Calculus I, Linear Algebra, Physics

The objectives of the course are 1) to introduce the basic concepts of signals and systems, and 2) as an application of the above, to introduce the basic concepts of electric circuit analysis. 1.- Specific objectives: - Signal concepts - Signal representation of physical magnitudes - Classification of signals: continuous and discrete time - Time operations: time reversal, scaling, time-shift - Signal operations: integration, differentiation - Special signals: unit impulse and step; exponentials. - Signal Synthesis as linear spaces composition. - System concepts - Interconnection: series, parallel, feedback - Properties: memory, causality, time invariance, stability, linearity - Impulse response - Signal Processing - Convolution, Filtering - Application to Electric Circuit Analysis - Kirchhoff Laws - Sinusoidal steady-state analysis. 1.2.- Instrumental - Programming - Signal and Systems simulation - Analysis of basic electric circuits. - Using lab. equipment to monitor the circuit implementations

Topic 1. Signals Properties of signals Operations with signals Topic 2. Systems Properties of systems Interconnection of systems Linear and Time Invariant Systems (LIT) Topic 3. Resistive circuits Resolution of circuits by nodes and meshes Source transformation: Thèvenin and Norton Topic 4. Sinusoidal steady state Passive elements in the sinusoidal steady state: phasors and impedance Kirchhoff's laws in the phasor domain. Circuit analysis Topic 5. Linear circuits as linear and time invariant systems. Passive circuit elements First order analogue filters

The course consists of the following elements: lectures, exercises, and laboratories: LECTURES (2.5 ECTS) The lectures provide the students with explanation of the core material in the course. Numerous examples of signals and systems, their properties and behavior will be given using backboard and audiovisual support (slides, video, ...). In the second part of the course, the analysis and design of simple electric circuits will be discussed as a practical example to understand the application of the mathematics for lineal systems. EXERCISES (2.5 ECTS) Students will be encouraged to solve the exercises and to organize themselves forming small groups that will have to solve some basic problems given in advance. LABORATORIES (1 ECTS) The laboratories provide the students with hands-on experience to understand the fundamentals of signals, systems and circuits. Some basic signals processing demos and simple electric circuits will be analyzed. Students will also learn how to use of Matlab for signal processing and circuit analysis. Students must come prepared for the laboratory sessions.