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Signal Processing: A Mathematical Approach (Monographs and Research Notes in Mathematics)
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Top Customer Reviews
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.Read more ›
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.