Lecture 3&4
I learned about Laplace and Z transform!
There is a homework due next tuesday (7/17/12): Solve analytically for an impulse and ramp response then plot using Matlab. Got the first part done :)

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Lecture 3&4
I learned about Laplace and Z transform!
There is a homework due next tuesday (7/17/12): Solve analytically for an impulse and ramp response then plot using Matlab. Got the first part done :)
Lecture 2
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"
--> Should review Taylor Series and Integration By Parts (IBP)!
Lecture 1- Welcome to Signals & Systems (& Controls)
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).
See how a problem of dry friction is not a linearizable problem.