
The student:
 can classify signals and systems
 can find the zeroinput solution of a linear differential equation, given initial conditions
 can find the zerostate solution of a linear differential equation given an input signal
 can find the complete solution of a linear differential equation, given initial conditions and input signal
 can determine stability
 knows the convolution representation of LTI systems and can determine stability for general LTI systems
 can transform a differential equation into a state space representation
 can solve state space equations in the time domain
 can determine three different Fourier series representations of periodic signals and determine the dispersion effect of LTI filtering on a periodic signal
 can determine the Fourier transform of a signal, explain the frequency interpretation and state its relationship with Fourier series
 can use properties of the Fourier transform and relate time domain properties and operators to the corresponding frequency domain properties and operators
 can determine the effect of LTI filtering in the frequency domain by means of the transfer function
 can determine unilateral and bilateral Laplace transform of time domain signals
 can explain the relationship between bilateral Laplace transform and the Fourier transform
 can use properties of the Laplace transform and relate time domain properties and operators to the corresponding s domain properties and operators
 can determine the effect of LTI filtering in the s domain by means of the transfer function
 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
 can solve state space equations in the s domain and transform it back to the time domain
 can recognize dependency of frequency response on poles and zeros of transfer function
 can explain properties of low pass Butterworth, Chebyshev and elliptic filters
 can apply simple transformation to convert low pass filters to band pass, high pass and notch filters



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.
Module 8 will pick up the discrete counterpart of CLS, including sampling.
Assessment
The CLS grade is determined by a test of 180 min on all topics and if you do not pass, there will be a resit of 180 min.





Bachelor Electrical Engineering 
  Required materialsBookSignal Processing and Linear Systems, B.P. Lahti, Oxford University Press, ISBN 9780195392579 

 Recommended materialsInstructional modesAssignment
 Lecture
 Self study without assistance
 Tutorial

 TestsContinuous Linear Systems


 