p. 62, in the sentence after equation (3.78): “. . . D_N = diag {1, −1, 1, …, −1} is the diagonal odd sign changing diagonal matrix, . . .”, the third word “diagonal” was removed.

Chapter 4

On p. 106, on the right-hand side of equation (4.17) from the argument in the cosine transform kernel under sum the redundant variable “n” was removed.

On p. 145, in the first paragraph of subsection 4.3.7, correct the following sentence as follows: “For a particular radix number q, the radix-q fast algorithms recursively divide the entire transform computation into q shorter $\frac {N}{q}$-point transforms [72].” (Append word “transforms” at the end of sentence).

On p. 145, in the last paragraph of subsection 4.3.7, the sentence was corrected as follows: “This DIT mixed-radix fast algorithm was extended . . .”.

4. On p. 149, on the left-side of equation (4.133) correct notation “c_3k+1” by “$c^{{ }^O}_{3k+1}$”.

5. On p. 168, on the right-hand side of equation (4.191) under sums, replace all terms “c_k” by “$c^{{ }^{\mathrm{MLT}}}_k$” (two times).

6. On p. 170, on the right-hand side of equation (4.200) under the sum, replace “c_k” by “$c^{{ }^{\mathrm{MLT}}}_k$”.

Chapter 5

On p. 215, in the first sentence after equation (5.18) the closing parenthesis was removed after $\frac {N}{2}$-point DCT-III.

On. p. 234, on the right-hand side of equation (5.53) the “D” was changed to bold (“${D}_{\frac {M}{2}}$” by “${\boldsymbol D}_{\frac {M}{2}}$”)

Chapter 6

On p. 338, 3rd paragraph, 4th line, “Appendices” was corrected.

Chapter 9

On p. 498, the correct form of the sentence immediately after equation (9.23) is as follows: “where $\boldsymbol {G}^{{ }^T}_N$ is the transposed rotation matrix G_N defined by (9.12).”, (the superscript T denoting transposition was removed).

Appendix B

On p. 593, in the part B.1, the correct form of equation on the left-hand side in (B.2) is as follows:

$$\displaystyle \begin{aligned} u_n = -u_{N-1-n}, \qquad \qquad v_n = v_{N-1-n}, \qquad n = 0, 1, \ldots , \frac{N}{2}-1. \end{aligned}$$

Appendix D

On p. 620, in the part D.7.1, the following paragraph was appended at the end:

$$\displaystyle \begin{aligned} \begin{array}{ll} c^{{}^{II}}_0 = x_2 + a_5 &\\ c^{{}^{II}}_1 = m_2 - m_3 &\\ c^{{}^{II}}_2 = m_1 - a_8 &\\ c^{{}^{II}}_3 = m_4 - m_2 &\\ c^{{}^{II}}_4 = m_1 + a_8 & \end{array} \end{aligned}$$