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Cursus: 202001138
202001138
Continuous Linear Systems
Cursus informatie
Cursus202001138
Studiepunten (ECTS)5
CursustypeOnderwijseenheid
VoertaalEngels
Contactpersoondr. C.G. Zeinstra
E-mailc.g.zeinstra@utwente.nl
Docenten
Docent
dr. C.G. Zeinstra
Contactpersoon van de cursus
dr. C.G. Zeinstra
Collegejaar2020
Aanvangsblok
1A
AanmeldingsprocedureZelf aanmelden via OSIRIS Student
Inschrijven via OSIRISJa
Cursusdoelen
  • Student can classify signals and systems
  • Student can find the zero-input solution of a linear differential equation, given initial conditions
  • Student can find the zero-state solution of a linear differential equation given an input signal
  • Student can find the complete solution of a linear differential equation, given initial conditions and input signal
  • Student can determine stability
  • Student knows the convolution representation of LTI systems and can determine stability for general LTI systems
  • Student can transform a differential equation into a state space representation
  • Student can solve state space equations in the time domain
  • Student can determine three different Fourier series representations of periodic signals and determine the dispersion effect of LTI filtering on a periodic signal
  • Student can determine the Fourier transform of a signal, explain the frequency interpretation and state its relationship with Fourier series
  • Student can use properties of the Fourier transform and relate time domain properties and operators to the corresponding frequency domain properties and operators
  • Student can determine the effect of LTI filtering in the frequency domain by means of the transfer function
  • Student can determine unilateral and bilateral Laplace transform of time domain signals
  • Student can explain the relationship between bilateral Laplace transform and the Fourier transform
  • Student can use properties of the Laplace transform and relate time domain properties and operators to the corresponding s domain properties and operators
  • Student can determine the effect of LTI filtering in the s domain by means of the transfer function
  • Student can use the unilateral Laplace transform to convert a linear differential equation in the time domain into an algebraic problem in the s domain, solve this problem and transform it back to the time domain
  • Student can solve state space equations in the s domain and transform it back to the time domain
  • Student can recognise dependency of frequency response on poles and zeros of transfer function
  • Student can explain properties of low pass Butterworth, Chebyshev and elliptic filters
  • Student can apply simple transformation to convert low pass filters to band pass, high pass and notch filters
  • Student is briefly introduced to challenges when going from the continuous to the discrete domain (sampling, quantisation and stability effects). This topic will not be tested
Inhoud
This course starts with a general introduction to continuous linear systems, signals and their properties.
After this general approach, a method to solve general linear differential equations is presented. Stability and the state space representation are further explored.
Periodic signals can often be represented by Fourier series. The effect of LTI filtering of periodic signals is studied.
The Fourier series are generalized to the Fourier transform. Several properties of the Fourier transform are studied, including the effect of LTI filtering.
The Fourier transform can be further generalized to the Laplace transform. Several properties are studied.  The effect of LTI filtering, the role of the Laplace transform in solving linear differential equations and state space equations and stability will be discussed. .
Some topics in analog filter design are presented:  dependency of frequency response on poles and zeros of transfer function, classic low pass filters (Butterworth, Chebyshev and elliptic) are presented and how they can be transformed into general filters.
Finally, the challenges of the transition from the continuous to the discrete domain are briefly discussed (sampling, quantisation and stability effects).This topic will not be tested, but serves as a natural transition to Modules 6 and 8. Module 8 will pick up the discrete counterpart of CLS, including sampling and quantisation.
Participating study
Bachelor Electrical Engineering
Module
Module 5
Verplicht materiaal
Book
Signal Processing and Linear Systems, B.P. Lahti, Oxford University Press, ISBN 978-0-19-539257-9
Aanbevolen materiaal
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