This lecture covers an introduction to the theory of continuous signals and continuous linear time-invariant systems. At the beginning, elementary signals, the delta impulse, the convolution, and the correlation of signals are discussed. Subsequent to this, the frequency domain representation of signals by means of Fourier and Laplace transform is introduced, including the theorems and correspondences of these transforms. Next, the time domain description of linear time-invariant systems by impulse response and convolution, differential equations, and state-space representation is presented. In addition to this, the description of systems in the frequency domain using eigen functions, the transfer function, the system function, and state-space representation is given. Furthermore, linear time invariant systems with initial conditions are considered. Following, after linear phase, minimum phase, idealized, and all-pass system have been introduced, causality, the Hilbert transform, stability and feed back systems are discussed. The lecture closes with an overview of sampling systems and the sampling theorem for lowpass and bandpass signals.
For this lecture, a basic knowledge of electric circuits with resistance, capacitance and inductance is presupposed. Furthermore, knowledge of complex-valued pointers and transfer behavior of simple linear networks is required. This can be gained for example from the two modules "Fundamentals of Electrical Engineering I" and "Fundamentals of Electrical Engineering II" or by a combination of the modules "Introduction to Information and Communication Technologies" and "Electronics and Circuit Design". Students which did not attend these lectures (e.g. from study course Computational Engineering) can obtain the required prerequisites as well by private studies with the help of chapter 2 about physical fundamentals of electric circuits and chapter 3 about passive networks from the book "Elektronik und Schaltungstechnik" written by Oehme, Huemer, Pfaff and published by Hanser Verlag, München 2007.
Course materials can be downloaded via StudOn
The book to the lecture: B. Girod, R. Rabenstein, A. Stenger, Einführung in die Systemtheorie, B. G. Teubner Verlag, Stuttgart
The course finishes with an exam that has a length of 90 minutes. For support, a hand-written
formulary of one DIN A4 page (two-sided)
length and a non-programmable calculator may be used. A computer-generated formulary is not permitted. The tables for Laplace- and Fourier-transform will be provided with the exam.