Signals and systems

The course Signals and Systems covers the basics of signal and system analysis, adapted to the knowledge and demands of engineers, and includes the mathematical skills for handling matrices and matrix equations.

Topics that are covered in the signals part include convolution, Fourier series, Fourier transform, Discrete Fourier Transform and the Sampling Theorem Students learn that the representation of signals in frequency domain is just as important as the time domain representations they already know. In the systems part the focus lies on dynamical systems that convert input signals into output signals as is essential in many engineering applications and forms the basis of controller design. Different representations of systems are discussed including state-space models, transfer functions and frequency response functions (FRF), which will be connected to Fourier series, Fourier transform, Laplace transform of input and output signals.

The course begins with an introduction on the relevance of signal analysis and the use of frequency domain characterizations. The course starts by introducing some basic concepts of signals including convolution. Then it focuses on the decomposition of periodic signals into harmonic components via the Fourier series. The concepts are extended to general aperiodic signals, leading to the Fourier Transform. Additional topics such as the Discrete Fourier Transform and the Sampling Theorem are covered to enable students to use these concepts in real-life applications. This is the main focus of the project.

Based on this knowledge the step is then made towards system representations and analysis. Input/output (I/O) measurements form the basic starting point to obtain the Frequency Response Function (FRF) of a system. The FRF as a system representation is then connected to alternative system descriptions. The connection between FRF and state-space models via the transfer function is discussed in detail. The use of state-space models and transfer functions motivates a deeper understanding of mathematical analysis of matrix equations. This leads to a discussion of many important concepts including rank, eigenvalues, and eigenvectors of matrices, characteristic equation, the concept of basis (L5c) in R^n and coordinate transformations, similarity of matrices, diagonalization and (real) Jordan form. The connections between these mathematical notions and signal and system analysis will be clarified through various examples.

For Student Mobility Alliance students: This course requires knowledge of: This course requires knowledge of: - complex numbers, - differentiation; - integration; - solving systems of linear equations, i.e., solve Ax = b; - inverse of a matrix, determinant of a matrix; - linear combination of vectors; and - first-order differential equations. The lectures will mostly be delivered in a hybrid format allowing you to follow online. The course assessment will be through a project and an exam with weights for the final grade of 25% and 75%, respectively. The project also requires group work. The final exam is a written on campus exam

• To analyze and manipulate signals in both discrete and continuous time by applying fundamental transformations and determining key system properties such as causality, memory, linearity, and time-invariance.
• To characterize linear time invariant (LTI) systems using convolution and compute their responses to exponential and sinusoidal inputs in both continuous and discrete time.
• To apply continuous and discrete-time Fourier series and Fourier transforms to efficiently compute signal representations and solve real-world problems involving sampled signals.
• To write ordinary differential equations of LTI systems in state-space form and compute their transfer functions, as well as those of systems in cascade and feedback loops.
• To perform linear algebra operations such as computing the rank, null space, and column space of matrices, as well as computing eigenvalues and eigenvectors.
• To compute time and frequency responses of LTI systems in state-space form using coordinate transformations and the Laplace transform.
• To determine the poles and zeros of transfer functions, and sketch and interpret Bode plots.

Je moet voldoen aan de volgende eisen

• Geen van onderstaande cursussen mag zijn behaald
• Linear Algebra and Applications (2DBI00)
• Vector Analysis (32VAN)
• Signals and systems (4CB00)
• Systems (5ESB0)

• Signals and Systems (ISBN 9781292025902)
• Linear Algebra and Its Applications (ISBN 9781292351216)
• Via Canvas
• Feedback Control of Dynamic Systems (ISBN 9781292274522)
• Linear Systems Theory (ISBN 9780691179575)