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

2. 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

3. Square Wave Function The square-wave function has a period of 2  and an be thought of as follows: x = 0:0.0001:20; plot( x, square( x ) ) ylim( [-1.2 1.2] ) square( 0 ) ans = 1 square( pi ) ans = -1 3 Interesting Functions in Matlab

4. Saw-toothed Wave Functions The default saw-toothed has a period of 2  and an be thought of as follows: x = 0:0.0001:20; plot( x, sawtooth( x ) ) ylim( [-1.2 1.2] ) sawtooth( 0 ) ans = -1 sawtooth( pi ) ans = -1 4 Interesting Functions in Matlab

5. Saw-toothed Wave Functions A second argument indicates what proportion into the interval [0, 2  ] 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 1.2] ) 0.5 5 Interesting Functions in Matlab

6. 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 1.2] ) square( 0 ) ans = 1 square( pi ) ans = -1 6 Interesting Functions in Matlab

7. 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 1.2] ) 7 Interesting Functions in Matlab

8. 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 1.2] ) 8 Interesting Functions in Matlab

9. 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

10. References [1]Jack Little, Cleve Moler, and Steve Bangert, Matlab, Mathworks, 1984- 2012. 10 Interesting Functions in Matlab