#mae143a

I learned about Laplace and Z transform!

Quiz 1 questions: 

dry friction problem (conveyor belt) is non linearizable.

Laplace transform method is to solve ODE.

Z transform method is for discrete and difference equations.

Objectives:

--> Know how to generally linearize any problem!

--> Should review Partial fraction. Get Algebra book!

--> Should review complex number/plane for signal analysis. Riemann sphere! (a point at infinity is actually a singular point)=>Mind blowing, no?!

--> Laplace and "Dirac Delta"

Book: Numerical Renaissance by Professor Thomas Bewley

Chapter 17: Transforms based methods

3 types of transforms:

Fourier transform (for continuous or discrete signals and signals on infinite/bounded domains), built on sinusoidal basis functions-->Analysis of the various sinusoidal components of a signal at different spacial frequencies or temporal wavenumbers.

Laplace transform (for continuous on semi-infinite domains and differential systems with IC t=0), built on exponential basis functions-->Analysis of the evolution of continuous-time systems and discrete-time systems.

Z transform (for discrete signals on semi-infinite domains and difference systems), built on polynomial basis functions

They are linear and invertible-->practical utility of analysis, filtering, and control techniques.

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Fourier transform forms: 

infinite series

integral form

finite series

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See examples on how to describe a physical problem into ODE then apply Laplace transforms to solve. (Linearization). Note the number of input/output. (SISO/MIMO model).