ECE 202 Lesson 5

ECE 202 Lesson 5 - the positive and negative half-cycles...

Info iconThis preview shows pages 1–11. Sign up to view the full content.

View Full Document Right Arrow Icon
Circuit Theory II Lesson 5 Objective: To introduce the Fourier series and to present the various types of symmetry in periodic signals. Sections 16.1 to 16.3, pp. 758-767
Background image of page 1

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

View Full DocumentRight Arrow Icon
2 Fourier Series ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 + + + = = = = = = + + = ± = T t t k T t t k T t t n n n n dt t k t f T b dt t k t f T a dt t f T a T t n b t n a a t f nT t f t f 0 0 0 0 0 0 0 0 0 1 0 1 0 sin 2 cos 2 1 2 sin cos ϖ π υ (16.1) (16.3) (16.4) (16.5) (16.2)
Background image of page 2
3 Types of Symmetry Even-Function Symmetry ( 29 ( 29 t f t f - = Odd-Function Symmetry ( 29 ( 29 t f t f - - = No sine components present in Fourier Series No cosine components present in Fourier Series
Background image of page 3

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

View Full DocumentRight Arrow Icon
4 Types of Symmetry Half-Wave Symmetry ( 29 ( 29 2 T t f t f - - = When the function is multiplied by –1 and shifted one-half period, the same function is obtained. No d.c. term and no even-harmonics present in Fourier Series
Background image of page 4
5 Types of Symmetry Quarter-Wave Symmetry 1. The function has half-wave Symmetry 2. There is symmetry about the midpoint of
Background image of page 5

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

View Full DocumentRight Arrow Icon
Background image of page 6
Background image of page 7

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

View Full DocumentRight Arrow Icon
Background image of page 8
Background image of page 9

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

View Full DocumentRight Arrow Icon
Background image of page 10
Background image of page 11
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: the positive and negative half-cycles Need only integrate only over a quarter period 6 Triangle Wave Even symmetry Odd symmetry Half-wave symmetry Quarter-wave symmetry yes no + + +- 2 2 2 5 5 cos 3 3 cos 1 cos 4 2 x x x Triangle Wave 7 ( 29 2 f x -8 Right Triangular Wave Even symmetry Odd symmetry Half-wave symmetry Quarter-wave symmetry yes no -+- 3 3 sin 2 2 sin 1 sin 2 x x x Right Triangular Wave 9 ( 29 2 f x T--10 Saw Tooth Wave Even symmetry Odd symmetry Half-wave symmetry Quarter-wave symmetry yes no + + +- 3 3 sin 2 2 sin 1 sin 2 x x x Sawtooth Wave 11 ( 29 2 f x T--...
View Full Document

This note was uploaded on 03/12/2009 for the course ECE 202 taught by Professor Deanschmidlin during the Fall '08 term at UMass Dartmouth.

Page1 / 11

ECE 202 Lesson 5 - the positive and negative half-cycles...

This preview shows document pages 1 - 11. Sign up to view the full document.

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