2011_Tutorial_5 - n-1) x 2 n-1 4. Find the Fourier series...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
NATIONAL UNIVERSITY OF SINGAPORE Department of Mathematics MA 1505 Mathematics I Tutorial 5 1. Show that the Fourier series for f ( x ) = 1 2 ( x + | x | ) , - π < x < π ; f ( x + 2 π ) = f ( x ) is given by π 4 + X 1 ( - 1) n - 1 πn 2 cos nx + ( - 1) n +1 n sin nx ± . 2. Find the Fourier series that represent the following graph: Ans . 3 2 - 2 π X n =1 sin(2 n - 1) x 2 n - 1 3. Sketch the graph of the following periodic function. Determine whether it is an even or odd function, and find its Fourier series. f ( x ) = ( 1 - π/ 2 < x < π/ 2 0 π/ 2 < x < 3 π/ 2 , f ( x + 2 π ) = f ( x ) . Ans . 1 2 + 2 π X n =1 ( - 1) n +1 cos(2
Background image of page 1

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

View Full DocumentRight Arrow Icon
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: n-1) x 2 n-1 4. Find the Fourier series of a half-wave rectifier u ( t ) = (-π/w &lt; t &lt; sin wt &lt; t &lt; π/w and u ( t + 2 π w ) = u ( t ). Ans . 1 π + 1 2 sin wt-2 π ( 1 1 · 3 cos2 wt + 1 3 · 5 cos4 wt + ··· ) MA1505 Tutorial 5 5. Find the Fourier series for the function f ( x ) = (-2-x-2 &lt; x &lt; 2-x &lt; x &lt; 2 and f ( x + 4) = f ( x ). Ans . 4 π ∞ X n =1 1 n sin nπx 2 2...
View Full Document

Page1 / 2

2011_Tutorial_5 - n-1) x 2 n-1 4. Find the Fourier series...

This preview shows document pages 1 - 2. Sign up to view the full document.

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