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21. Fourier Series and Harmonic Analysis
22. Fourier Integrals in Classical
23. Analysis II: Differential and
24. Fourier Analysis in Several Complex
25. Fourier Analysis of Time Series:
26. A First Course in Harmonic Analysis
27. Introduction to Fourier Analysis
28. Discrete and Continuous Fourier
29. Fast Fourier Transform and Its
30. Fourier Transform Infrared Spectrometry
31. The Fourier Transform & Its
32. A Handbook of Real Variables:
33. Fast Fourier Transforms: Second
34. The Fourier Integral and Its Applications
35. Chebyshev and Fourier Spectral
36. Handbook of Fourier Analysis &
37. Fourier Techniques and Applications
38. The Evolution of Applied Harmonic
39. Introduction to Fourier Optics
40. Harmonic Analysis

21. Fourier Series and Harmonic Analysis
by K. A. Stroud
 Hardcover: 212 Pages (1986-12)
list price: US$69.00
Isbn: 085950137X
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22. Fourier Integrals in Classical Analysis (Cambridge Tracts in Mathematics)
by Christopher D. Sogge
Paperback: 252 Pages (2008-04-24)
list price: US$50.00 -- used & new: US$42.69
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Asin: 0521060974
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Fourier Integrals in Classical Analysis is an advanced treatment of central problems in harmonic analysis. The main theme of the book is the interplay between ideas used to study the propagation of singularities for the wave equation and their counterparts in classical analysis. Using microlocal analysis, the author in particular studies problems involving maximal functions and Riesz means using the so-called half-wave operator. This self-contained book starts with a rapid review of important topics in Fourier analysis. The author then presents the necessary tools from microlocal analysis, and goes on to give a proof of the sharp Weyl formula which he then modifies to give sharp estimates for the size of eigenfunctions on compact manifolds. Finally, the tools that have been developed are used to study the regularity properties of Fourier integral operators, culminating in the proof of local smoothing estimates and their applications to singular maximal theorems in two and more dimensions. ... Read more

23. Analysis II: Differential and Integral Calculus, Fourier Series, Holomorphic Functions (Universitext) (Pt. 2)
by Roger Godement
Paperback: 448 Pages (2005-12-01)
list price: US$69.95 -- used & new: US$11.89
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Asin: 3540209212
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Functions in R and C, including the theory of Fourier series, Fourier integrals and part of that of holomorphic functions, form the focal topic of these two volumes. Based on a course given by the author to large audiences at Paris VII University for many years, the exposition proceeds somewhat nonlinearly, blending rigorous mathematics skilfully with didactical and historical considerations. It sets out to illustrate the variety of possible approaches to the main results, in order to initiate the reader to methods, the underlying reasoning, and fundamental ideas. It is suitable for both teaching and self-study. In his familiar, personal style, the author emphasizes ideas over calculations and, avoiding the condensed style frequently found in textbooks, explains these ideas without parsimony of words. The French edition in four volumes, published from 1998, has met with resounding success: the first two volumes are now available in English.

... Read more

24. Fourier Analysis in Several Complex Variables (Dover Books on Mathematics)
by Leon Ehrenpreis
Paperback: 528 Pages (2006-05-12)
list price: US$27.95 -- used & new: US$25.16
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Asin: 0486449750
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This text develops comparison theorems to establish the fundamentals of Fourier analysis and to illustrate their applications to partial differential equations. It begins by establishing the quotient structure theorem or fundamental principle of Fourier analysis, and then focuses on applications to partial differential equations. The final section explores functions and their role in Fourier representation. Problems. 1970 edition.
... Read more

25. Fourier Analysis of Time Series: An Introduction (Wiley Series in Probability and Statistics)
by Peter Bloomfield
Hardcover: 288 Pages (2000-02-04)
list price: US$148.00 -- used & new: US$72.00
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Asin: 0471889482
Average Customer Review: 5.0 out of 5 stars
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A new, revised edition of a yet unrivaled work on frequency domain analysis

Long recognized for his unique focus on frequency domain methods for the analysis of time series data as well as for his applied, easy-to-understand approach, Peter Bloomfield brings his well-known 1976 work thoroughly up to date. With a minimum of mathematics and an engaging, highly rewarding style, Bloomfield provides in-depth discussions of harmonic regression, harmonic analysis, complex demodulation, and spectrum analysis. All methods are clearly illustrated using examples of specific data sets, while ample exercises acquaint readers with Fourier analysis and its applications. The Second Edition:
* Devotes an entire chapter to complex demodulation
* Treats harmonic regression in two separate chapters
* Features a more succinct discussion of the fast Fourier transform
* Uses S-PLUS commands (replacing FORTRAN) to accommodate programming needs and graphic flexibility
* Includes Web addresses for all time series data used in the examples

An invaluable reference for statisticians seeking to expand their understanding of frequency domain methods, Fourier Analysis of Time Series, Second Edition also provides easy access to sophisticated statistical tools for scientists and professionals in such areas as atmospheric science, oceanography, climatology, and biology. ... Read more

Customer Reviews (1)

5-0 out of 5 stars excellent treatment of frequency domain time series methods
As a time series analyst who studied time series in graduate school when the first edition of Bloomfield's book came out, I really appreciated it. The frequency approach to time series is not natural because we tend to look at the series to see how it changes (fluctuates) over time. This makes the time domain approach very natural. It is only when one sees periodicity in the series and can relate the series to a summation of sine and cosine waves that the frequency domain ideas get appreciated.
Bloomfield introduces Fourier series in a gentle way, making it clear. Concepts are introduced as needed to deal with specific aspects of real time series data.

I particularly liked his treatment of complex demodulation, which could be a very difficult concept to grasp if not presented carefully. But Bloomfield explains it well and provides another way to look at the famous Wolfer sunspot data using an approach based on complex demodulation (assuming a slowly changing period for the series).

The second edition is now outwith additional topics and corrections.I have only read the first edition.So my comments only pertain to that edition.This is the best introductory text to frequency domain time series analysis that I have ever read.

... Read more

26. A First Course in Harmonic Analysis (Universitext)
by Anton Deitmar
Paperback: 204 Pages (2005-03-09)
list price: US$64.95 -- used & new: US$41.99
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Asin: 0387228373
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From the reviews of the first edition:

"This lovely book is intended as a primer in harmonic analysis at the undergraduate level. All the central concepts of harmonic analysis are introduced using Riemann integral and metric spaces only. The exercises at the end of each chapter are interesting and challenging..."

Sanjiv Kumar Gupta for MathSciNet

"... In this well-written textbook the central concepts of Harmonic Analysis are explained in an enjoyable way, while using very little technical background. Quite surprisingly this approach works. It is not an exaggeration that each undergraduate student interested in and each professor teaching Harmonic Analysis will benefit from the streamlined and direct approach of this book."

Ferenc Móricz for Acta Scientiarum Mathematicarum

This book is a primer in harmonic analysis using an elementary approach. Its first aim is to provide an introduction to Fourier analysis, leading up to the Poisson Summation Formula. Secondly, it makes the reader aware of the fact that both, the Fourier series and the Fourier transform, are special cases of a more general theory arising in the context of locally compact abelian groups. The third goal of this book is to introduce the reader to the techniques used in harmonic analysis of noncommutative groups. There are two new chapters in this new edition. One on distributions will complete the set of real variable methods introduced in the first part. The other on the Heisenberg Group provides an example of a group that is neither compact nor abelian, yet is simple enough to easily deduce the Plancherel Theorem.

Professor Deitmar is Professor of Mathematics at the University of T"ubingen, Germany. He is a former Heisenberg fellow and has taught in the U.K. for some years. In his leisure time he enjoys hiking in the mountains and practicing Aikido.

... Read more

27. Introduction to Fourier Analysis
by Norman Morrison
Paperback: 240 Pages (1995-10-19)
list price: US$55.95 -- used & new: US$50.35
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Asin: 0471128481
Average Customer Review: 4.0 out of 5 stars
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Contains 36 lectures solely on Fourier analysis and the FFT. Time and frequency domains, representation of waveforms in terms of complex exponentials and sinusoids, convolution, impulse response and the frequency transfer function, modulation and demodulation are among the topics covered. The text is linked to a complete FFT system on the accompanying disk where almost all of the exercises can be either carried out or verified. End-of-chapter exercises have been carefully constructed to serve as a development and consolidation of concepts discussed in the text. ... Read more

Customer Reviews (1)

4-0 out of 5 stars Good choice for the novice interested in Fourier Analysis

Throughout my graduate career, I searched desperately for a book that covered Fourier Analysis in a manner that would be lucid to a novice.Of all the books that I've seen dealing with the subject, I rank Morrison's as the best in this category.

Most books dealing with Fourier Analysis appear tobe written for someone with a degree in mathematics.Although I would say that this book is an excellent introduction to Fourier analysis and the Fourier transform, the reader must possess a strong working knowledge of calculus at the least.

The book is presented in the classic textbook format, where each section is introduced and explained with examples, then a series of problems are presented to reinforce the concepts presented.

The first half of the book covers continuous Fourier analysis, and the second half of the book covers discreet Fourier analysis.Some may argue that these two concepts could have been introduced simultaneously, however I found this dichomtomy to be an effective way of presenting the material.The book is geared towards undergraduate students of electrical engineering, but I think that it is appropriate for anyone wishing to learnFourier analysis.The book is replete with exercises to be completed with the accompanying diskettes (both Mac and PC are included), but I never used them.

This book is the best I've seen dealing with the subject, but I did have to proceed very slowly.I did not understand all of the concepts presented, perhaps because of my limited mathematics background (as high as calculus).For this reason, I rate the book a seven. ... Read more

28. Discrete and Continuous Fourier Transforms: Analysis, Applications and Fast Algorithms
by Eleanor Chu
Hardcover: 424 Pages (2008-03-19)
list price: US$94.95 -- used & new: US$81.42
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Asin: 1420063634
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Long employed in electrical engineering, the discrete Fourier transform (DFT) is now applied in a range of fields through the use of digital computers and fast Fourier transform (FFT) algorithms. But to correctly interpret DFT results, it is essential to understand the core and tools of Fourier analysis. Discrete and Continuous Fourier Transforms: Analysis, Applications and Fast Algorithms presents the fundamentals of Fourier analysis and their deployment in signal processing using DFT and FFT algorithms.

This accessible, self-contained book provides meaningful interpretations of essential formulas in the context of applications, building a solid foundation for the application of Fourier analysis in the many diverging and continuously evolving areas in digital signal processing enterprises. It comprehensively covers the DFT of windowed sequences, various discrete convolution algorithms and their applications in digital filtering and filters, and many FFT algorithms unified under the frameworks of mixed-radix FFTs and prime factor FFTs. A large number of graphical illustrations and worked examples help explain the concepts and relationships from the very beginning of the text.

Requiring no prior knowledge of Fourier analysis or signal processing, this book supplies the basis for using FFT algorithms to compute the DFT in a variety of application areas. ... Read more

29. Fast Fourier Transform and Its Applications
by E. Brigham
Paperback: 416 Pages (1988-04-08)
list price: US$133.00 -- used & new: US$109.99
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Asin: 0133075052
Average Customer Review: 5.0 out of 5 stars
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The Fast Fourier Transform (FFT) is a mathematical method widely used in signal processing. This book focuses on the application of the FFT in a variety of areas: Biomedical engineering, mechanical analysis, analysis of stock market data, geophysical analysis, and the conventional radar communications field. ... Read more

Customer Reviews (15)

5-0 out of 5 stars Old is gold
I got this book as a gift by helping one of the faculty members load some books in his truck and I am cherishing that moment every bit. All I have to say is ...what a great book, enjoyed reading every page of it. But this book is not for the beginners in DSP. If you want to learn about DSP please refer to " Discrete time signal processing" by Alan V. Oppenheim, Ronald W. Schafer, and John R. Buck.
The beginning of the book as I consider is a review till chapter 7 and then onward you start with FFT.
Highly recommended book... a must have.

5-0 out of 5 stars The best
This book provides excellent intuition into the fourier transform, discrete fourier transform, and fast fourier transform.There are no others that provide the depth of intuition.

If a reader should find it difficult, then he/she should be satisfied that the struggle is worth it and will lead to an exceptional understanding of the subject matter.All complaints are unjustified (though it might be nice if Brigham treated the Z transform as well).

5-0 out of 5 stars The Best DFT / FFT Book on the Market
I purchased the first edition of this book way back on January 10, 1975, when I was young design engineer, just breaking into the Digital Signal Processing business.I bought the book at the Stanford University Book store for a whopping $19.95. The receipt is still in the book.

The book was considered to be a DSP industry bible back then, and in my opinion, it is still the best DFT/FFT book on the market today.

Mr. Brigham seems to be very detailed oriented.He methodically progresses from one subject to the next and explains each topic in a clear and concise manner. The book is loaded with extremely detailed graphics that give the reader a very good picture of the operation, properties, and mechanics of the Discrete Fourier Transform.His mathematical derivations of various DFT/FFT properties are straight forward and can be read and understood in short order.

I consider Mr. Brigham's book to be an essential engineering resource. I have relied upon, and utilized the information provided in this book for over 30 years of successful DSP design.

If I ever misplace my time worn book, would I purchase it again?The answer is a definite yes.The money is well spent.

5-0 out of 5 stars An accessible examination of the FFT great for self study
This book is not just another terse math or signal processing book. It tries to provide an alternative to standard DSP techniques that develop the FFT adequately enough, but show nothing about applications and have the student believing that "The Butterfly Element" is something he can buy an armful of at an electronics store and assemble. All developments in this book use graphical techniques and examples that insure clarity in the presentation. The book provides not only a readable introduction to the FFT but a thorough and unified reference for applying it to various fields of interest. It is great for self-study. The text is divided into five major subject areas:

1. The Fourier Transform and its properties
2. The Discrete Fourier Transform - It is developed from the continuous Fourier Transform both graphically and theoretically. Its properties are examined as are numerous waveform classes via illustrative examples. Discrete convolution and correlation are defined and compared with the continuous equivalents via examples.
3. The FFT - The FFT algorithm is developed along with an explanation of why the FFT is efficient. Computer programs are developed that can calculate the FFT.
4. Basic Applications of the FFT - Presents the application of the FFT to the computation of discrete and inverse discrete Fourier transforms. There is an emphasis on graphical examination of resolution and common FFT user mistakes such as aliasing, time domain truncation, noncausal time functions, and periodic functions. The applications examined include Laplace transform computation, discrete convolution and correlation, and two-dimensional Fourier transform convolution. Computer programs are provided.
5. Signal Processing and System FFT Applications - The design and application of digital filters using the FFT are explored. A novel application of the FFT to multichannel band-pass filtering is developed in a way that can readily be expanded by the reader.

I highly recommend this book to readers who want a complete explanation and investigation of the FFT and its applications that is clear enough for self-study.

4-0 out of 5 stars Written with the reader in mind.
I think this is one of the most understandable books in signal processing that I've ever come across.I get the feeling that Brigham had been frustrated by technical texts that were poorly written, and decided he wasn't going to commit the same sin.Plenty of carefully planned illustrations designed to help the reader start from a known place, and move step-by-step to an understanding of something new.Not just a bunch of faceless equations.I think this would be an excellent college text.

Like any in-depth text dealing with a mathematically complex topic, there appear to be a number of mistakes left in to keep the reader on his/her toes.But fewer than most.I highly recommend this book, even though I'm usually a pretty tough critic.I too have been frustrated by too many poorly written books. ... Read more

30. Fourier Transform Infrared Spectrometry (Chemical Analysis: A Series of Monographs on Analytical Chemistry and Its Applications)
by Peter Griffiths, James A. De Haseth
Hardcover: 560 Pages (2007-04-25)
list price: US$130.00 -- used & new: US$93.70
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Asin: 0471194042
Average Customer Review: 4.5 out of 5 stars
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A bestselling classic reference, now expanded and updated to cover the latest instrumentation, methods, and applications

The Second Edition of Fourier Transform Infrared Spectrometry brings this core reference up to date on the uses of FT-IR spectrometers today. The book starts with an in-depth description of the theory and current instrumentation of FT-IR spectrometry, with full chapters devoted to signal-to-noise ratio and photometric accuracy. Many diverse types of sampling techniques and data processing routines, most of which can be performed on even the less expensive instruments, are then described. Extensively updated, the Second Edition:

Discusses improvements in optical components

Features a full chapter on FT Raman Spectrometry

Contains new chapters that focus on different ways of measuring spectra by FT-IR spectrometry, including fourteen chapters on such techniques as microspectroscopy, internal and external reflection, and emission and photoacoustic spectrometry

Includes a new chapter introducing the theory of vibrational spectrometry

Organizes material according to sampling techniques

Designed to help practitioners using FT-IR capitalize on the plethora of techniques for modern FT-IR spectrometry and plan their experimental procedures correctly, this is a practical, hands-on reference for chemists and analysts. It's also a great resource for students who need to understand the theory, instrumentation, and applications of FT-IR. ... Read more

Customer Reviews (4)

5-0 out of 5 stars Fourier Transform Infrared Spectrometry
If you want a single book to learn how and why FT-IR spectrometers work, this is your best bet. I upgraded to the second edition because my first edition was falling apart after 20 years. I bought the print edition because I didn't like the way the Kindle edition displayed the diagrams, spectra, and other figures.

The authors are highly-regarded practitioners and professors of applied spectroscopy, and they present a wide and deep enough scope of applicable technique to provide a great deal of useful reference material. It's a most useful book. If you want another single book to learn how to interpret FT-IR spectra buy "Introduction to Infrared and Raman Spectroscopy" by Colthup, Daly, and Wiberley, another one I have used for years.

5-0 out of 5 stars Good Book
I work in semiconductor industry and use FTIR for in line metrology. This book was recommended by the vendor of the FTIR which we have and seems to be a good read. Have a good description of the Hardware required for FTIR and is complemented by spectroscopic studies of different materials.

4-0 out of 5 stars FTIR Bible
This is a great reference for anyone designing or using FTIR instruments.This book is really intended for the advanced users and is worth the price.The only major drawback is that it is getting a little dated.

The book is really geared to the chemist,however, additional material on alignment techniques and a more complete and jointed discussion on design trade-offs and instrument characterization would make it much more useful to other users.

Bottom line:It is still a great reference

4-0 out of 5 stars The Classic Reference on FTIR
This book is the Bible of FTIR, written by the twin gods of FTIR,Griffiths and DeHaseth.It contains as complete an introduction to thetheory and practice of this field as is available.Anyone who wants adetailed understanding of this field, and in particular how FTIRs work,should own this book.However...there are 2 reasons why I gave the book4 stars instead of 5.

1. The book is written at a rather advanced level,and is full of mathematics.For doctorate level scientists and engineersthis is fine, but it blows away anyone without the appropriate math andscience background.As a result, beginners to the field are often timesfrustrated with this book.The book is more approriate for instrumentdesigners and lab managers than it is for the average technician runningspectra.

2. The book was written in 1986, and parts of it are terriblyoutdated.Not surprisingly, discussions of specific computers, software,and instruments were outdated years ago.Things that the book predictswill happen, have long ago come to pass.Certain important newdevelopments, such as IR Microscopy, FT-Raman, and new applications of StepScanning, are totally missing.Come on guys...its time for a new edition. ... Read more

31. The Fourier Transform & Its Applications
by Ronald Bracewell
Hardcover: 640 Pages (1999-06-08)

Isbn: 0073039381
Average Customer Review: 4.0 out of 5 stars
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This text is designed for use in a senior undergraduate or graduate level course in Fourier Transforms.This text differs from many other fourier transform books in its emphasis on applications.Bracewell applies mathematical concepts to the physical world throughout this text, equipping students to think about the world and physics in terms of transforms.

The pedagogy in this classic text is excellent.The author has included such tools as the pictorial dictionary of transforms and bibliographic references.In addition, there are many excellent problems throughout this book, which are more than mathematical exercises, often requiring students to think in terms of specific situations or asking for educated opinions.To aid students further, discussions of many of the problems can be found at the end of the book. ... Read more

Customer Reviews (14)

5-0 out of 5 stars A godsend to electron microscopists!
When I was a just neophyte graduate student, a famous electron microscopist recommended this book to me.Within its pages are so many elements that have proven to be incredibly useful.Certainly, one would expect that a detailed knowledge of Fourier transforms is essential to anyone doing research involving the imaging of a periodic object like the crystals studied by many of us in the electron microscopy community (as you would expect from Bloch's theorem).Bracewell provides easy to follow derivations of the theorems essential to the proper application of Fourier transforms and series to whatever problem may be at hand.It is also helpful that digital Fourier transforms are also explained--and in a way that is sufficiently explicit for performing actual calculations.

I should note that not only are Fourier transforms necessary for understanding dynamical diffraction theory (both Howie-Whelan and Cowley-Moodie), the study of electron energy loss spectroscopy (and the study of plasmon losses in particular) is significantly elucidated by a proper understanding of Fourier transforms.Much of the usefulness of Fourier transforms can be ascribed to the fact that the complicated convolution operation is reduced to simple multiplication by application of the Fourier transform!

The fact that Fourier transforms are useful in data reduction in general and image processing in particular is also considered in this book.The concept of aliasing is explored in sufficient detail--allowing the reader to determine to pixel density necessary in order extract the necessary information from a given image--an especially important consideration now that most transmission electron microscopy images are acquired digitally by CCD cameras.

2-0 out of 5 stars Good intuitive description but loaded with errors.
This book has a nice "intuitive" description of the Fourier integral pair and provides matching graphical representations/examples. With that being said, the book is loaded with typos when it comes to the equations, and the notation is not a standard mathematical or engineering notation; something in between. The author obviously understands the subject better than most, and provides reasoning for most of the notation, but there are so many errors ( in critical places ) that, in many cases, you must completely toss aside the provided explanation, and rework the examples from scratch ( probably not a bad idea with any book ). Long story short, if you're pretty familiar with the standard fourier integral coursework, you may find this book useful. If you're just learning the basics, go somewhere else or you'll regret it.

5-0 out of 5 stars Just a Timeless Classic!
I bought this book 7 years ago when i had to take graduate courses in FT theory in physics. After going through a number of FT books, i still find myself returning to it to refresh, learn, or for reference.
The notation is definetly unique, but well worth the time to get used to it. For example, the sampling or replicating symbol "shah" (it looks like three spikes connected by a horizontal line at the bottom) represents an impulse train of equispaced delta functions. At first it seems that yet another symbol is barely needed (as if we didn't have enough already!), but i think that the ease with which sampling and basic theorems are demonstrated with this symbol justifies its invention.
The book gravitates on discrete signals, but continuous signals are used throughout along with their discrete equivalents.
The book is probably more theoretical than computational; a little bit more on the applied physics side than pure electrical engineering. I understand that this is an EE book, and i don't want to give you the impression that is a pure mathematical treatement of the subject. But i think it belongs to the era of seriously "grounded" EE books, and by "grounded" i mean on theoretical grounds. Even so, the reader will usually find very insightful discussions on "practical considerations." These considerations, however, are not of the "cookbook" approach. They are really embedded in a deeper theoretical framework.
The figures are well chosen and superbly illustrative. Where theory gets heavy, a careful study of the pictures should clarify the concepts. Of particular interest is the last chapter (Ch. 22), a "Pictorial Dictionary of FTs" where you will find figures of some 70 functions and their FTs.
Bracewell starts from the very basics and covers the fundamental theorems, the FT, DFT, DTFT, FFT algorithms, dynamic spectra, z-transform (briefly), Hartley and Laplace transforms, and then moves to applications like Antennas and Optics, Heat, Statistics, Noise, and Acoustics. The exercises are reasonable, but not easy.
There are definetly alternatives to this book for beginners. But i think that Bracewell's perspective is unique and invaluable. Truely a timeless classic.

5-0 out of 5 stars A fine general introduction to the Fourier Transform
Most of the positive reviews speak to the general good qualities of this book.I agree with them but, in addition, would like to point out that this book is way more than just a good intro to the subject for electrical engineers.As the author points out Fourier was not working on problems in electrical engineering, he was concerned with heat.

In the later part ofthe book, after introducing the mathematical properties of the FT and then their application in electrical engineering, the author considers heat and general conduction problems, as well as statistics, waveforms and noise. Bracewell shows clearly how the concepts,so useful for electical engineering are more general than traditonal EE aplications and can be used to acquire information, devise theories and solve problems in a variety of scientific endeavors.

Thus, the book is really comprehensive and will introduce the reader to the basics of FTs and their myriad applications in a variety of areas.This is a real strength of the author's and is a real positive for this book, either as a first text on FT, or as a reference to scientists and engineers working in any of the areas where the FT is routinely used.

4-0 out of 5 stars value more than prices!
I bought this textbook more than 7 years ago. But I just read a little bit!.
But recently I found that maybe this book is important for my research.
I still don't know why we usually use Laplace Transform to analyzed transistor network to plot frequency response. But use inverse Fourier transform to plot spectrum of the signal in frequency domain. Maybe I will find answer in this book. ... Read more

32. A Handbook of Real Variables: With Applications to Differential Equations and Fourier Analysis
by Steven G. Krantz
Hardcover: 201 Pages (2003-11-18)
list price: US$69.95 -- used & new: US$11.05
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Asin: 081764329X
Average Customer Review: 2.0 out of 5 stars
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Product Description
This concise, well-written handbook provides a distillation of the theory of real variables with a particular focus on the subject's significant applications to differential equations and Fourier analysis. Ideal for the working engineer or scientist, the book uses ample examples and brief explanations---without a lot of proofs or axiomatic machinery---to give the reader quick, easy access to all of the key concepts and touchstone results of real analysis. Topics are systematically developed, beginning with sequences and series, and proceeding to topology, limits, continuity, derivatives, and Riemann integration. In the second half of the work, Taylor series, the Weierstrass Approximation Theorem, Fourier series, the Baire Category Theorem, and the Ascoli--Arzela Theorem are carefully discussed. Picard iteration and differential equations are treated in detail in the final chapter.

Key features:

* Completely self-contained, methodical exposition for the mathematically-inclined researcher; also valuable as a study guide for students

* Realistic, meaningful connections to ordinary differential equations, boundary value problems, and Fourier analysis

* Example-driven, incisive explanations of every important idea, with suitable cross-references for ease of use

* Illuminating applications of many theorems, along with specific how-to hints and suggestions

* Extensive bibliography and index

This unique handbook is a compilation of the major results, techniques, and applications of real analysis; it is a practical manual for applied mathematicians, physicists, engineers, economists, and others who use the fruits of real analysis but who do not necessarily have the time to appreciate all of the theory. Appropriate as a comprehensive reference or for a quick review, "A Handbook of Real Variables" will benefit a wide audience. ... Read more

Customer Reviews (1)

2-0 out of 5 stars I Kinda Wish I Had Not Bought This
Don't get me wrong - Krantz is good but this is essentially Baby Rudin - without the proofs - which is sort of like a bar without beer. ... Read more

33. Fast Fourier Transforms: Second Edition (Studies in Advanced Mathematics)
Hardcover: 464 Pages (1996-10-22)
list price: US$94.95 -- used & new: US$94.95
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Asin: 0849371635
Average Customer Review: 4.5 out of 5 stars
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Product Description
This new edition of an indispensable text provides a clear treatment of Fourier Series, Fourier Transforms, and FFTs. The unique software, included with the book and newly updated for this edition, allows the reader to generate, firsthand, images of all aspects of Fourier analysis described in the text. Topics covered include : ... Read more

Customer Reviews (2)

5-0 out of 5 stars Excellent service
Fast delivery, reliable packaging, superb condition of the book and the accompanying diskette.Extremely satisfied with my purchase.

4-0 out of 5 stars Can be understood by an undergraduate physics major.
This is a book written for mathematicians, yet it is accessible to an upper level physics undergraduate. Much of the book explains concepts very well, at other times I was very frustrated. The DOS based software includedwith the book did not seem to work as billed on my systems. A high point ofthe book is Walkers 2 dimensional Fourier optics section. This section doesan excellent job on a complex topic. ... Read more

34. The Fourier Integral and Its Applications (Classic Textbook Reissue Series)
by A. Papoulis
 Hardcover: 320 Pages (1962-06-01)
list price: US$164.20
Isbn: 0070484473
Average Customer Review: 5.0 out of 5 stars
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5-0 out of 5 stars DSP Bible
Written by one of the biggest DSPs Gurus. I can say that this book is my bible on DSP, it toke me some time to understand some parts of the book, but this i due to the huge amount of knowledge present on it. Bestdescription "Open Minder"... ... Read more

35. Chebyshev and Fourier Spectral Methods: Second Revised Edition
by John P. Boyd
Paperback: 688 Pages (2001-12-03)
list price: US$37.95 -- used & new: US$18.34
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Asin: 0486411834
Average Customer Review: 4.5 out of 5 stars
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Completely revised text focuses on use of spectral methods to solve boundary value, eigenvalue, and time-dependent problems, but also covers Hermite, Laguerre, rational Chebyshev, sinc, and spherical harmonic functions, as well as cardinal functions, linear eigenvalue problems, matrix-solving methods, coordinate transformations, methods for unbounded intervals, spherical and cylindrical geometry, and much more. 7 Appendices. Glossary. Bibliography. Index. Over 160 text figures.
... Read more

Customer Reviews (2)

4-0 out of 5 stars For the Experienced User
Spectral methods, as presented by Boyd, are techniques for numerically solving differential equations.His book is a collection of A LOT of practical information presented mostly through a mathematical frame work.Practical means different things to different people; in Boyd's case, he discusses the details of what happens in putting the mathematics to use (the pitfalls), and when each technique should be used.Supporting numerical methods, such as matrix techniques, are discussed where needed.Example computer code is scarce.Worked examples are inconsistently used, and sometimes abstract.

As a novice to the field, I found the level of presentation a notch too high to be able to put it to use.It was more abstract than applied.I'm not saying it is not informative, only that this is not a good first book on the topic.I might get this as a second or third book.

I give it 4 starts due to two complaints.There are not a lot of illustrations, and moreover those that are included are often too simple or need more annotation.A little more thought should go into them, and there should be a more of them for some of the more abstract topics.Additional thought should go into the organization too.Information at different levels of expertise are scattered throughout so you either (a) need to know the answers already, (b) skip ahead several chapters, or (c) go on an aside in another text.

5-0 out of 5 stars Prof. Boyd's book is a gift from the sky
Prof. Boyd's book is god-sent,

I discovered it during a self-embarked journey inthe blooming world of spectral methods. Unfortunately,
these very potent and promising techniques have only recently
escaped the confines of the field of Applied Mathematics where
they were first developed. Thus, most existing literature is too
mathematically oriented and rather opaque to the engineer and
applied scientist, as it does not offer them the basic
operational knowledge that they would require. This book is
one of the first to overcome this chasm. It provides
a survey of all the necessary fundamentals for the application
of spectral methods to various disciplines of computational
engineering but also delves deep into various advanced topics.
At the same time it provides one with sufficient ammunition
to explore, otherwise intimidating, more theoretically-oriented
texts. The text, reflecting the author's extensive knowledge
on the subject, has an unusually flowing writing style to it
and throughout it are interspersed some quite entertaining
snippets of the author's humor.

I recommend this book to all students of spectral methods, regardless
of level of expertise. ... Read more

36. Handbook of Fourier Analysis & Its Applications
by Robert J Marks II
Hardcover: 800 Pages (2009-01-08)
list price: US$150.00 -- used & new: US$39.99
(price subject to change: see help)
Asin: 0195335929
Average Customer Review: 3.5 out of 5 stars
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Fourier analysis has many scientific applications - in physics, number theory, combinatorics, signal processing, probability theory, statistics, option pricing, cryptography, acoustics, oceanography, optics and diffraction, geometry, and other areas.In signal processing and related fields, Fourier analysis is typically thought of as decomposing a signal into its component frequencies and their amplitudes.

This practical, applications-based professional handbook comprehensively covers the theory and applications of Fourier Analysis, spanning topics from engineering mathematics, signal processing and related multidimensional transform theory, and quantum physics to elementary deterministic finance and even the foundations of western music theory.

As a definitive text on Fourier Analysis, Handbook of Fourier Analysis and Its Applications is meant to replace several less comprehensive volumes on the subject, such as Processing of Multifimensional Signals by Alexandre Smirnov, Modern Sampling Theory by John J. Benedetto and Paulo J.S.G. Ferreira, Vector Space Projections by Henry Stark and Yongyi Yang and Fourier Analysis and Imaging by Ronald N. Bracewell. In addition to being primarily used as a professional handbook, it includes sample problems and their solutions at the end of each section and thus serves as a textbook for advanced undergraduate students and beginning graduate students in courses such as:Multidimensional Signals and Systems, Signal Analysis, Introduction to Shannon Sampling and Interpolation Theory, Random Variables and Stochastic Processes, and Signals and Linear Systems. ... Read more

Customer Reviews (3)

1-0 out of 5 stars seriously flawed
This book is not organized as a handbook,
that you would open to find an answer to your question.
Instead of answers it has exercises for the reader.
Its lack of clarity and details, would make it a poor choice for a textbook

5-0 out of 5 stars Like having an extra Bible
I learned much of this material from Marks when I was his grad student.I won't get rid of the books we used then but do plan to turn to this one first as a reference.The homework problems with selected solutions would also make this ideal for a course adoption in one of several topics.I agree with the previous reviewer that there's a lot of material here that one won't find in other books, and that the exposition is superior.

5-0 out of 5 stars An Unusual Book
I don't write many reviews, but this is an unusual book.

If you are looking for a conventional treatment of Fourier analysis, this is not it.The treatment is not only clear, but refreshingly creative.Marks is talented at explaining complex ideas in simple terms.He uses figures.LOTS of figures.Despite the clarity of presentation, there is no loss of foundational rigor. It is all there.

Marks is a very bright polymath and this book shows an incredible block of material. It would seem that the book has been developed over a number of years to reflect the particular lectures he has given as he taught graduate level courses on signal analysis, multivariate Fourier analysis, image processing, Shannon sampling theory, image compression, associative memories, etc. What I find to be most valuable is the relatively "new" material(from the past two decades) on multivariate Fourier analysis and its applications and on sampling, signal recovery, image processing ... areas where Marks has a deep knowledge of the literature.Likewise, the chapter on alternating projection onto convex sets bubbles over with fascinating applications like subpixel resolution, brachytherapy treatment of prostate cancer, recovery of lost portions of digital images, tomography, and image deblurring.

A LOT of new ideas are presented in unique ways.I particularly like the author's problem sets; he includes many of the solutions in the book.Many problems are not rote exercises from the chapters, but introduce new ideas from incisive perspectives.Who knew all elementary finance could be modeled as a convolution?

The author writes clearly and the illustrations are numerous, nicely done, and very helpful. I found that I could "learn" new ideas by studying sections of the book that were unfamiliar to me.And I found that the author displayed a mature up to date knowledge of the topics with which I am thoroughly acquainted.It reminded me of reading the encyclopedia when I a kid.I would start looking up one thing, something else would catch my interest, and I would read about it instead.

This book claims it can be used in junior and senior level courses such as Signals and Systems, Digital Signal Processing, and graduate level courses related to Fourier analysis such as Adaptive Signal Processing (on the topic of power spectral analysis), Probability Theory and Random Process (on the topics of characteristic functions of random variables), and Multidimensional Signal Processing.

There are imperfections.I've found a half dozen typos which doesn't seem bad for a book this thick.The bibliography looks a bit bloated and an Appendix listing of obscure probability models seems out of place. There were a few topics, like multidimensional IIR filters, that are fundamental but not treated.I guess you can't have everything.

Overall, this is a great book by a great author. Currently the material covered is scattered in different books or papers. It is very nice to see such an accessible volume put together by an expert in the field. ... Read more

37. Fourier Techniques and Applications
 Hardcover: 231 Pages (1985-10-01)
list price: US$93.00 -- used & new: US$27.00
(price subject to change: see help)
Asin: 0306421003
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38. The Evolution of Applied Harmonic Analysis: Models of the Real World
by Elena Prestini
Paperback: 349 Pages (2003-12-16)
list price: US$59.95 -- used & new: US$45.39
(price subject to change: see help)
Asin: 0817641254
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From the Foreword by R.N. Bracewell, Stanford University:

"...can be thoroughly recommended to any reader who is curious about the physical world and the intellectual underpinnings that have lead to our expanding understanding of our physical environment and to our halting steps to control it. Everyone who uses instruments that are based on harmonic analysis will benefit from the clear verbal descriptions that are supplied."

A sweeping exploration of essential concepts and applications in modern mathematics and science through the unifying framework of Fourier analysis! This unique, extensively illustrated book describes the evolution of harmonic analysis, integrating theory and applications in a way that requires only some general mathematical sophistication and knowledge of calculus in certain sections.

Key features:

* Historical sections interwoven with key scientific developments showing how, when, where, and why harmonic analysis evolved* Exposition driven by more than 150 illustrations and numerous examples* Concrete applications of harmonic analysis to signal processing, computerized music, Fourier optics, radio astronomy, crystallography, CT scanning, nuclear magnetic resonance imaging and spectroscopy* Includes a great deal of material not found elsewhere in harmonic analysis books* Accessible to specialists and non-specialists

"The Evolution of Applied Harmonic Analysis" will engage graduate and advanced undergraduate students, researchers, and practitioners in the physical and life sciences, engineering, applied mathematics. ... Read more

39. Introduction to Fourier Optics
by Joseph W. Goodman
Hardcover: 491 Pages (2004-12-10)
list price: US$98.50 -- used & new: US$48.00
(price subject to change: see help)
Asin: 0974707724
Average Customer Review: 4.5 out of 5 stars
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Editorial Review

Product Description
Fourier analysis is a ubiquitous tool that has found application to diverse areas of physics and engineering. This book deals with its applications in optics, and in particular with its applications to diffraction, imaging, optical data processing, holography and optical communications. ... Read more

Customer Reviews (11)

5-0 out of 5 stars Provides the necessary background for diffraction physics
I read this book thirty years ago in order to get up to speed on Fresnel diffraction and the Kirchhoff integral as discussed in John Cowley's seminal work "Diffraction Physics".Indeed, this book is recommended by Cowley as a necessary prerequisite.Goodman does a good job laying the groundwork for Fresnal diffraction, complete with a detailed exploration of the boundary conditions.After reading the first several chapters of this book, the reader should be ready to tackle Cowley.

5-0 out of 5 stars The Bible for Ultrasound Beamforming
This is probably my favorite text book of all time.Dr. Goodman's writing is excellent, providing heuristic insight into complex concepts using a very readable style.He is the Richard Feynman of optics.

And other than chapters specific to polarization, this book is entirely applicable to phased array ultrasound.For anyone whos works or studies in the ultrasound field, this book is a must, especially if you have an interest in acoustic beamforming.All the wave and Fourier concepts that apply to light also apply to ultrasound.

5-0 out of 5 stars Should be on every optiker's book shelf
I use this book all the time as a reference for Fourier optics.It has useful tables of common Fourier transforms found in optics work and far-field diffraction patterns worked out for popular beam profiles.

4-0 out of 5 stars Amazing, a textbook that's easy to understand!
I took a class in Fourier Optics and found this text to be indispensable.It explains everything very clearly and concisely, which is a minor miracle for a text at this level.I didn't have any particular background in optics, and was able to pick this up and understand every word.

I do agree with the earlier poster that more 'physical' or graphical representations of concepts would have been useful as I tend to be a visual learner.

5-0 out of 5 stars Simply the best
Only the best will do - and this is it.

Mandatory reading for anyone involved in optics.Goodman's books are treasure troves. ... Read more

40. Harmonic Analysis
by Elias M. Stein
Hardcover: 716 Pages (1993-07-12)
list price: US$105.00 -- used & new: US$83.68
(price subject to change: see help)
Asin: 0691032165
Average Customer Review: 5.0 out of 5 stars
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Product Description
This book contains an exposition of some of the main developments of the last twenty years in the following areas of harmonic analysis: singular integral and pseudo-differential operators, the theory of Hardy spaces, L\sup\ estimates involving oscillatory integrals and Fourier integral operators, relations of curvature to maximal inequalities, and connections with analysis on the Heisenberg group. ... Read more

Customer Reviews (2)

5-0 out of 5 stars A pinnacle
This is beautiful elegant mathematics. I have read much of this beautiful book and Stein and Weiss's companion book on Singular Integrals. If you want to know harmonic analysis, own these and spend many hours with them.

5-0 out of 5 stars Nothing better than learning from the experts.
If you get involved in analysis sooner or later you will have to read Elias Stein. Why? Because the core of analysis is harmonic analysis, and this man has been one of the leading experts in the field over at least 35 years, so, whatever branch of analysis you choose, Dr. Stein will bethere.

This thick book (695 pages) includes most of the topics inharmonic analysis which have been researched extensively during the last 20years. It should be taken as a complement to Stein's "SingularIntegrals and Differentiability Properties of Functions" (1970) andStein & Weiss' "Introduction to Fourier Analysis on EuclideanSpaces" (1971).

Its contents are: Real variable theory (coveringlemmas, maximal function, generalized Calderón-Zygmund decomposition,etc.), maximal functions (vector-valued max. functions, Carlesson measures,etc.), Hardy spaces (characterization, atomic decomposition, singularintegrals, etc.), H^1 and BMO (sharp function, interpolation, etc.),weighted inequalities (the class A_p, etc.), Fourier transform, almostorthogonality, oscillatory integrals, maximal operators, maximal averages,the Heisenberg group.

The style is concise and presents motivation foreach topic. Includes excercises - called "further results" -which are short research topics on their own, and an extensive list ofreferences. The cloth bound is lovely.

Superb book; a must in everyanalyst's library.

Please check my other reviews (just click on my nameabove). ... Read more

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