Linear systems: System properties (stability, causality, time-invariance), block diagrams, impulse response, convolution.
Frequency description: Frequency response, frequency function, filtering.
Transform methods for time continuous and time discrete signals and systems, Fourier tranforms, Laplace transform and Z-transform.
Sampling, pulse amplitude modulation and sampled systems.
The aim is to provide basic knowledge about continuous-time and discrete-time linear systems and their dynamical properties.
After completing the course You should be able to
- understand the meaning and practice relevance of system properties such as linearity, time invariance, stability and causality.
- use mathematical transform methods to analyze linear time invariant systems, both continuous time and discrete time systems and combinations thereof. Especially:
- analyze continuous time systems using Fourier transform as well as unilateral and bilateral Laplace transform.
- analyze discrete time systems using Discrete Time Fourier Transform as well as unilateral and bilateral Z-transform.
- interprete, analyze and synthesize continuous time systems in the form of electrical circuits and discrete time systems in the form of block diagrams or program code.
- describe LTI systems and calculate their output signal, using impulse response, convolution, transfer function and frequency response.
- calculate poles and zeros of an LTI system and relate their position to system properties like transfer function and frequency response.
- in a simple way calculate the output signal for a stationary sinusoid.
- use mathematical software like MATLAB to analyze and simulate LTI systems and for basic filter design.
- describe and calculate the output of sampling and reconstruction (pulse amplitude modulation), for arbitrary input signals, sampling frequencies and pulse shapes, in the time and frequency plane.
- know about the theoretical and practical relevance of the sampling theorem.
- analyze sampled systems.
- know about filter concepts like bandwidth and ideal filter types.