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Systems and Signals
Engineering & Social Sciences Program
Madrid, Spain
Dates: early Sep 2025 - mid Dec 2025
Systems and Signals
OVERVIEW
CEA CAPA Partner Institution: Universidad Carlos III de Madrid
Location: Madrid, Spain
Primary Subject Area: Electrical Engineering
Instruction in: English
Course Code: 15545
Transcript Source: Partner Institution
Course Details: Level 300
Recommended Semester Credits: 3
Contact Hours: 42
Prerequisites: Calculus I
Calculus II
Linear Algebra
Differential Equations
DESCRIPTION
The goal of the 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 the time and frequency domain.
Unit 1. Signals
1.1. Definition and introduction to biomedical signals
1.2. Properties of the signals: regularity, symmetry, etc.
1.3. Characterization of signals: energy and average power.
1.4. Basic operations with signals: time reversal, scaling, shifting.
1.5. Introduction to random processes.
Unit 2. Systems
2.1. Introduction. Examples of systems in biomedical engineering.
2.2. Properties of the systems: causality, stability, time invariance, linearity.
2.3. Linear Time-Invariant Systems (LTI).
2.4. Convolution.
2.5. Properties of LTI systems.
2.6. Random Processes and LTI systems.
Unit 3. Fourier Series Representation of Continuous-Time Periodic Signals and sequences
3.1. Introduction: Response of LTI Systems to Complex Exponentials.
3.2. Fourier Series Representation of Continuous-Time Periodic Signals: Analysis and Synthesis Equations.
3.3. Properties of Continuous-Time Fourier Series. Examples.
3.4. Fourier Series Representation of Discrete-Time Periodic Signals: Analysis and Synthesis Equations.
3.5. Properties of Discrete-Time Fourier Series and comparisons with the Continuous Case. Examples.
Unit 4. The Continuous-Time Fourier Transform
4.1. Introduction.
4.2. The Continuous-Time Fourier Transform for Aperiodic Signals.
4.3. The Continuous-Time Fourier Transform for Periodic Signals.
4.4. Properties of the Continuous-Time Fourier Transform. Examples. Parseval's Theorem.
4.5. The Discrete-Time Fourier Transform. Properties.
4.6. Characterization of random processes in the frequency domain.
Unit 5. Sampling
5.1. Introduction.
5.2. The Sampling Theorem.
5.3. Reconstruction of Continuous-Time Signals from Its Samples Using Interpolation.
5.4. Discrete-Time Processing of Continuous-Time Signals.
5.5. Decimation and Interpolation.
5.6. Examples and applications.
Unit 6. Discrete Fourier Transform
6.1. Introduction.
6.2. Sampling of the Fourier Transform.
6.3. Discrete Fourier Transform.
6.4. Properties.
6.5. Circular Convolution and Linear Convolution.
Unit 7. The z-Transform
7.1. Introduction.
7.2. The z-Transform.
7.3. The Region of Convergence. Properties.
7.4. The Inverse z-Transform.
7.5. Properties of the z-Transform.
7.6. Evaluation of the Frequency Response from the Pole-Zero Plot.
7.7. Analysis and Characterization of LTI Systems Using the z-Transform.
7.8. Block Diagram Representation.
Unit 1. Signals
1.1. Definition and introduction to biomedical signals
1.2. Properties of the signals: regularity, symmetry, etc.
1.3. Characterization of signals: energy and average power.
1.4. Basic operations with signals: time reversal, scaling, shifting.
1.5. Introduction to random processes.
Unit 2. Systems
2.1. Introduction. Examples of systems in biomedical engineering.
2.2. Properties of the systems: causality, stability, time invariance, linearity.
2.3. Linear Time-Invariant Systems (LTI).
2.4. Convolution.
2.5. Properties of LTI systems.
2.6. Random Processes and LTI systems.
Unit 3. Fourier Series Representation of Continuous-Time Periodic Signals and sequences
3.1. Introduction: Response of LTI Systems to Complex Exponentials.
3.2. Fourier Series Representation of Continuous-Time Periodic Signals: Analysis and Synthesis Equations.
3.3. Properties of Continuous-Time Fourier Series. Examples.
3.4. Fourier Series Representation of Discrete-Time Periodic Signals: Analysis and Synthesis Equations.
3.5. Properties of Discrete-Time Fourier Series and comparisons with the Continuous Case. Examples.
Unit 4. The Continuous-Time Fourier Transform
4.1. Introduction.
4.2. The Continuous-Time Fourier Transform for Aperiodic Signals.
4.3. The Continuous-Time Fourier Transform for Periodic Signals.
4.4. Properties of the Continuous-Time Fourier Transform. Examples. Parseval's Theorem.
4.5. The Discrete-Time Fourier Transform. Properties.
4.6. Characterization of random processes in the frequency domain.
Unit 5. Sampling
5.1. Introduction.
5.2. The Sampling Theorem.
5.3. Reconstruction of Continuous-Time Signals from Its Samples Using Interpolation.
5.4. Discrete-Time Processing of Continuous-Time Signals.
5.5. Decimation and Interpolation.
5.6. Examples and applications.
Unit 6. Discrete Fourier Transform
6.1. Introduction.
6.2. Sampling of the Fourier Transform.
6.3. Discrete Fourier Transform.
6.4. Properties.
6.5. Circular Convolution and Linear Convolution.
Unit 7. The z-Transform
7.1. Introduction.
7.2. The z-Transform.
7.3. The Region of Convergence. Properties.
7.4. The Inverse z-Transform.
7.5. Properties of the z-Transform.
7.6. Evaluation of the Frequency Response from the Pole-Zero Plot.
7.7. Analysis and Characterization of LTI Systems Using the z-Transform.
7.8. Block Diagram Representation.