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Principles of Signals and Systems : Deterministic Signals - Bernard Picinbono

Principles of Signals and Systems

Deterministic Signals


Published: 19th August 1988
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This handy reference introduces essential signal processing principles, enabling you to solve practical design problems. It provides more than 500 equations, 30 illustrations, and dozens of examples and graphs.

Prefacep. xi
Introduction to Signals and Systemsp. 1
The concept of signalsp. 1
The concept of a linear systemp. 3
The concept of linear filtersp. 5
The concept of signal representation and transformp. 12
Problemsp. 13
Representations of Continuous-time Signalsp. 15
Energy and power; scalar product of signalsp. 15
Fourier seriesp. 17
Time-limited signalsp. 17
Periodic signalsp. 21
Principal properties of Fourier series of periodic signalsp. 23
Fourier transforms of signals of finite energyp. 28
Definitions and notationp. 28
Examples of Fourier transformsp. 30
Principal properties of Fourier transformsp. 32
Examplesp. 37
Fourier representation of signals with infinite energyp. 41
The unit impulse functionp. 41
Fourier transforms of periodic signalsp. 44
The Dirac comb signalp. 45
Fourier transform of the unit step signalp. 46
Real narrowband signals: instantaneous amplitude and phase, duration and bandwidthp. 47
Analytic signal of a real signalp. 48
Instantaneous amplitude and phase of a signalp. 50
Application to the case of narrowband signalsp. 51
Laplace representationp. 55
Definition and notationp. 55
Region of convergencep. 56
Inversion of the Laplace transformp. 60
Inverse Laplace transform of rational functionsp. 63
Principal properties of the Laplace transformp. 68
Problemsp. 71
From Continuous Time to Discrete Time by Samplingp. 79
The principle of sampling: the sampling theoremp. 79
The sampling formula and consequencesp. 81
Sampling and signal representationp. 81
Sampling and interpolationp. 82
Sampling and linear spacesp. 83
Minimum sampling ratep. 83
Exact position of the sampling time instantsp. 83
Exact position of the frequency bandp. 83
Some practical commentsp. 84
Sampling and filteringp. 84
The sampling transformation Tp. 85
Physical structure of the transformation Tp. 86
Interpretation of the sampling theoremp. 87
Aliasing; undersampling and oversamplingp. 88
Duality between sampling and periodicityp. 88
Sampling and Fourier representationp. 90
Geometrical interpretation of samplingp. 91
Discrete Fourier transform of a continuous signalp. 94
Principle of the discrete Fourier transformp. 94
Calculation of the discrete Fourier transformp. 95
Relation between the Fourier transform and the discrete Fourier transformp. 96
Problemsp. 97
Representations of Discrete-time Signalsp. 101
Time-limited and periodic signals: the discrete Fourier transformp. 101
Fourier transform of discrete-time signalsp. 105
The z transformp. 106
Definition and notationp. 106
Region of convergencep. 107
Inversion of the z transformp. 110
Principal properties of the z transformp. 114
The z transform of sampled signalsp. 115
Some algebraic properties of discrete-time signals: the fast Fourier transformp. 116
The discrete Fourier transform as an eigenvalue problem: circulant matricesp. 117
The discrete Fourier transform as a linear problem: the fast Fourier algorithmp. 118
Problemsp. 124
Linear Filteringp. 129
Definitions and examplesp. 129
Some basic properties of filtersp. 133
Causality of linear filtersp. 142
Causality and impulse responsep. 142
Causality and the transfer functionp. 143
Causality and frequency responsep. 145
Multidimensional filtersp. 148
Problemsp. 150
Dynamical Filtersp. 155
Definitions and basic propertiesp. 155
Representations of dynamical filtersp. 159
The continuous-time casep. 159
The discrete-time casep. 161
Stability problemsp. 169
The continuous-time casep. 169
The discrete-time casep. 171
Impulse and unit step responsesp. 172
The continuous-time casep. 172
Examplesp. 174
The discrete-time casep. 183
Problemsp. 186
Internal Representation of Dynamical Filtersp. 191
Introductionp. 191
Principles of the internal representation of linear systemsp. 193
Canonical internal representation of dynamical filtersp. 195
First continuous-time canonical representationp. 195
Second continuous-time canonical representationp. 197
First discrete-time canonical representationp. 198
Diagonal and quasi-diagonal representationsp. 199
Solution of the state equation in the discrete-time casep. 201
Solution of the state equation in the continuous-time casep. 203
Free system: transition matrixp. 204
Driven systemp. 206
Input-output relationshipp. 208
Modes of a dynamical filterp. 210
Problemsp. 215
On the Routh criterionp. 221
Reflection coefficients and stabilityp. 227
Bibliographyp. 233
Glossaryp. 237
Indexp. 239
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780890062951
ISBN-10: 0890062951
Series: Acoustics & signal processing library
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 260
Published: 19th August 1988
Publisher: Artech House Publishers
Country of Publication: US
Dimensions (cm): 22.9 x 15.2  x 1.9
Weight (kg): 0.55