Multifunction Plotter - Illustration of Fourier Series
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Description Fourier Series Loan Payments |
We will use the multifunction plotter to show how a square wave can be represented as a sum of sine waves using the Fourier series. A square wave of amplitude of 2 and length 2L can be written as  (See this page for details of the equation.) In the multifunction plotter, we key in the functions as follows: Function 1 = 0.5-mod(int(x),2) Function 2 = 2/pi()*sin(pi()*x) + 2/pi()*sin(pi()*3)/3 + 2/pi()*sin(pi()/5)/5 Function 3 = B5 + 2/pi()*sin(pi()*7)/7 + 2/pi()*sin(pi()/9)/9 + 2/pi()*sin(pi()*11)/11 + 2/pi()*sin(pi()/13)/13 + 2/pi()*sin(pi()*15)/15 + 2/pi()*sin(pi()/17)/17 The first function generates a square wave of amplitude 1, the second adds the first 3 terms of the Fourier expansion while the third adds the next 7 terms. The result is shown below. The first equation is plotted in orange, the second in pink and the third in blue.  |