TI-92 -- Analyzing a Periodic Function

You may want to look at the help modules below for this module.

• Graphing a Function

• Entering a Program

• Integration

The screen at the right shows the function -1 if t < 1 f(t) = { 1 if 1 <= t in the TI-92. You may want to look at the help module Entering a Program for more information about how to enter a function like this into the TI-92.
The screen at the right shows the computation of the two coefficients - a and b in the component a cos(2 pi t/lambda) + b sin(2 pi t/lambda) of the function f(t).
The next screen defines this component
and the next screen compares the graph of this component with the graph of the original function.

The TI-92 program below fourpoly will define the Fourier polynomial of degree n for the function f(t) on the interval [0, lambda]. As usual if your workstation has the TI-Graph Link cable then you can download it from the computer. You can also obtain it from someone who has it on another TI-92 using the TI linking cable, or as a last resort you can type it in.

The program fourpoly always uses the following names.

n for the degree of the Fourier polynomial. You must store the appropriate value in n before running fourpoly as shown in the screen at the right lambda for the length of the period. You must enter the appropriate value in lambda before running fourpoly as shown in the screen at the right. i, k, and t. These variables cannot be used for anything else. Be sure they are undefined before running fourpoly. f. This function must be defined before running fourpoly. g. This will be the Fourier polynomial. It will be defined by fourpoly.

Many of the functions involved in this module either have discontinuities or have points where they are not differentiable. As a result the numerical integration routines built into the TI-92 cannot achieve their usual accuracy. As the program fourpoly runs you may see the message questionable accuracy in very small type at the bottom of the TI-92 screen. See the screen above. The actual type on the TI-92 screen is smaller.

The screen below shows one example of a Fourier polynomial approximating a function. It was graphed in the usual way on the TI-92.