My book Mathematics for Multimedia, ISBN 978-0-8176-4879-4, was formerly managed by Elsevier/Academic Press. It is currently published by Birkhaeuser Verlag and should be available by November 24th, 2009. An instructor's manual with more than 300 additional solved exercises is available. Please contact me by email for downloading instructions. I would appreciate correspondence detailing any errors that readers may find. Please use the contact information maintained at the home page link below.

Software

All references are to the first printing, uncorrected. See my utility software page for links to free public Standard C compilers and PostScript graphics systems.

Chapter 1: Numbers and Arithmetic quotrem.c: compute the quotient and remainder table in Sec.1.1.0, p.3. gcd.c: Euclid's algorithm and its recursive version. Sec.1.1.0, p.4, and Sec.A.1, Solution 2, p.223. quasiinv.c: compute the quasi-inverse of an integer with respect to a modulus. Sec.1.1.1, p.8, and Sec.A.1, Solution 5, p.224. tobinary.c: compute the binary and hexadecimal digits of a decimal integer. Sec.1.1.2, p.9, and Sec.A.1, p.225. pihex.c: compute the hexadecimal expansion of pi. Sec.1.1.2, p.9, and Sec.A.1, Solution 10, p.226. sum.c: add up 100,000,000 1.0's to demonstrate single-precision truncation error. Sec.1.2.2, p.16, and Sec.A.1, Solution 12, p.226. ieee32.c: interpret 32 ones and zeroes as an IEEE 32-bit floating-point number. Sec.1.2.2, pp.16-18, and Sec.A.1, Solution 13, pp.226-227. Chapter 2: Space and Linearity gramschm.c: orthonormalize three vectors in four-dimensional space using the Gram-Schmidt algorithm. Sec.2.1, pp.38-39, and Sec.A.2, p.230. gepp.c: Gaussian elimination with partial pivoting gepp(); LU decomposition lupp(); matrix inversion mipp(); linear system solution from LU and pivoting data sslu(). Sec.2.2, pp.58-61. Chapter 3: Time and Frequency fray.c: midpoint fraying and splicing. Sec.3.1.2, pp.78-80. fft.c: factored discrete Fourier transform, or FFT, and its inverse iFFT. Sec.3.2.1, p.98. fht.c: factored discrete Hartley transform, or FHT, and its inverse iFHT. Sec.3.2.2, p.100. Chapter 4: Sampling and Estimation poly.c: polynomial algorithms from Sec.4.1, pp.108-116. sincerr.c: integrate the tail of the sinc function. Sec.4.1.3, p.122. gsincerr.c: integrate the tail of the Gaussian sinc function. Sec.4.1.3, p.122.

Chapter 5: Scale and Resolution makefile: compilation instructions for all C codes from this chapter. dwt.c: Mallat's discrete wavelet transform to specified depth, implemented by filter convolution. Sec.5.2.3, p.160. pcqfilt.c and testpcqf.c: combined periodic conjugate quadrature filter transforms, with a program to test invertibility. Sec.5.2.3, p.162, and Sec.A.5, p.257. pdwt.c: mallat's periodic discrete wavelet transform to specified depth, implemented by periodic filter convolution. Sec.5.2.3, p.163, and Sec.A.5, pp.257-258. pdwt0.c: complete periodic discrete wavelet transform implemented by filter convolution. Sec.5.2.3, p.163. haarlift.c: lifting implementation of the orthogonal Haar wavelet transform. Sec.5.2.4, p.166. hsldht.c and hslift.c: half-sample symmetric lifting implementation of the biorthogonal discrete Haar wavelet transform. Sec.5.2.4, p.168, and Sec.A.5, pp.260-263. wsl97.c and wslift.c: whole-sample symmetric lifting implementation of the JPEG-2000 biorthogonal 9-7 wavelet transform. Sec.5.2.4, pp.169-173, and Sec.A.5, pp.259-260. wsl97.gp: plotting commands for Gnuplot to graph the output of wsl97.c, scaling function and wavelets produced by biorthogonal 9-tap and 7-tap filters. Sec.A.5, Solution 19, pp.259-260. daub4.c and daub4.gp (commands for Gnuplot): prepare and plot data showing the graphs of the wavelet and scaling function produced by Daubechies' 4-tap orthogonal conjugate quadrature filters. Sec.A.5, Solution 17, pp.257-259. Chapter 6: Redundancy and Information hammcode.c: find a Hamming-type code of specified radius, size, and number of codewords. Sec.6.2.2, p.204, and Sec.A.6, Solution 12, pp.268-269. checksum.c: compute checksums modulo 255 and 257. Sec.6.2.3, p.205. polymod2.c: generate addition and multiplication tables for polynomials wih coefficients in the integers modulo 2. Sec.6.2.3, Table 6.3, pp.209-210. mod2poly.c: functions to manipulate mod-2 polynomials of arbitrary size. Sec.6.2, pp.210-213. intpoly2.c: functions to manipulate integer-sized mod-2 polynomials. Sec.6.2, pp.210-213. irreduce.c: test whether a polynomial modulo 2 is irreducible. Sec.A.6, Solution 17, p.270. cycle.c: determine the smallest N for which a given mod-2 polynomial divides (t to the N) plus 1. Sec.6.2.3, p.217, and Sec.A.6, Solution 19, pp.270-271. elephant.c: encode some text strings concerning elephants. Sec.A.6, Solutions 20 and 21, pp.271-272.

Errata

• [2006-02-08] Chapter 2, Sec.2.1.3, p.38: Lemma 2.5 should say that Y intersect Y perp is contained in {0}. This change applies to Exercise 5 in Sec.2.3, p.65, and Solution 5 on p.229. Download corrected pages 38, 65, and 229 here (155 943 bytes).
• [2006-02-08] Chapter 2, Sec.2.1.3, p.35: The second inner product axiom needs to be "Positive definiteness," and there should be index entries for nondegeneracy and positive definiteness pointing to this page. Download corrected pages 35 and 300--302 here (100 310 bytes).
• [2004-08-20] Appendix A, Sec.6, p.272: In Solution 21, the sequence mod2poly[]={1,1,0,1} should be used to represent 1+t+t^3, with the coefficient of t^3 at index 3. The checksums are then 0, 1, and 0 respectively. Download corrected page 272 here (27 027 bytes).
• [2004-08-17] Chapter 6, Sec.6.2.3, p.217: In Theorem 6.19, the hypothesis on S(t) should be "not divisible by t" rather than "with at least two terms." Download corrected page 217 here (48 565 bytes).
• [2004-08-17] Appendix A, Sec.6, p.270: In Solution 17(a), the factorizations and remainders from dividing the polynomial are incorrect. Also, the function least_power() in Solution 18 has been enhanced to work for problem 19 as well. Download corrected page 270 here (29 972 bytes).
• [2004-08-12] Chapter 6, Sec.6.2, p.212: In Theorem 6.14, input array p2 should be indexed p2[0],...,p2[d2], and line [5] of mod2polydivision() should read "For n=0 to d2-1,...". Also, on p.213: In mod2polygcd(), line [3] should read "If dr>=0, then go to [0]." Download corrected pages 212 and 213 here (51 217 bytes).
• [2004-07-29] Appendix A, Sec.6, p.266: In Solution 8, the codeword length array is mislabeled M; it should be n. Download corrected page 266 here (28 928 bytes).
• [2004-04-26] Chapter 4, Sec.4.2.1, p.124: In paragraph 3, inaccuracy should be defined as sqrt{ E(|Y_x-x|^2) } rather than sqrt{ E(|Y-y|^2) }, and this is minimized when x=E(Y_x), the calibrated case. Download corrected page 124 here (36 842 bytes).
• [2004-04-13] Appendix A, Sec.5, p.260: In solution 19, the ones in arrays u0,u1,u2 should be at indices 32,36, and 41. Download corrected page 260 here (31 031 bytes).
• [2004-04-12] Ch.5, Sec.5.2, p.153: Equations 5.47 are constraints on real-valued filters only. Download corrected page 153 here (37 206 bytes).
• [2004-04-11] Chapter 5, pages 150-176 and Appendix A, pages 253-257: Complex conjugation is missing in various formulas, in exercises 12, 14, and 16, and in the solutions to those exercises. Download corrected pages 150-152, 154-155, 157-161, 165-166, 170-171, 175-176, 253-254, 256-257 here (294 875 bytes).
• [2004-04-09] Appendix A, Sec.A.5, p.253: The normalization constant for Solution 9 should be log 2. Also, the notation of solutions 8, 9, 10, and 11 differs from that of the text. Download corrected page 253 here (34 853 bytes).
• [2004-03-12] Ch.3, Sec.3.1.2, p.74: The formula for the Fourier series of ((1-cos 2pi t)/2)^n is wrong. Download corrected page 74 here (49 120 bytes).
• [2004-03-09] Ch.3, Sec.3.1.2, p.73: Remove the "B"s from the calculation of u' just after Eq.3.5. Download corrected page 73 here (46 863 bytes).
• [2004-01-20] Ch.1, Sec.1.1, p.4: The third useful fact about gcd is missing the important condition that a and b must both be nonzero. Download corrected page 4 here (51 054 bytes).
• [2003-10-15] Appendix A, Sec.A.3, p.236: Solution 3 should have v_I, u_I and (L_I F_0 F_1 u)_I instead of v^I, u^I and (L_I F_0 F_1 u)^I. Download corrected page 236 here (44 192 bytes).
• [2003-10-14] Ch.3, Sec.3.1, p.82: Equation 3.23 should have u(a+b-t) instead of u(2a-t) and u(2b-t). Download corrected page 82 here (45 737 bytes).
• [2003-07-31] Ch.2, Sec.2.3, p.65: Exercise 4, statement (ii) should have ||ax+by|| on the left-hand side of the inequality. Download corrected page 65 here (53 761 bytes).
• [2003-07-22] Ch.1, Sec.1.3, p.21: Exercises 3 through 12 should be numbered 6 through 15 to correspond to the solutions in Appendix A, Section A.1, pages 225-228. Download corrected pages 21 and 22 with new exercises 3, 4, and 5 here (71 421 bytes). Solutions to the three new exercises are on pages 223-225 already.