ES240_FourierSeries

# ES240_FourierSeries - ES 240: Scientific and Engineering...

This preview shows pages 1–8. Sign up to view the full content.

ES 240: Scientific and Engineering Computation. Introduction to Fourier Series Trigonometric Fourier Series Trigonometric Fourier Series Outline Introduction Visualization Theoretical Concepts Qualitative Analysis Example Class Exercise

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

View Full Document
ES 240: Scientific and Engineering Computation. Introduction to Fourier Series Introduction Introduction What is Fourier Series? Representation of a periodic function with a weighted, infinite sum of sinusoids. Why Fourier Series? Any arbitrary periodic signal, can be approximated by using some of the computed weights These weights are generally easier to manipulate and analyze than the original signal
ES 240: Scientific and Engineering Computation. Introduction to Fourier Series Periodic Function Periodic Function What is a periodic Function? A function which remains unchanged when time-shifted by one period f(t) = f(t + T o ) for all values of t What is T o T o T o

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

View Full Document
ES 240: Scientific and Engineering Computation. Introduction to Fourier Series Properties of a periodic function 1 Properties of a periodic function 1 A periodic function must be everlasting From –∞ to ∞ Why? Periodic or Aperiodic?
ES 240: Scientific and Engineering Computation. Introduction to Fourier Series Properties of a periodic function Properties of a periodic function You only need one period of the signal to generate the entire signal Why? A periodic signal cam be expressed as a sum of sinusoids of frequency F 0 = 1/T 0 and all its harmonics

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

View Full Document
ES 240: Scientific and Engineering Computation. Introduction to Fourier Series Visualization Visualization Can you represent this simple function using sinusoids? Single sinusoid Single sinusoid representation representation
ES 240: Scientific and Engineering Computation. Introduction to Fourier Series Visualization Visualization

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 09/04/2011 for the course ES 240 taught by Professor Dr,uche during the Spring '11 term at Montgomery College.

### Page1 / 23

ES240_FourierSeries - ES 240: Scientific and Engineering...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online