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Signal Processing: A Mathematical Approach (Monographs and Research Notes in Mathematics)

4.8 out of 5 stars 4 customer reviews
ISBN-13: 978-1568812427
ISBN-10: 1568812426
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Editorial Reviews

Review

He encountered a gap in this realm in the late 1970s when he began working as a mathematician in signal processing for the Naval Research Laboratory... -SciTech Book News, September 2005

About the Author

Charles L. Byrne earned a BA from Georgetown University and his MA and Ph.D. from the University of Pittsburgh, all in Mathematics. He is currently a professor in the Department of Mathematical Sciences at the University of Massachusetts, Lowell, and served as department chair from 1987-1990. From 1979 to 1993 he was a consultant to the Acoustics Division, US Naval Research Laboratory and since 1990 he has also been a consultant to the Department of Radiology, University of Massachusetts Medical School, Worcester.
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Product Details

  • Series: Monographs and Research Notes in Mathematics
  • Hardcover: 397 pages
  • Publisher: A K Peters/CRC Press (January 15, 1993)
  • Language: English
  • ISBN-10: 1568812426
  • ISBN-13: 978-1568812427
  • Product Dimensions: 1 x 6 x 8.8 inches
  • Shipping Weight: 1.1 pounds
  • Average Customer Review: 4.8 out of 5 stars  See all reviews (4 customer reviews)
  • Amazon Best Sellers Rank: #4,013,705 in Books (See Top 100 in Books)

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Top Customer Reviews

By Charles Bradley on May 23, 2007
Format: Hardcover
This relatively small (364 pages + bibliography and index) book contains an amazing amount of

material. There are numerous exercises, and many of them have hints. Answers to many but not

all, are available at the author's web site, available through the Math department at University

of Massachusetts Lowell. There is also a list of errors/typos. It is impressively shorter than

for many other technical books

The book contains a lot of information about signal processing and a lot of mathematics used

to construct signal processing algorithms. The author uses the text when he teaches "Mathematics

of Signal Processing." The title of the course is more accurate than the title of the book.

The author says the book was written with the title of the course but the publisher insisted

on changing it.

The introduction tells us the author was drawn into the field of signal processing by

accident in 1979, from the pure math fields of topology and functional analysis. The book is

his attempt to make the transition easier for others. This is applied math at the level of

rigor often found in texts with "Methods of ..." as the first words of the title. There are

no existence proofs. Orders of summation and integration are changed without detailed

justification. Matrices are assumed invertible, but workarounds are given for the rare

instances when they are not. The level of rigor seems appropriate for the subject. The emphasis

is on what might work, rather than on why something might not work.

The phrase "what might work" is important.
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Format: Hardcover
An amazing amount of data being collected out in the real world comes in the form of digital signals. This includes radar, sonar, ultra-sound or other medical imaging system, and more. Once the data is captured (the realm of the pure enginnering types) some kind of processing has to be done to convert the data (a string of 0's and 1's) into something that comes across to us as information.

Now the problem moves to the mathematician who has to decide how to best take this data and process it to get it in a form that provides useful information. The basic mathematical techniques are not new (Fourier did his work about 1800, Hilbert around 1900) but nor are they the things you normally study in high school. As digital computers have become possible, new techniques have been developed to speed the processing task.

This book is positioned at the intersection of the engineer producing the signal, and the programmer who has to do something with it. It is the solid mathematical background to signal processing. It is basically a selection of the mathematical techniques needed to do signal processing.
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Format: Hardcover
Signal Processing: A Mathematical Approach is a solid, college-level text about the mathematics behind signal processing, focusing on the mathematical background and tools needed to comprehend and employ signal processing techniques. Covering such topics as Fourier series and transforms, transmission and emission topography and image reconstruction, optimization techniques, high-resolution methods, and much more, Signal Processing includes descriptive instructionals, examples, figures and graphs, and exercises to refine one's grasp of the mathematical principles. A singularly valuable textbook or self-study resource for students and professionals, whether preparing for a future career or brushing up on standby skills.
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Format: Hardcover
This textbook is not an easy read but the author makes it clear enough so if you spend sometime you'll understand eventually.
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