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 Asymptotic Analysis (Applied Mathematical Sciences).

4 comments about Harmonic Analysis and Applications (Studies in Advanced Mathematics).

1. After struggling with this book for a semester, it became apparent to me that while the book is rich in scope, its allusions to so many branches of mathematics and incomplete detailing of these allusions merely serve to bewilder the undergraduate and rookie grad. student of mathematics. Indeed, the book is an excellent reference for those who are already EXTREMELY well-versed in the subject and/or are looking to branch out into more detail and abstraction. For the rest of us, however, this book is ENTIRELY unsuitable--even, I daresay, for the "advanced undergraduate" this book purports to aim itself at. So ignore the hype of professional book reviewers and take it from someone in the trenches: buy something intelligible from the myriad of books out there on Fourier Theory and Harmonic Analysis.



2. I am not really sure if this book is good or not; for an electrical engineering student this book might as well be written in another language. Being a senior I had already covered about 50% of the material in this book in previous classes; I found it amazing that despite this, I could not confirm my knowledge by reading the same material out of the Benedetto book. The probalem is that the text is written EXTREMELY cryptically. I am not sure if this is standard notation for math students; but the notation used is incredible unfamilar and irratating for any of the engineering fields. In addition the book appears to lack any type of contunity. Although the chapters are laid out nicely, the inter-chapter organization seems to be comprised of a series of random theorms thrown together. Conclusion: In reading this book I had to "stop and translate" every few lines, the notation is not standard for engineering, and this book feels more like a series of scholarly papers tied together, than like a real book.



3. I used this book in my teaching of a beginning grad level math (harmonic) analysis course, but relying on three books in all. Harmonic analysis is a big subject with many points of view (infinite in all directions, if you will!). One of the directions is the link to engineering problems. Specific areas of math often serve as service courses for engineers; and harmonic analysis is one area with a rich set of links to engineering problems. Things are complicated however by the the difference in terminology which is used in the two worlds. You might almost say that they speak different languages;-and they have different aims, by necessity! --Benedetto's book makes a heroic, and, in my view, very sucessful effort in highlighting the engineering significance of the basic principles of harmonic analysis. Few harmonic analysis books even try. Benedetto's book may be a bit hard for beginning students(there is a lot in it!), but the investment my students put into it was well worth the effort.



4. No examples, just a book of proof's. This is a horrible book and the professor that is teaching this class for the first time said the same thing. Notation is not standerd which is a big problem in understanding what the author is tring to do.

No comments about Spectral Decomposition and Eisenstein Series: A Paraphrase of the Scriptures (Cambridge Tracts in Mathematics).

2 comments about A Panorama of Harmonic Analysis (Carus Mathematical Monographs).

1. This book is not a textbook on harmonic analysis; it is an essay on how this important discipline has evolved and what are its main results and applications.

   I find this book to be an excellent companion text because it includes a lot of subtle explanations that the usual textbooks lack. It is suitable also for non-mathematicians willing to get a fast introductory survey of the theory.

   Its contents are: Overview of Measure Theory and Functional Analysis; Fourier Series Basics; The Fourier Transform; Multiple Fourier Series; Spherical Harmonics; Fractional Integrals, Singular Integrals, and Hardy Spaces; Modern Theories of Integral Operators; Wavelets; A Retrospective; 9 appendices.

   Full of interesting comments and historical anecdotes. Extensive Bibliography.

   Please take a look at the rest of my reviews.




2. Outside of regurgitating timeworn examples
   the author does not appear to have any direction
   for the text. Save your money.

No comments about Euler Products and Eisenstein Series (Cbms Regional Conference Series in Mathematics).

2 comments about A Brief History of Infinity.

1. This book tells the history of infinity and the ways it was dealt with by thinkers of different times and cultures.
   The subjects touched upon by this (relatively short) book extends overs an astonishingly wide range: philosophy, medieval theology, mathematics, logic, litterature
   But although it is well written and in an engaging style, it is certainly no light reading
   My main critic is that it is too elliptic: many items are introduced matter-of-factly without an attempt to an expository introduction. To a person not acquainted with the domain these remain just words without meaning.
   For instance, what is the "axiom of choice" or Cantor's "transfinite" or a "monadology"? These words just appear "out of the blue". This book expects its reader to be familiar with philosophy (from Aristotle to Leibniz), medieaval theology ( A third of the book), modern mathematics and logic and what else; do you know anybody who is, except the author?
   To sum it up, I didn't understand 60% of this book although I must say it awoke my curiosity about all those subjects (esp a writer named Musil who is often mentionned)



2. A Brief History of Infinity is a serious, in depth study of man's evolving concept of infinity. Paolo Zellini's thoughtfully examines and distills the ideas of philosophers, theologians, writers, and mathematicians.
   
   Zellini's terse style requires close attention and I found it necessary to reread many sections. Zellini begins with Aristotle's negative notion of infinity (apeiron) as an incomplete and unrealized potentiality, and demonstrates that Aristotle view largely explains the inability (or refusal) of Greek mathematicians to introduce a concept of an actual, or real infinity.
   
   The inexhaustibility of the unlimited and the impossibility of finding an absolute minimum or maximum became focal points of discussion in Oxford and Paris in the fourteenth century. Discourse on these topics remained important in the Renaissance, continued with Leibniz and Newton, and culminated in the nineteenth century with Cauchy's and Weierstrass' definitive formulation of infinitesimal calculus.
   
   Having less familiarity with philosophy, I found it profitable to skip for a short period to later chapters that more directly addressed mathematical infinity, a topic of especial interest to me. These chapter included The Principle of Indiscernibles - Classes; The Actual Infinite - Indefinite and Transfinite; and The Antinomies, or Paradoxes of Set Theory.
   
   Paolo Zellini's sources are wide ranging, almost intimidatingly so. We readers encounter the philosophical thoughts of the Platonists, Aristotle, the Pythagoreans, Anaximander, the Chaldeans, Duns Scotus, St. Thomas Aquinas, Giordano Bruno, Nicholas of Cusa, Raymond Lull, Descartes, Leibniz, Goethe, Kant, Hegel, Russell, Simone Weil, Quine, Popper, Wittgenstein, and many others. Similarly, on the literary front we meet Cervantes, Kafka, Borges, Musil, and others.
   
   Mathematicians are prominent also. Zellini discusses the provocative ideas of Descartes, Newton, Leibniz, Dedekind, Poincare, Cauchy, Weierstrass, Bolzano, Frege, Du Bois-Raymond, Cantor, Russell, Whitehead, Godel, Von Neumann, Zermelo, Skolem, Brouwer, and many others.
   
   In the end Paolo Zellini's analysis leans away from Cantor's actual mathematical infinity and toward a potential infinity, somewhat in accordance with Brouwer's finite constructive methods (intuitionism).
   
   Key Idea: I was intrigued with Hermann Weyl's conciliatory observation: the infinite is intuitively accessible as an indefinitely open field of possibility, and in this respect would seem analogous to a series of numbers that can be extended unlimitedly. Yet completeness, the so-called actual infinite, lies beyond our reach. Nonetheless, the demands for a totality impel the mind to imagine the infinite, using some symbolic construction, as a closed entity. Hence, the primary philosophical interest of mathematics should consist in attaining a fundamental understanding of these symbolic constructions.

4 comments about Understanding FFT Applications, Second Edition.

1. I am working in surface phenomena and I needed to interpret data of ocillating drops. This book has allowed me to understand not only the fundamentals but also the appications of FFT. Highly recommended.



2. Hi
   I've bought this book for having a deeper inside into algorithms and techniques for doing fft with micro's and little circuits for RF and audio purposes. I think, it's a very good source for working with - it's straightforward for those, who will do their own processes with every type of micro or pc. I rate this book with all stars.



3. I bought this book and its companion "Understanding the FFT" to add to my basic knowledge of Fourier transforms. I need to know how to implement FTs and so far these books have been a better reference for this than any of the others I've read. Aquiring this practical understanding has been made much easier. Thanks, Andy!



4. I own both the Understanding the FFT volume and its companion, Understanding FFT Applications. They have their place on my technical bookshelf. If you are new to the FFT, or just so-so with undergrad level engineering math, then this series of volumes on the FFT is likely to prove a gold mine. If you eventually tire of being taught by example at a sometimes slow and tedious pace after you are exposed to the basics, look elsewhere.
   
   The complete titles of the books say it all. They are tutorials for laymen, students, technicians and working engineers. They are NOT sophisticated. If you are seeking enough understanding to grasp some fundamentals by example they can be highly recommended as a place to start.
   
   Unfortunately, despite its strengths, the series feeds into the "this is all you have to know if you are a practical person" mentality frequently expressed by many I've met in the technical areas. The ideas of "practical and useful" should always be qualified by the terms "for what and to whom". It all depends on who you are and what you are trying to do.
   
   It is true that sometimes it is better to cut to the heart of the matter with simplistic approaches, but challenging problems are not all reducible to these kinds of "seat of the pants" approaches. The trick is knowing when to "hold or fold". Sometimes it is actually more "practical" to acquire a more sohpisticated approach to a subject, as it saves huge amounts of time and effort later on, and can provide insights that are not initially obvious.
   
   Fourier transforms are a sophisticated mathematical tool with broad applications frequently found in areas where analysis of complex data sets is important. They are not just "tools for the working engineer". If you are serious about mastering them, you must spend the time and effort.
   
   This series is a good place to start, it is hardly the final definitive text, even for the working technical person who wants a powerful understanding of the subject. If you want some good powerful intros to the subject at a more advance level, just look at the Bibliography of Understanding the FFT.

No comments about Discrete Wavelet Transformations: An Elementary Approach with Applications.

3 comments about First Course in Wavelets with Fourier Analysis.

1. At the time of writing of this review (October 2001), a standard academic search procedure
   produces about twenty references per week of scientific papers using wavelet analysis in a very wide spectrum of sciences. More than 160 english language books have been published on wavelets since the first books appeared around 1990. Yet even now it is rare to find a book on this subject which is aiming at undergraduate students and yet is mathematically responsible, without being heavy going. Boggess and Narcovich have tried to do just that, and to my mind have admirably succeeded.
   Assuming a standard background knowledge in calculus and linear algebra that many science and engineering students acquire in their first two years at university, they present the basics of Fourier analysis and wavelets in eight brief chapters. To prepare the way, they start in chapter 0 with an introduction to inner product spaces, without using advanced analysis, and building on the experience with ordinary vector spaces.
   Also a sniff of linear operator theory is offered.
   Chapter 1 introduces Fourier series in real and complex form. These originated in the eighteenth century study of vibrations and in the theory of heat, made famous by Fourier's classic book of 1808: Analytical Theory of Heat. The mathematical claims Fourier made, but which he could not all prove himself, gave the impetus to an enormous development of both mathematical theory and applications in all fields of natural science, which is still going on today. The applications briefly mentioned here are denoising and compression of signals, and finding the solution of partial differential equations. Various aspects of the convergence of Fourier series are dealt with. All concepts are illustrated with a good set of clear figures, and the chapter finishes with exercises that are going from very elementary to a little more ambitious, sometimes involving the use of simple computer algebra tasks. This format is maintained thorugh the entire text, except for the last chapter.
   Chapter 2 proceeds with the Fourier Transform, including the important theory of linear time invariant filters. The existence of the impulse response function and its convolution character are shown. As an example the noise reducing Butterworth filter is presented. Sampling and the Nyquist frequency are touched upon, and a derivation of the uncertainty relations, originally coming from quantum mechanics, is given.
   To analyse discrete data, one needs the discrete Fourier Transform, which is the subject of chapter 3, including of course the Fast Fourier Transform. Also the z-transform is introduced. Examples given are elementary cases of parameter identification in vibration, numerical solution of ordinary differential equations, as well as in the exercises: noise reduction and data compression.

   These first 153 pages serve as a good undergraduate introduction to Fourier analysis.
   The second half of the book is devoted to wavelets. Chapter 4 deals exclusively with Haar wavelets which are the oldest wavelets because they date from 1910! These wavelets constitute an orthonormal basis of functions, which makes for fast calucation, a very important aspect for many applications. The core ideas of the central concept of a "multiresolution analysis" of a signal, can be demonstrated with these simple wavelets. All of this is already understandable without the machinery of the preceding Fourier analysis, so you could jump into the book here and start reading about wavelets right away, picking up the Fourier analysis from the first part bit by bit as the need arises. As applications denoising and compression are mentioned again, as is the detection of a discontinuity in a signal.
   The general case of a multiresolution analysis is the subject of chapter 5. Again a large part of the discussion can be swallowed without the need of the Fourier transform point of view. The explanation of the structure of a multiresolution analysis leading to an orhtonormal basis of wavelets is straightforward and clear. It is only when we want to go into more detail about the precise characteristics of the underlying wavelet and scaling function that the Fourier point of view is introduced. This then leads up to the presentation of the famous Daubechies wavelets in chapter 6. These wavelets revolutionised the field after their publication in 1988.
   Chapter 7 which closes the book, gives several short remarks about various other topics among which are two-dimensional wavelets, and the continuous wavelet transform.
   This chapter is more sketchy than the others, and left me much less satisfied. Also the motivation why these subjects are chosen was lacking almost completely, and there are no exercises. I was particularly disappointed not to find any discussion of the relative merits of the continuous versus the discrete wavelet transform, and there is no mention of any application of the continuous case. Yet the latter is also used frequently in many important scientific applications, and it started the modern wavelet endeavour in the early eighties in France.
   That being said I still think this is a very useful book for anybody wanting to start with wavelets at an undergraduate level. A few helpful Matlab Codes are collected in an appendix as well as the more difficult parts of some proofs. The exercises make this good course material, but as a text for self study it will also be quite satisfactory for many newcomers that find most of the existing books too demanding.




2. ...this book is one of most informative and legible books on wavelt theories and applications.

   The author paves the theoretical development about wavelets and multi-resolution analysis EXCELLENTLY. With this book, you can construct wavelets for your own applications in engineering and science disciplines.

   This book is very good for first year engineering-majored graduate students and all engineering scholars.




3. If you want to learn Wavelet theory in a easy way like reading a story book then this is the book. It deals with the most complicated thing in the easiest way.