5 f x 1 1 2 2 1 05 1 2 10 10 15 15 1 0 1x0 0x1 2 05 05

Info iconThis preview shows page 1. Sign up to view the full content.

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

Unformatted text preview: e on [- 1,1] 101 term approximaSon to square wave on [- 1,1] 1.5 1.5 1.5 1.0 1.0 0.5 -2 -1 -0.5 1.5 1.0 0.5 1 2 , -2 -1 -0.5 2 -2 -1 -0.5 -1.0 -1.0 -1.5 1.5 1.0 1.0 0.5 -1 , 0.5 1.5 1.0 2 -1.5 1.5 1 -1.0 -1.5 -2 1.0 0.5 1 , -0.5 0.5 1 2 , -2 -1.0 -1 -0.5 f ( x) = ⇢ -1 1 2 , -2 -1 -0.5 1 2 -1.0 -1.0 -1.5 -1.5 1 0 1x<0 0x<1 2 -0.5 0.5 1 -1.0 -1.5 -2 f ( x) = ⇢ 1-1.5 0 1x<0 0x<1 1 14- 01- 31 Odd periodic extension from just 1 up to sum of 6 terms Error of 101- term approx 1.5 1.0 1.0 1.0 0.5 -3 0.5 -2 -1 1.0 0.5 1 2 3 , -3 -2 -1 0.5 1 2 3 , -3 -2 -1 1 -1.0 1.0 0.5 -3 -2 -1 1 2 3 , -3 -2 -1 0.5 1 2 3 , -3 -2 -1 -0.5 ⇢ -1.5 -0.5 -0.5 -1.0 -1.0 1 0 -1.0 -1.0 1x<0 0x<1 f ( x) = 100 term sum of odd periodic extension ⇢ 0x<1 1x<2 x 1 Even periodic extension 1 to 6 terms 1.0 1.2 1.2 1.0 1.0 0.8 0.8 0.6 0.5 1.2 1.0 0.8 0.6 , 0.6 , 0.4 -4 -1 1 0.4 0.2 0.2 -2 2 2 -4 4 -2 2 -4 4 -2 2 1.2 1.2 1.0 0.8 0.6 0.6 , 0.4 ⇢1.0 x f ( x) = 1 0x<1 1x<2 -2 4 0.8 0.6 , 0.4 0.2 -4 2 1.0 0.8 4 1.2 1.0 -0.5 , 0.4 0.2 -2 3 1.0 -0.5 f ( x) = 2 1.0 0.5 0.5 , -1.0 1.0 -0.5 3 -0.5 -1.0 -1.0 2 1 -0.5 -0.5 0.2 2 4 -4 f ( x) = -2 ⇢ 0.4 0.2 2 x 1 4 -4 -2 0x<1 1x<2 2 14- 01- 31 100 terms of even periodic extension 20 terms of even periodic extension 1.2 1.0 0.6 0.4 0.4 0.2 -2 0.8 0.6 f ( x) = 1.0 0.8 -4 1.2 0.2 ⇢ x 1 0 2 x < 1 1x<2 4 -4 -2 f ( x) = ⇢ x 1 0 2 x < 1 1x<2 4 3...
View Full Document

This note was uploaded on 02/12/2014 for the course MATH 358 taught by Professor Danielcoombs during the Winter '14 term at The University of British Columbia.

Ask a homework question - tutors are online