No comments about Wavelets and Their Applications (Digital Signal and Image Processing series).

No comments about Acoustics and the Performance of Music: Manual for Acousticians, Audio Engineers, Musicians, Architects and Musical Instrument Makers (Modern Acoustics and Signal Processing).

No comments about Fourier Analysis.

No comments about AN ELEMENTARY TREATISE ON FOURIER'S SERIES AND SPHERICAL, CYLINDRIC, AND ELLIPSOIDAL HARMONICS: With Applications to Problems in Mathematical Physics.

No comments about Wavelets and Operators: Vol. 37 (Cambridge Studies in Advanced Mathematics).

1 comments about Time Warps, String Edits, and Macromolecules: The Theory and Practice of Sequence Comparison.

1. This book, originally published in 1983, was reissued in 1999, no doubt because of the importance of genetic sequencing in recent years. What is neat about the book is it shows how algorithms from one field can be applied to solve problems in another, possibly totally disparate field, one example being computational linguistics and sequence algorithms in computational biology.

   A general overview of sequence comparison is given in chapter 1 with applications to molecular biology, human speech, computer science, coding theory, gas chromotography, and bird songs discussed. The author discusses how deletion-insertion, compression-expansion, and substitution are employed in sequence comparison. Different metrics are introduced, such as the Levenshtein distance. Dynamic programming, which pretty much dominates the book, is introduced here also.

   Part 1 of the book discusses sequence comparison in molecular biology. The use of dynamic programming is emphasized and its importance continues to this day. The advantages of using the dynamic programming method are outlined, and it is shown how to find the substring in a longer sequence with most optimum agreement to a shorter sequence. In addition, given an RNA molecule with a known nucleotide sequence, methods are discussed for predicting the way different parts of the molecule will bond to each other. These methods are based on dynamic programming. Mathematicians considering doing research on or about entering the field will profit from the section on the biological background. The treatment of RNA secondary structures is excellent.

   In part 2, the emphasis is on speech processing and what is called "time-warping", which is a technique for comparing functions by altering the time axis. An interesting application is given to the comparison of bird songs. An algorithm is given for adjusting the time scales for two songs to arrange them in the most optimal alignment. In addition, the differences between compression and expansion and deletion and insertion are discussed in this part.

   In part 3, a modified Smith-Waterman algorithm is employed to find similar portions in two sequences. Called local alignment in computational biology, it is shown in detail how to define the recurrences for the alignment and how to keep track of the pointers for backtracking. This part also generalizes the operations of substitution and Levenshtein distance. In addition, the strategy of doing sequence comparison by allowing transpositions is discussed. Such a strategy entails a generalized concept of trace, wherein trace lines can intersect each other, leading to entangling of the traces into knots or plaids. The usual dynamic programming techniques must then be extended to deal with these complications. One particular algorithm for this is discussed, called CELLAR, which involves the construction of a directed graph whose paths correspond to admissible sequences of generalizations of traces, called cuts. The computational complexity of this algorithm is discussed. In addition, an O(n^2/logn) algorithm is given for computing string-edit distances.

   The last part of the book deals with studying comparisons between random sequences. Combinatorial arguments are used to derive upper bounds on the expected length of the longest common subsequences of two random sequences. Other miscellaneous results dealing with comparing common subsequences of two random sequences are given.

No comments about A Handbook of Integer Sequences.

2 comments about Wavelets: Algorithms & Applications.

1. Although this book emphasis is on algorithms and applications, the general presentation of wavelets for signal processing is great. The introduction to the subject is really excellent and great care has been given to explaining the use of wavelets for applications in signal processing. On the other side i found the last chapters dealing with applications a little too light for being useful...

   Anyway, a great book for "wavelets and applications in signal processing"...(also go to "Time-Frequency Time-scale analysis" by Patrick Flandrin which is wonderful).




2. Of the many recent books on wavelets, this one by Jaffard, Meyer et al stands out. This is a new edition of earlier ones, starting with a French one, then a first translation, and now this expanded version. There is lots of new material, covering new developments, both with regards to theory and applications. The authors communicate the main points in a clear and attractive way, and it stresses lucid presentation of ideas over formulas. And with an infectious enthusiasm! The presentation is especially refreshing, in that the authors do not hide behind excessive technicalities and mathematical jargon. It is the central idea that shines through. And yet the mathematically sophisticated reader is paid his dues,-- in some cases via the appendices. At that point, the technical mathematical points have been well motivated. The emphasis of the book is the mathematics behind the many algorithms that emerged from the wavelet trends since the 1980ties. And lots of new stuff added (for example JPEG-2000), right up to the present. The book is rich in applications, many of which are not found elsewhere. The inclusion of motivation and historical remarks is welcome, and makes the book enjoyable reading.

3 comments about Elements of Wavelets for Engineers and Scientists.

1. This is an excellent short introductory book for anyone who wants to understand and use wavelets via the filtering route. The presentation is entirely self-contained, and includes completely worked out wavelet examples and answers to all exercises. The authors develop wavelets as multirate quadrature mirror filters (explained within the text). Sample matlab source code is provided. Like Mix's text on Random Signal Processing, this one shines as being practical, easy-to-understand, filled with examples and prepares the reader for more advanced work.



2. Wavelets is a mathematically intensive subject. As such many books on the subject present the topic as an endless list of equations with very little insight.
   
   This book on the other hand presents the material in a fashion that is digestable to the average engineer. This is a credit to their writting and teaching skill. They write as if their first goal is to let you understand (teach) not simply write.
   
   I would say that the first books to read on this subject would be this one and the book by Walker. These books are sufficient to get a good understanding of Wavelets and to be able to use them. They also pave the way for more advanced books on the subject if desired.



3. This is one of the best books on wavelets for engineers. As the authors mention most of the wavelet books currently on the market are targeted to mathematicians not engineers. Trust me my dissertation involves wavelets. If you are new to this topic my recommendation is to make sure you understand linear algebra and and some digital signal processing first. The books by Richard Lyons and R. W. Hamming are great. I also really like DSP by Michael Weeks. The classic would be Oppenheim & Schafer.
   
   Probably the first to read is "A primer on wavelets by Walker" This book would be the second as it gets deeper into the definition and mathematical formalism than Walker yet is understandable to engineers. After that I would probably recommend Ripples in Mathematics on lifting and A wavelet tour by Mallat.

No comments about Fourier Integrals in Classical Analysis (Cambridge Tracts in Mathematics).