FourierSeries1

# FourierSeries1 - Fourier Series In Lecture 2, we discussed...

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Fourier Series In Lecture 2, we discussed basis functions and signal decomposition: The idea that a signal can be represented as a sum of weighted basis functions. These basis functions are usually easy to understand and represent. An important set of basis functions are the sinusoids.

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Fourier Series ) cos( 0 θ + t w A Typical sinusoid: In particular, PERIODIC signals can be decomposed into a sum of sinusoids which are harmonically related. ,.... ) 4 , 3 , 2 , ( 0 0 0 0 w w w w Recall that harmonically related sinusoids are orthogonal to each other.
Periodic Signals-Properties Smallest value of T 0 is the period. t T t f t f all for ) ( ) ( 0 + = f(t) can be generated by periodic extension of any segment of duration T 0 (period) Area under f(t) is the same for any interval of duration T 0 real , ) ( ) ( 0 0 b a b a dt t f dt t f T b b T a a = + +

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The Fourier Series frequency) al (fundament 2 2 ersion) (compact v ) cos( ) ( ) sin( ) cos( ) ( tion representa signal for formula general ) ( 0 0 0 1 0 0 1 0 0 0 T F w where t nw C C t f t nw b t nw a a t f a t f n n n n n n N N n n n π θ φ = = + + = + + = = = = - =
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## This note was uploaded on 06/08/2009 for the course BME 513 taught by Professor Yen during the Spring '07 term at USC.

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FourierSeries1 - Fourier Series In Lecture 2, we discussed...

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