Cover -- Title Page -- Copyright -- Contents -- Preface -- 1. Introduction, Generalities, Definitions of Systems -- 1.1. Introduction -- 1.2. Signals and communication systems -- 1.3. Signals and systems representation -- 1.3.1. Signal -- 1.3.2. Functional space L2 -- 1.3.3. Dirac distribution -- 1.4. Convolution and composition products - notions of filtering -- 1.4.1. Convolution or composition product -- 1.4.2. System -- 1.5. Transmission systems and filters -- 1.5.1. Convolution and filtering -- 1.6. Deterministic signals - random signals - analog signals -- 1.6.1. Definitions -- 1.6.2. Some deterministic analog signals -- 1.6.3. Representation and modeling of signals and systems -- 1.6.4. Phase-plane representation -- 1.6.5. Dynamic system -- 1.7. Comprehension and application exercises -- 2. Transforms: Time - Frequency - Scale -- 2.1. Fourier series applied to periodic functions -- 2.1.1. Fourier series -- 2.1.2. Spectral representation (frequency domain) -- 2.1.3. Properties of Fourier series -- 2.1.4. Some examples -- 2.2. FT applied to non-periodic functions -- 2.3. Necessary conditions for the Fourier integral -- 2.3.1. Definition -- 2.3.2. Necessary condition -- 2.4. FT properties -- 2.4.1. Properties -- 2.4.2. Properties of the FT -- 2.4.3. Plancherel theorem and convolution product -- 2.5. Fourier series and FT -- 2.6. Elementary signals and their transforms -- 2.7. Laplace transform -- 2.7.1. Definition -- 2.7.2. Properties -- 2.7.3. Examples of the use of the unilateral LT -- 2.7.4. Transfer function -- 2.8. FT and LT -- 2.9. Application exercises -- 3. Spectral Study of Signals -- 3.1. Power and signals energy -- 3.1.1. Power and energy of random signals -- 3.2. Autocorrelation and intercorrelation -- 3.2.1. Autocorrelation and cross-correlation in the time domain -- 3.2.2. A few examples of applications in steady state.

3.2.3. Powers in variable state -- 3.3. Mathematical application of the correlation and autocorrelation functions -- 3.3.1. Duration of a signal and its spectrum width -- 3.3.2. Finite or zero average power signals -- 3.3.3. Application for linear filtering -- 3.4. A few application exercises -- 4. Representation of Discrete (Sampled) Systems -- 4.1. Shannon and sampling, discretization methods, interpolation, sample and hold circuits -- 4.1.1. Sampling and interpolation -- 4.2. Z-transform - representation of discrete (sampled) systems -- 4.2.1. Definition - convergence and residue -- 4.2.2. Inverse Z-transform -- 4.2.3. Properties of the Fourier transform -- 4.2.4. Representation and modeling of signals and discrete systems -- 4.2.5. Transfer function in Z and representation in the frequency domain -- 4.2.6. Z-domain transform, Fourier transform and Laplace transform -- 4.3. A few application exercises -- 5. Representation of Signals and Systems -- 5.1. Introduction to modeling -- 5.1.1. Signal representation using polynomial equations -- 5.1.2. Representation of signals and systems by differential equations -- 5.2. Representation using system state equations -- 5.2.1. State variables and state representation definition -- 5.2.2. State-space representation for discrete linear systems -- 5.3. Transfer functions -- 5.3.1. Transfer function: external representation -- 5.3.2. Transfer function and state-space representation shift -- 5.3.3. Properties of transfer functions -- 5.3.4. Associations of functional diagrams -- 5.4. Change in representation and canonical forms -- 5.4.1. Controllable canonical form -- 5.4.2. Controllable canonical form -- 5.4.3. Observability canonical form -- 5.4.4. Observable canonical form -- 5.4.5. Diagonal canonical form -- 5.4.6. Change in state-space representations and change in basis.

5.4.7. Examples of systems to be modeled: the inverse pendulum -- 5.4.8. System phase-plane representation -- 5.5. Some application exercises -- 6. Dynamic Responses and System Performance -- 6.1. Introduction to linear time-invariant systems -- 6.2. Transition matrix of an LTI system -- 6.2.1. Transition matrix -- 6.3. Evolution equation of an LTI system -- 6.3.1. State evolution equation -- 6.3.2. Transition matrix computation -- 6.4. Time response to the excitation of continuous linear systems -- 6.4.1. System response -- 6.4.2. Solution the state equation -- 6.4.3. Role of eigenvalues of the evolution matrix A within the system dynamics -- 6.5. Sampling and discretization of continuous systems -- 6.5.1. Choice of the sampling period (Shannon) and integration methods -- 6.5.2. Euler's method -- 6.5.3. Order n Runge-Kutta method -- 6.5.4. Method using the state transition matrix with zeroth-order holder -- 6.5.5. Evolution equation for a time-invariant discrete system (DTI) -- 6.6. Some temporal responses -- 6.6.1. Response to an impulse excitation -- 6.6.2. Response to step excitation -- 6.7. Transfer function frequency responses -- 6.7.1. Bode plot -- 6.7.2. Nyquist plot -- 6.7.3. Black-Nichols plot -- 6.8. Parametric identification -- 6.8.1. Identification by analogy -- 6.8.2. Parameters identification: examples of systems -- 6.8.3. Strejc method (minimal dephasing) -- 6.9. Dynamics of linear systems -- 6.9.1. Link between frequency domain and time domain -- 6.10. System performance and accuracy -- 6.10.1. Damping factor of a system -- 6.10.2. System speed and transient -- 6.10.3. System static error, speed, sensitivity to noise and accuracy -- 6.10.4. Conclusion -- 6.11. Some application exercises -- 7. System Stability and Robustness Analysis Methods -- 7.1. Introduction -- 7.2. Definitions related with the stability of a dynamic system.

7.2.1. Equilibrium state of a system -- 7.2.2. Stable system: bounded input bounded output -- 7.3. Stability criteria -- 7.3.1. Routh criterion and stability algebraic criterion -- 7.3.2. Jury criterion and discrete system example -- 7.4. Some application exercises -- 7.4.1. Exercises: circle criterion, causes of instability and practical cases -- Bibliography -- Index -- Other titles from iSTE in Digital Signal and Image Processing -- EULA.