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24 August 2001

Sine Curve Fitting Progam

By Don Sieber

This is the derivation of my sine curve fit pogram developed in 1968. By usng the MATHCAD program the solution was quickly found once it was determined what the program wanted.

Given 4 readings taken at equally spaced time intervals give values E0, E1, E2, and E3. Each reading may be defined by the following equations:

Expand this expression symbolically

The equation becomes too large to print in its entirety but when simplified symbolically, gives the following:

	Write this equation so all the terms are on one side and solve for variable (da).
	This is the solution for (da). By substituting the value of U back into the equation, the final result is:

Thus the incremental angle (da) may be solved for in terms of the 4 original readings. The values for E, A, and V may be solved for by substituting (da) back into the original defining equations as follows:

	Equation defining A
	A as a function of (da)
	This is the defining expression for E
	This is the defining expression for V

This represents all the unknowns in terms of E0, E1, E2, and E4.