The student:
- can classify signals and systems
- can find the zero-input solution of a linear differential equation, given initial conditions
- can find the zero-state 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
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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 an individual assignment (Pass/Fail) and a test of 180 min on all topics.
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