FourierSeries1

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

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
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.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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.
Background image of page 2
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 = + +
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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 = = + + = + + = = = = - =
Background image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 06/08/2009 for the course BME 513 taught by Professor Yen during the Spring '07 term at USC.

Page1 / 26

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

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online