Signals and Systems
Contents
Description of continuous functions in the time domain, real and idealised signals, complex signals, complex exponential oscillation, step function/signum function, generalised functions (distributions), delta impulse (Dirac pulse), rectangular function, triangular function - Vector spaces and signals, Definition of vector spaces, Euclidean vector spaces/scalar product, vector space, orthogonality, signal spaces, lp norm - description of continuous-time signals in the frequency domain, approximation using exponential oscillations, periodic signals/Fourier series, aperiodic signals/Fourier transform, Properties of the Fourier transform, examples of the Fourier transform - Laplace transform, right-sided Laplace transform, two-sided Laplace transform, properties of the right-sided (one-sided) Laplace transform, solution of linear differential equations using the Laplace transform - signal transmission using linear invariant systems, Basic response, properties of linear time-invariant systems, the transfer function, impulse response of an LTI system, relationship between h(t) and H(p), step response of an LTI system, causality, stability, properties of systems, ideal filters - special signal classes, analytical signal, pulse amplitude modulated signals/sampling theorem - discrete-time signals, numerical sequences, important discrete-time signals, frequency domain representation of discrete-time signals, z-transform - signal transmission through linear time-invariant discrete systems, Basic response, properties of linear time-invariant discrete systems, the transfer function, classification of discrete-time LTI systems in terms of stability, impulse response of a discrete LTI system, relationship between h(n) and H(z), causality, stability, properties of systems - analogies, Bilinear transformation - special classes of discrete-time systems, linear differential equations with constant coefficients, discrete-time systems described by linear difference equations, synthesis of difference equations - state-space description of finite-order discrete-time LTI systems, state equations, solution of the state equations, stability, normal forms for single-magnitude systems, observability, controllability - state-space description of finite-order continuous-time LTI systems, state equations, solution of the state equations, stability, other properties.
Dates
The Signals and Systems course is offered every summer semester. Please refer to the lecture announcement for the start of lectures and lecture times.
Examination
The examination is offered twice a year during the lecture-free period. The exact dates and locations are determined by the Examination Office and announced on the homepage and in Moodle. Students have 3 hours to complete the written examination. Relevant aids such as books, laptops, calculators etc. are not permitted. Please bring with you: Paper, pens and a ruler if necessary. The collection of formulae already used in the exercise will be handed out at the beginning of the exam. Depending on the subject, registration for the exam is done via the Examination Office or via Moodle. If you do not have to register via the examination office and therefore via Moodle, you can register via Moodle up to seven days before the exam. A list of successfully registered students will be published in Moodle in good time before this date. Successful registration can also be checked in Moodle on the registration page using the checkbox. You can cancel your enrolment there at any time. As soon as the registration deadline in Moodle has expired and the number of students registered for the exam has been determined, the lecture hall plans with fixed seat assignments will be created and announced both in Moodle and here.
Moodle
The course is also available online. All students at the University of Wuppertal can register free of charge on the Moodle learning platform to access additional teaching materials. This includes, for example, tests accompanying the course and an online forum where questions can be asked and answered online.
You will find the link to the respective Moodle course in the current lecture announcement.
