Linear System Applications and Transformations
Explore the practical applications and properties of linear systems, including communication systems, circuits, and signal processing. Learn about the transformation processes and their significance in various fields. Discover the concept of PM2.5 applications and the relationship between variables in linear systems.
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Presentation Transcript
What are we going to learn? Hung-yi Lee
A system has input and output (function, transformation, operator) System Speech Recognition System How are you Dialogue System (e.g. Siri, Alexa) How are you I am fine Communication System Hello Hello
Linear System Linear system have two properties 1. Persevering Multiplication Linear System Linear System x y kx ky 2. Persevering Addition Linear System x1 y1 x1+x2 y1+y2 Linear System Linear System x2 y2
Linear System x2 x System Linear system have two properties 1. Persevering Multiplication Linear System Linear System k2x2 kx2 x2 x kx 2. Persevering Addition Linear System ?1 2 ?1 2 ?1+ ?2 ?1+ ?2 Linear System Linear System 2 ?2 ?2 2+ ?2 2 ?1
?1 ?2 ?1+ ?2 ?1 ?2 Linear System System Two properties 1. Persevering Multiplication ?1 ?2 ?1+ ?2 ?1 ?2 ??1 ??2 ??1+ ??2 ??1 ??2 System System 2. Persevering Addition ?1+ ?1 + ?2+ ?2 ?1 ?2 ?1+ ?2 ?1 ?2 System ?1+ ?1 System ?1 ?2 + ?2 ?2 ?1 ?1 ?2+ ?2 ?1+ ?1 ?2+ ?2 System
Applications Most system are (assumed to) be linear Input: voltage source, current source output: voltage and current on the load ( ) Linear Circuit + v i - input output Linear System ( )
Applications Most system are (assumed to) be linear Communication System Linear Channel Transmitter Receiver Linear System ( )
Applications time frequency Fourier Transform ( ) Linear System (Transform)
Applications y: A B C N PM2.5 xK: A B C N K PM2.5 x1 x2 x3 y Linear system y = w1x1 + w2x2 + w3x3 Where do w1, w2 and w3 come from?
Applications P336 of Textbook http://incomebully.com/does-pr- pagerank-still-matter/
Applications - PageRank hyperlink
Applications - Computer Graphics Section 7.9 of Textbook ? ? ? Linear System ? ? ? http://www.c-jump.com/bcc/common/Talk3/Math/Matrices/Matrices.html
What are we going to learn? Beyond vector in Chapter 6 Chapter 1, Chapter 2, Chapter 3 ? ? 3 6 Linear System vector vector ? 9 Does it have solution? Does it have unique solution? How to find the solution? Determinants ( ) Beyond 3 X 3 Different view from high school
What are we going to learn? Simpler Linear System Chapter 4 Change the description How to describe this set ? Linear System Approximation Chapter 7
What are we going to learn? Chapter 5: EigenXXX Enlarge the input Decrease the input ?1 ?2 2?1 2?2 ?1 ?2 0.5?1 0.5?2 Linear System Linear System ?? 2?? ?? 0.5?? Filter
