Interesting Functions in Matlab Douglas Wilhelm Harder M

Interesting Functions in Matlab Douglas Wilhelm Harder, M. Math. LEL Department of Electrical and Computer Engineering University of Waterloo, Ontario, Canada ece. uwaterloo. ca dwharder@alumni. uwaterloo. ca © 2012 by Douglas Wilhelm Harder. Some rights reserved.

Interesting Functions in Matlab Outline You are already familiar with trigonometric and exponential functions We will now look at: – – square wave functions saw-toothed wave functions triangular pulses the cardinal sine function 2

Interesting Functions in Matlab Square Wave Function The square-wave function has a period of 2 p and an be thought of as follows: x = 0: 0. 0001: 20; plot( x, square( x ) ) ylim( [-1. 2] ) square( 0 ) ans = 1 square( pi ) ans = -1 3

Interesting Functions in Matlab Saw-toothed Wave Functions The default saw-toothed has a period of 2 p and an be thought of as follows: x = 0: 0. 0001: 20; plot( x, sawtooth( x ) ) ylim( [-1. 2] ) sawtooth( 0 ) ans = -1 sawtooth( pi ) ans = -1 4

Interesting Functions in Matlab Saw-toothed Wave Functions A second argument indicates what proportion into the interval [0, 2 p] the peak of the tooth appears – The defualt is identical to sawtooth( x, 1 ) x = 0: 0. 0001: 20; plot( x, sawtooth( x, 0. 5 ) ) ylim( [-1. 2] ) 0. 5 5

Interesting Functions in Matlab Saw-toothed Wave Functions The last interesting case has the parameter as 0: x = 0: 0. 0001: 20; plot( x, sawtooth( x, 0 ) ) ylim( [-1. 2] ) square( 0 ) ans = 1 square( pi ) ans = -1 6

Interesting Functions in Matlab The Cardinal Sine Function The sinc function is not periodic and is defined as: x = -10: 0. 0001: 10; plot( x, sinc( x ) ) ylim( [-1. 2] ) 7

Interesting Functions in Matlab The Triangular Pulse Function The triangular-pulse function is not periodic and is defined as: x = -2: 0. 0001: 2; plot( x, tripuls( x ) ) ylim( [-1. 2] ) 8

Interesting Functions in Matlab Summary We have quickly covered some of the special functions in Matlab – square, sawtooth, tripuls and sinc This will be used later in applications 9

Interesting Functions in Matlab References [1] Jack Little, Cleve Moler, and Steve Bangert, Matlab, Mathworks, 19842012. 10