set_1_fourier_series

set_1_fourier_series - class notes, M. Rodwell, copyrighted...

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Unformatted text preview: class notes, M. Rodwell, copyrighted 2011 ECE 2C, notes set 1: Fourier Series Mark Rodwell University of California, Santa Barbara rodwell@ece.ucsb.edu 805-893-3244, 805-893-3262 fax class notes, M. Rodwell, copyrighted 2011 Fourier Transforms and Fourier Series intuition. and ing understand better want We this. do to tools efficient need We equations. al differenti partial and ordinary solve often must We ? Why class notes, M. Rodwell, copyrighted 2011 Solving Simple Differential Equations class notes, M. Rodwell, copyrighted 2011 Solving Simple Differential Equations class notes, M. Rodwell, copyrighted 2011 Phasors class notes, M. Rodwell, copyrighted 2011 Differential Equations: Easy to Solve with Sinewaves class notes, M. Rodwell, copyrighted 2011 Sinewaves and Complex Exponentials 2 ) ( ) sin( ) sin( 2 __________ __________ ) sin( ) cos( ) sin( ) cos( 2 ) ( ) cos( ) cos( 2 __________ __________ ) sin( ) cos( ) sin( ) cos( ) sin( ) cos( : identity Euler ? it is What ? ith Why work w j e e t t j e e t j t e t j t e e e t t e e t j t e t j t e t j t e e t j t j t j t j t j t j t j t j t j t j t j t j t j t j class notes, M. Rodwell, copyrighted 2011 Sinewaves and Complex Exponentials ls. exponentia of pair a it with driving as same the is wave sine or cosine a th circuit wi a Driving 2 ) ( ) sin( and 2 ) ( ) cos( j e e t e e t t j t j t j t j ) cos( t V V in ) exp( ) 2 / ( ) exp( ) 2 / ( 2 1 j t j V V j t j V V in in applied. with and applied with for solving separately ion, superposit by problem the Solve 1 1 V V V V out out class notes, M. Rodwell, copyrighted 2011 Complex Exponentials: Ignoring the Real Part ) exp( ) exp( || || ) exp( ) ( ) exp( ) exp( || || ) exp( ) ( t j j V t j V t V t j j V t j V t V o u t in V in out out V in in in notes. of page previous from steps though Working : 2 Proof ion. superposit of Principle : 1 Proof output. the of part imaginary the ignore input, complex Apply the ) cos( )} sin( ) Re{cos( } Re{ of part Real t t j t e e t j t j ) cos(...
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set_1_fourier_series - class notes, M. Rodwell, copyrighted...

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