Signals and Communication Technology

Mathematics of Digital Information Processing

By: Peter Seibt

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Hardcover | 18 August 2006

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452 Pages

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22.86 x 15.24 x 1.27

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Shall we be destined to the days of eternity, on holy-days, as well as working days, to be shewing the RELICKS OF LEARNING, as monks do the relicks of their saints - without working one - one single miracle with them? Laurence Sterne, Tristram Shandy This book deals with information processing; so it is far from being a book on information theory (which would be built on description and estimation). The reader will be shown the horse, but not the saddle. At any rate, at the very beginning, there was a series of lectures on "Information theory, through the looking-glass of an algebraist", and, as years went on, a steady process of teaching and learning made the material evolve into the present form. There still remains an algebraic main theme: algorithms intertwining polynomial algebra and matrix algebra, in the shelter of signal theory. A solid knowledge of elementary arithmetic and Linear Algebra will be the key to a thorough understanding of all the algorithms working in the various bit-stream landscapes we shall encounter. This priority of algebra will be the thesis that we shall defend. More concretely: We shall treat, in ?ve chapters of increasing di?culty, ?ve sensibly di?erent subjects in Discrete Mathem- ics. The?rsttwochaptersondatacompaction(losslessdatacompression)and cryptography are on an undergraduate level - the most di?cult mathematical prerequisite will be a sound understanding of quotient rings, especially of- nite ?elds (mostly in characteristic 2).

Industry Reviews

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"This book, consisting of five chapters, deals with information processing. ... The format of chapters ... is very good. ... It is very readable and provides a valuable source about information processing. This is a good book on the subject ... . it is a welcome addition." (Arjun K. Gupta, Zentralblatt MATH, Vol. 1136 (14), 2008)

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Data Compaction	p. 5
Entropy Coding	p. 5
Discrete Sources and Their Entropy	p. 5
Towards Huffman Coding	p. 10
Arithmetic Coding	p. 32
Universal Codes: The Example LZW	p. 43
LZW Coding	p. 43
The LZW Decoder	p. 45
Cryptography	p. 49
The Data Encryption Standard	p. 50
The DES Scheme	p. 50
The Cipher DES in Detail	p. 53
The Advanced Encryption Standard: The Cipher Rijndael	p. 60
Some Elementary Arithmetic	p. 60
Specification of Rijndael	p. 77
The Key Schedule	p. 86
Decryption with Rijndael	p. 92
The Public Key Paradigm and the Cryptosystem RSA	p. 93
Encryption and Decryption via Exponentiation	p. 93
The Cryptosystem RSA	p. 97
Digital Signatures	p. 101
Message Digests via SHA-1	p. 101
DSA: Digital Signature Algorithm	p. 112
Auxiliary Algorithms for DSA	p. 116
The Signature Algorithm rDSA	p. 122
ECDSA - Elliptic Curve Digital Signatures	p. 125
Information Theory and Signal Theory: Sampling and Reconstruction	p. 171
The Discrete Fourier Transform	p. 172
Basic Properties	p. 172
The Fast Fourier Transform Algorithm	p. 183
Trigonometric Interpolation	p. 190
Trigonometric Polynomials	p. 191
Sampling and Reconstruction	p. 193
The Whittaker-Shannon Theorem	p. 198
Fourier Series	p. 198
The Whittaker-Shannon Theorem for Elementary Periodic Functions	p. 203
The (Continuous) Fourier Transform: A Sketch	p. 209
The Sampling Theorem	p. 214
Error Control Codes	p. 221
The Reed-Solomon Codes	p. 221
Preliminaries: Polynomial Codes	p. 221
Reed-Solomon Codes	p. 225
Convolutional Codes	p. 239
Encoding: Digital Filtering in Binary Arithmetic	p. 239
Decoding: The Viterbi Method	p. 253
Data Reduction: Lossy Compression	p. 267
DFT, Passband Filtering and Digital Filtering	p. 268
The Discrete Cosine Transform	p. 274
Functional Description of the DCT	p. 275
The 2D DCT	p. 293
The Karhunen-Loeve Transform and the DCT	p. 305
Filter Banks and Discrete Wavelet Transform	p. 314
Two Channel Filter Banks	p. 314
The Discrete Wavelet Transform	p. 372
References	p. 435
Index	p. 439
Table of Contents provided by Publisher. All Rights Reserved.

Signals and Communication Technology

Mathematics of Digital Information Processing

At a Glance

Hardcover

Industry Reviews

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How to return your order

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