Curriculum 1994  COURSE DETAILS 2013/2014
Sistemas lineales (STLN 090000276 )

Cycle/Year/Semester 
First Cycle / 2^{o} / First Semester 
Type 
Required 
Credits 
6 (4,5 T + 1,5 P) 
ECTS Credits 
4.8 
Department 
SSR 
Objectives 
This program covers basics aspects of signal and system analysis, in continuous time and in discrete time. Taking as starting point the basics and mathematical tools known at the beginning of the second course, the main new concepts presented are: linear and time invariant systems characterisation using the impulse response, convolution, continuous and discrete time Fourier Transform, and signal and system analysis in the transform domain (Laplace and Z transforms). All these concepts will be used in the remaining subjets of this career. 
Coordinator 
Gonzalo de Miguel Vela 
Professors 
Javier Portillo García Gonzalo de Miguel Vela (coordinador) gonzalo@grpss.ssr.upm.es José Luis Sanz González Santiago Zazo Bello Juan Alberto Besada Portas 
Syllabus 
Presentation . Tema 1. Introduction to signals and systems 1.1. Signal concept: Contionuous time and discrete time signals. 1.2. Basic operations with signals: sum, product and time variable transformations 1.3. Basic signals: sinusoidal, exponential, unit impulse, unit step, ramp 1.4. Characteristics and paramenters of the signals:mean value, peak value, energy, power, periodicity, symmetries 1.5. System concept. System association. Linear and time invariant (LTI) systems 1.6. Differentia (difference) equationswith initial rest conditions as LTI systems Tema 2. LTI systems 2.1. Characterisation of discrete time LTI systems using the impulse response. Convolution 2.2. Realisation of the convolution in discrete time 2.3. Characterisation of continuoustime LTI systems using the impulse response. Convolution . 2.4. Realisation of the convolution in continuous time 2.5. Convolution properties: Unit element, conmutative, associative, distributive, differentitation, shifting 2.6. LTI system properties: Memory, invertibility, causality and stability Tema 3. Fourier Transform of continuous time signals 3.1. Complex exponentials and LTI systems. Eigenfunctions and frequency response 3.2. Fourier series of periodic signals 3.3. Periodic signals and LTI systems 3.4. Introduction to Fourier Transform from the Fourier Series 3.5. Definition and existence conditions 3.6. Generalized Fourier Transform 3.7. Properties of the Fourier Transform. Applications 3.8. Fourier transform of Periodic signals. Relationship with the Fourier Series. Poisson sum formula 3.9. Analysis of systems described by differential equations. Computing the frequency response and the impulse response 3.10 Introduction to Laplace transform (bilateral) 3.10.1 Concept of Region Of Convergence 3.10.2 Some properties: linearity, delay 3.10.3 Analysis of rational Laplace transforms. Concepts of pole and zero 3.10.4 Properties of LTI systems in the transform domain: stability, causality and invertibility Tema 4. Transformada de Fourier (TF) de señales en tiempo discreto 4.1. Complex exponentials and LTI systems. Eigenfunctions and frequency response 4.2. Fourier series of periodic signals 4.3. Periodic signals and LTI systems 4.4. Introduction to Fourier Transform from the Fourier Series 4.5. Definition and existence conditions 4.6. Generalized Fourier Transform 4.7. Properties of the Fourier Transform. Applications 4.8. Fourier transform of Periodic signals. Relationship with the Fourier Series. Poisson sum formula 4.9. Analysis of systems described by differenceequations. Computing the frequency response and the impulse response 4.10 Introduction to Z transform (bilateral) 4.10.1 Concept of Region Of Convergence 4.10.2 Some properties: linearity, delay 4.10.3 Analysis of rational Z transforms. Concepts of pole and zero 4.10.4 Properties of LTI systems in the transform domain: stability, causality and invertibility Tema 5. Sampling: continuous time signal representationfrom its equiespaced samples 5.1. Ideal sampling. Nyquist sampling theorem, time interpolation and spectral aliasing 5.2. Natural sampling and instantaneous sampling 5.3. Discrete time simulation of continuous time systems 
Bibliography 
Básica Signals and Systems, (2ª edición) A.V. Openheim, A.S. Willsky S.H. Nawab,editarial PrenticeHall, y dentro de éste, total o parcialmente, los capítulos 17. Complementaria Signals and Systems Simon Haykin, Barry Van Been, editorial John Wiley and Sons, Inc. 
Course's Web 
www.gcs.ssr.upm.es 
Department's Web 
www.ssr.upm.es 

