Linear Systems 🔗
Linear systems, or systems defined by a linear operator, can be used to model many real-world systems, and find applications in control theory, signal processing, and telecommunication technologies, among other areas. The goal of this course is to provide the students with the theoretical and methodological knowledge necessary to work with continuous and discrete-time signals and LTI (linear and time-invariant) systems in both time and frequency domains.
Upon attending this course students will acquire:
Theoretical knowledge of signals and systems representation in the frequency domain.
Capacity for analyzing signals and systems in the frequency domain, with emphasis in applications related to communications.
Use of fundamental tools for the analysis of signals and systems in the frequency domain, with emphasis in communications.
Program
Unit 0. Review of Signals and Systems in the Time-Domain
Unit 1. Fourier Transform: continuous-time signals
Periodic signals: Fourier series representation
The continuous-time Fourier transform and its properties
Analysis of linear time-invariant systems
Applications: Filtering and systems described by linear differential equations
Unit 2. Fourier Transform: discrete-time signals
Discrete-time complex exponentials
Fourier series representation of discrete-time periodic signals
The Fourier transform of discrete-time sequences and comparison with continuous-time
Unit 3. Sampling in the time-domain
The sampling theorem and optimal signal reconstruction
Discrete-time processing of continuous-time signals
Decimation and interpolation
Unit 4. Discrete Fourier Transform (DFT)
Finite-length signals and periodic signals: DFT
Connection between Discrete Fourier Transform and the Fourier Transform
Efficient implementation and applications
Unit 5. The z-transform
Definition and connection with Fourier Transform
The region of convergence and its properties: zero-pole diagrams
Analysis and characterization of unstable LTI systems
Course material
Alan V. Oppenheim, Alan S. Willsky, with S. Hamid. Signals and Systems. 2nd edition. Prentice Hall. 1996.
Class notes (in Spanish). Available online soon.