Fast Fourier Transform and Its Applications

Customer Reviews:

An accessible examination of the FFT great for self study.......2007-01-01

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.

Written with the reader in mind........2004-10-02

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.

Very good, but be careful, though.......2003-04-22

The book I have is ISBN 0-13-307496. It was published in 1974.

I am very happy about this book, I first read it in 1979 when I was 19, and I found it really marvellous. I agree with the other reviewers, but I must add a note of caution - the edition I have contains some errors. They are as follows;

p155, p157 - the factors w(11) and w(10) are incorrectly placed on the butterfly diagram 10.3 and 10.4 respectively,

p166, p168, p169, equations 10-26 and most equations following to the end of the chapter - the factors R(N-n) and I(N-n) should be R(N-1-n) and I(N-1-n), respectively.

I hope I'm right about this, but the convention is that the indices are from 0 to N-1, and therefore if n=0, then N-n is N - which not an allowed index.

Apart from these sort of errors (I havn't been through the whole book with a fine toothcomb), its really very good, actually extraordinarily clear.

One of its main benefits is that it doesn't veer away from the FFT to the very complicated developments such as fractional transforms and other developments which might confuse the sort of audience it's aimed at (which is definitely the graduates).

But if you want to look deeply into FFTs for a real application you will need a lot more. I must mention,for instance, that the implementation of an FFT needs fairly careful error propagation and rounding analysis, and this isn't covered at all in the book. Neither are prime factor FFTs. In fact the chapter "FFT algorithms for arbirary factors" is only a method of factoring into powers of two, and certainly not the prime factor decomposition which was developed later by Winograd, Chuo, and others.

It must also be said that while the DCT is practically a kissing cousin of the FFT, this naturally isn't covered in this text... but neither are the finite field implementations that are now taking many peoples imaginations to faster and faster FFTS.

Also, there are jolly useful things to know about, such as the FFT when you only need a subset of the output data points. There are pruning algorithms which greatly simplify the computations.

But it's very good as a starter, I wouldn't do without my copy!

Outstanding classic.......2002-12-03

I am mainly a neurobiologist by training, but transform theory is very useful in visual neurobiology and visual psychophysics, and I've looked at and read dozens of books on various aspects of signal processing and transform theory. Much of this is surprisingly applicable to the brain science area, as the revolutionary work of David Marr and other scientists showed a quarter of a century ago.

But getting back to the present book, this is one of the best books I've read in the signal analysis area. Brigham's presentation of various aspects of the FT, including the continuous FT, digital FT, convolution integrals, and so on, is clear and concise, whether he's discussing theory or applications. Also, his disussion of the Nyquist sampling theorem is the best and easiest to understand I've read.

Interestingly, this theorem has quite practical applications, not just in digital sample theory, but in real life. According to the Nyquist theorem, no information is lost in converting from analog to digital form if the sampling frequency is twice that of the highest frequency in the signal. Well, have you ever used those audio headphones they have on commercial jetliners? The Nyquist theorem means they can switch the audio outputs at high frequency using well-known time-domain switching techniques rather than run copper to each passenger's seat. I've read that this saves 300 pounds of copper wire in a typical plane, the weight savings of which can of course be more profitably used for transporting other things. If you consider that 300 pounds is about the weight of your average couple, you can see how the savings would add up after even a few flights.

But getting back to the book, I first encountered this work 20 years ago, and I'm delighted to see it's still around. My neurobiology student friends and I all got turned on to this book early in grad school, and it was a great help. I still fondly recall the many enjoyable hours we spent talking about how Fourier analysis and other techniques such as the Laplace transform, temporal modulation transfer fuction, two-dimensional convolution integrals, two-dimensional point-spread functons, filter techniques such as the finite and infinite response filters, Kalman filter, Hammond filter, and so on, could be applied to our area. And it all started with this book. It's a true classic that has never been exceeded for it's clear and concise exposition of a very important mathematical tool in both engineering and neurophysiology.

One of the best technical monographs........2001-07-12

I'm delighted to see that Brigham's book is in print. (I bought my first copy 20 years ago!) I'm planning to use as part of a course on signal processing. I've read several books on FT's and this is the best. It is one of the few technical books whose presentation is genuinely complete and clear. For example, the relationships between the discrete and the continuous FT, the role of the convolution integral, and the Nyquist theorem are presented logically with both algebraic proofs and graphical explanations. I'm always on the look out for monographs that focus on one subject and make you feel like you've become an expert on it when you're through. This fits the bill.

Advanced Engineering Mathematics with MATLAB (Bookware Companion)

Average customer rating:

Excellent book, but missing import parts for Electronics/Com
Deserves 6 stars
Excellent reference for engineers

Advanced Engineering Mathematics with MATLAB (Bookware Companion)
Thomas L. Harman , James B. Dabney , and Norman John Richert
Manufacturer: Cengage-Engineering
ProductGroup: Book
Binding: Hardcover

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ASIN: 0534371647

Book Description

ADVANCED ENGINEERING MATHEMATICS WITH MATLAB® is written for engineers and engineering students who are interested in applying MATLAB® to solve practical engineering problems. The book emphasizes mathematical principles, not computations, with MATLAB® employed as a tool for analysis that shows how engineering problems are defined and solved. The book features complete MATLAB® integration throughout, abundant examples which show real practical applications, and end-of-chapter problems that reinforce techniques.

Customer Reviews:

Excellent book, but missing import parts for Electronics/Com.......2002-05-27

This is an excellent book for studying advanced math. Important concepts clearly explained with good matlab examples. But I was surprised to find this book titled "Engineering Math" with the miss out of some thing like probability and random variables which are of the critical importance for Electronics/Communications students.

Deserves 6 stars.......2001-07-05

If you are not already a superuser of MATLAB or a mathematician and want to choose one single book on MATLAB that also brings a solid math base, this is the one. The authors have chosen the subjects very well, with emphasys on the use of mathematical principles coupled with the use of the computing power offered by MATLAB.

In addition to a sound presentation of concepts - without however being extensive (or boring) on theoretical details that probably would not be relevant - this book addresses most areas of University Math (Physical Sciences undergraduate curriculum) with a wealth of good practical programming examples. I specially liked the chapters on Eigenvectors and Eigenvalues, those on Differential equations, Fourier analysis and the simple but very clear and didatic one on Discrete sytems.

In summary, although not a complete text, the subjects addressed in this book are so well presented that it can be forgiven for not covering some areas (like complex variables and calculus of variations, to name only two). There is no waste of pages in this book, but as a suggestion for future enhancement I would mention the inclusion of a chapter dedicated to exploring the graphing power available in MATLAB.

Also as a reference, for most needs you'll probably be able to start doing something productive right away after reading. Well worth its price!

Excellent reference for engineers.......2000-08-07

This is an excellent reference book not only for matlab, also an excellent reference book for the basic concepts such as Fourier Analysis. I think any engineers who work in electric design filed must have a copy.

Time-Frequency/Time-scale Analysis (Wavelet Analysis and Its Applications)

Average customer rating:

A great reference book.

Time-Frequency/Time-scale Analysis (Wavelet Analysis and Its Applications)
Patrick Flandrin
Manufacturer: Academic Press
ProductGroup: Book
Binding: Hardcover

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ASIN: 0122598709

Book Description

This highly acclaimed work has so far been available only in French. It is a detailed survey of a variety of techniques for time-frequency/time-scale analysis (the essence of "Wavelet Analysis"). This book has broad and comprehensive coverage of a topic of keen interest to a variety of engineers, especially those concerned with signal and image processing. Flandrin provides a discussion of numerous issues and problems that arise from a mixed description in time and frequency, as well as problems in interpretation inherent in signal theory.

Key Features
* Detailed coverage of both linear and quadratic solutions
* Various techniques for both random and deterministic signals

Customer Reviews:

A great reference book........2001-06-05

I do research in time-frequency analysis and have been amazed at the wealth of information in this book. This book covers many of the topics of recent and current research in the field of time-frequency analysis.

Although this is volume 10 in the "Wavelet Analysis and its Applications" series by Academic Press, don't be misled into thinking that this a book on wavelets alone. If you want a wavelet book I recommend the "Wavelets and Subband Coding" by Martin Vetterli and Jelena Kovacevic.

(From the cover) "This book offers a discussion of problems that emerge from a mixed description in time and frequency, and it comprises a detailed construction of the principle classes of admissible solutions (short-time Fourier, wavelets, Wigner-Ville, Cohen's class, affine distributions, etc.) It also addresses numerous issues of interpretation related to such representations and shows how to reformulate several important problems in signal theory by utilizing time-frequency distributions."

A bonus for researchers is that although it not mentioned in the book, Flandrin has a public domain set of Matlab routines to compute many of the techniques described in the book.

Finally, an indication of the scope and thoroughness of the book is that it concludes with a 20 page bibliography.

This book makes a nice companion to the book "Time-Frequency Analysis" by Leon Cohen. Although there is a good deal of overlap in the material they are different enough to warrant owning both.

Book Description

Nonlinear analysis is a broad, interdisciplinary field characterized by a remarkable mixture of analysis, topology, and applications. Its concepts and techniques provide the tools for developing more realistic and accurate models for a variety of phenomena encountered in fields ranging from engineering and chemistry to economics and biology. This volume focuses on topics in nonlinear analysis pertinent to the theory of boundary value problems and their application in areas such as control theory and the calculus of variations. It complements the many other books on nonlinear analysis by addressing topics previously discussed fully only in scattered research papers. These include recent results on critical point theory, nonlinear differential operators, and related regularity and comparison principles. The rich variety of topics, both theoretical and applied, make Nonlinear Analysis useful to anyone, whether graduate student or researcher, working in analysis or its applications in optimal control, theoretical mechanics, or dynamical systems. An appendix contains all of the background material needed, and a detailed bibliography forms a guide for further study.

Dynamics and Control (Stability and Control, Theory, Methods and Applications , Vol 9)

Average customer rating:

A Book that Shows the State-of-the-Art

Dynamics and Control (Stability and Control, Theory, Methods and Applications , Vol 9)

Manufacturer: CRC
ProductGroup: Book
Binding: Hardcover

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ASIN: 9056991728

Book Description

This multi-authored volume presents selected papers from the Eighth Workshop on Dynamics and Control. Many of the papers represent significant advances in this area of research, and cover the development of control methods, including the control of dynamical systems subject to mixed constraints on both the control and state variables, and the development of a control design method for flexible manipulators with mismatched uncertainties. Advances in dynamic systems are presented, particularly in game-theoretic approaches and also the applications of dynamic systems methodology to social and environmental problems, for example, the concept of virtual biospheres in modeling climate change in terms of dynamical systems.

Customer Reviews:

A Book that Shows the State-of-the-Art.......2001-01-08

This book contains a well-organized series of articles by individuals who have international renown for their reseach in the field of dynamics and control. Several of the articles represent substantial progress in our knowledge of uncertain systems, nonlinear systems and their applications to understanding physical and societal problems of topical interest. The book is divided into 3 section, of which I found the last one, on applications, fascinating. These latter papers show that mathematical analysis can indeed shed considerable light on our understanding of society and the environment.

Wavelets and Subband: Fundamentals and Applications

Average customer rating:

Great Book for understanding Wavelets!

Wavelets and Subband: Fundamentals and Applications
Agostino Abbate , Casimer DeCusatis , and Pankaj K. Das
Manufacturer: Birkhäuser Boston
ProductGroup: Book
Binding: Hardcover

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ASIN: 081764136X

Book Description

Recently there has been intense research activity on the subject of wavelet/subband theory and application. Experts in such diverse fields as mathematics, physics, electrical engineering and image processing have provided original and pioneering works and results. But this diversity, while rich and productive, has lead to a sense of fragmentation, especially to those new to the field, and nonspecialists, trying to understand the connections between the different aspects of wavelet and subband theory.

The book is designed to present an understanding of wavelets and their development from a continuous-domain transformation to a frame representation and finally to multiresolution analysis tools such as subband decomposition. The book presents a theoretical understanding of the subject that is intertwined with practical examples and practical applications of wavelets in ultrasonic and biomedical applications. There is special emphasis on applications in communications and compression as well as image processing.

Topics and Features:

* Provides an understanding of the link between continuous wavelet transform, the fast wavelet transform and subband decomposition.

* Algorithms and numerical examples are implemented in Matlab.

* The design of wavelet bases, and how to implement the transform both in hardware and software is discussed in detail.

* Covers the fundamentals and the developments of the links between areas such as time-frequency analysis, digital signal processing, image processing and Fourier and wavelet transform, both continuous and discrete.

Extended mathematical treatment and numerous examples, with particular emphasis to the transition from the continuous domain to multiresolution and subband. The book is an essential text/reference for graduates, researchers, and professionals in electrical engineering, communications engineering and computer engineering. Practitioners and professionals engaged in signal processing, wavelets and Fourier analysis will find the book a useful resource and comprehensive guide.

Customer Reviews:

Great Book for understanding Wavelets!.......2006-02-05

Simply the excellent book currently available in Market to understand Wavelets. Enjoy reading this book!

Tensor Algebra and Tensor Analysis for Engineers: With Applications to Continuum Mechanics

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Tensor Algebra and Tensor Analysis for Engineers: With Applications to Continuum Mechanics
Mikhail Itskov
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 3540360468

Book Description

There is a large gap between the engineering course in tensor algebra on the one hand and the treatment of linear transformations within classical linear algebra on the other hand. The aim of the book is to bridge this gap by means of the consequent and fundamental exposition. The book is addressed primarily to engineering students with some initial knowledge of matrix algebra. Thereby the mathematical formalism is applied as far as it is absolutely necessary. Numerous exercises provided in the book are accompanied by solutions enabling an autonomous study. The last chapters of the book deal with modern developments in the theory of isotropic an anisotropic tensor functions and their applications to continuum mechanics and might therefore be of high interest for PhD-students and scientists working in this area.

In the last decades, the absolute notation for tensors has become widely accepted and is now a current state of the art for publications in solid and structural mechanics. This is opposed to a majority of books on tensor calculus referring to index notation. The latter one complicates the understanding of the matter especially for readers with initial knowledge. Thus, this book aims at being a modern textbook on tensor calculus for engineers in line with the contemporary way of scientific publications.

The Transforms and Applications Handbook (Electrical Engineering Handbook Series)

Average customer rating:

A very comprehensive reference
A best seller in mathematics !

The Transforms and Applications Handbook (Electrical Engineering Handbook Series)

Manufacturer: CRC Press
ProductGroup: Book
Binding: Hardcover

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ASIN: 0849383420

Book Description

The Transforms and Applications Handbook brings together in a single volume the most important mathematical transforms that are frequently used by engineers and scientists. Each chapter covers one of the transforms and provides numerous examples. These examples highlight the use of the transform and its properties. Applications to different areas are also included in each chapter. The book begins with a treatment of the delta function and some of the classical orthogonal functions. The text details transforms such as:

Customer Reviews:

A very comprehensive reference.......2007-07-24

This book is basically a collection of monographs, each on a different integral transform (and most by different authors). There are additional sections which are general references, but they are probably redundant to most people who would actually be using this book.

The book is a bit weighted towards Fourier transforms, but I found the Laplace and Hankel transform sections very good also. I also learned a lot about other transforms I didn't know much about (e.g., Mellin and Radon transforms).

This book may be the best reference out there for non-mathematicians regarding integral transforms, especially regarding the lesser-known transforms. There are plenty of other books on Laplace and Fourier transforms, but not so on most of the others.

I liked the worked examples for almost each important property of each transform. For me, that I how I learn these things.

A best seller in mathematics !.......2000-04-15

This book contains great materials for engineering, research in mathematics. Every student or profesionnal can find all he needs. A top reference !

Calculus: Applications and Technology (with CD-ROM)

Average customer rating:

An OK calculus book
Only If You Already Know Calculus...

Calculus: Applications and Technology (with CD-ROM)
Edmond C. Tomastik
Manufacturer: Brooks Cole
ProductGroup: Book
Binding: Hardcover

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Accessories:

Student Solutions Manual for Tomastik's Calculus: Applications and Technology, 3rd

ASIN: 0534464963

Book Description

CALCULUS: APPLICATIONS AND TECHNOLOGY is a modern text that is guided by four basic principles: The Rule of Four, technology, the Way of Archimedes, and an exploratory teaching method. Where appropriate, each topic is presented graphically, numerically, algebraically, and verbally, helping students gain a richer, deeper understanding of the material. A pronounced emphasis in the text on technology, whether graphing calculators or computers, permits instructors to spend more time teaching concepts. Additionally, applications play a central role in the text and are woven into the development of the material. More than 500 referenced exercises and hundreds of data sets contained in the text make this text useful and practical for students. Most importantly, this text lets students investigate and explore calculus on their own, and discover concepts for themselves.

Customer Reviews:

An OK calculus book.......2000-09-21

I'm not really sure if this book stands out that much from the countless calc books that have been written, but the selection of problems is quite good. We use this book at Santa Barbara City college. It is a good book to teach from because the overall coverage of topics is good. Some of my students have complained that the book is hard to read. Well, I thought that too when I first learned from Larson and Hostetler. If you are are a student reading this, I would reccomend Stuart's Calculus book over this one. There is one thing I need to comment on that definitely has confused some of my students. Mr. Tomastik doesn't feel the need to devote a section of the text to partial fraction expansions, but he uses those ideas in the text, especially in the sections on solving differential equations!!

Only If You Already Know Calculus..........1999-03-13

Unfortunately you may be required to buy this book for your class, and have no say in whether it should be used. But if the option is there, my suggestion is you run as far as possible from this text. Unless you already have a good knowledge of calculus, you may find yourself thoroughly and ridiculously lost as you are led through this book. In my experience with mathematics texts, most follow a predictable pattern; most sample problems will follow a step-by-step explanation of how the problem is solved, while explaining WHY the problem is solved in that particular manner. Through its entirety, this text leaves out the WHY. Being that this book is not used for higher level calculus courses (at my university, it is a requirement for a freshman year math course), it is perplexing that it is not written to cater towards its audience. Assuming you are not a mathematician or do not absolutely love math, this particular book leaves one feeling mentally challenged.

Student Solutions Manual for Tomastik's Calculus: Applications and Technology, 3rd

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Student Solutions Manual for Tomastik's Calculus: Applications and Technology, 3rd
TOMASTIK
Manufacturer: Brooks Cole
ProductGroup: Book
Binding: Paperback

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Financial Accounting, 6e: A Focus on Interpretation and Analysis

ASIN: 0534492320

Book Description

The Student Solutions Manual provides worked out solutions to the odd-numbered problems in the text.

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