EE3TP4_13b_FourierSeriesProperties_v2_Lecture18

# EE3TP4_13b_FourierSeriesProperties_v2_Lecture18 - Fourier...

This preview shows pages 1–31. Sign up to view the full content.

Fourier Series Expansion x t = k =−∞ c k e jk ω 0 t Fourier Series (Complex Exponential Form) x t = A 0 k = 1 A k cos 0 t θ k Fourier Series (Trigonometric Form) These are 3 different forms for the same expression. x t = a 0 k = 1 [ a k cos 0 t  b k sin 0 t ] Fourier Series (Trigonometric Form) T = 2π/ω 0 ω 0 = fundamental frequency (rad/sec)

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

View Full Document
x t = k =−∞ c k e jk ω 0 t c k = 1 T t 0 t 0 T x t e jk ω 0 t dt Complex Exponential Form
Fourier Series Trigonometric Form f t = a 0 n = 1 [ a n cos n 0 t  b n sin n 0 t ] a n = 2 T T f t cos n 0 t dt n 0 b n = 2 T T f t sin n 0 t dt n 0 a 0 = 1 T T f t dt We can derive these results in the same way as the complex exponential case using orthogonal functions!

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

View Full Document

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

View Full Document

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

View Full Document

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

View Full Document
f(t) = 1 for t = [-T/2, T/2]

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

View Full Document
Fourier Series Properties

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

View Full Document

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

View Full Document

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

View Full Document

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

View Full Document
Fourier Series x t = k =−∞ c k e jk ω 0 t c k = 1 T t 0 t 0 T x t e jk ω 0 t dt T = 2π/ω 0 ω 0 = fundamental frequency (rad/sec) This is true for a very wide class of

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

View Full Document

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

View Full Document

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

View Full Document

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

View Full Document

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 02/01/2011 for the course ECE 3TP4 taught by Professor Drterrencetodd during the Fall '10 term at McMaster University.

### Page1 / 31

EE3TP4_13b_FourierSeriesProperties_v2_Lecture18 - Fourier...

This preview shows document pages 1 - 31. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online