Fourier Series Applet, Curve fitting
The Coefficients of the Fourier series are also what would be
obtained if a least squares curve fitting analysis is done with
sinusoidal harmonics being used to fit the function. The
analysis is illustrated in the MathCad file below for a
square wave defined by f(t). Both a1
and a3 have their correct values (4/p)
and (4/3p) when fitting is done.
The Applet below illustrates the connection between Least Squares
and the magitude of the Fourier Coefficient for a quadratic,
a triangular and a rectangular wave.
Fn = 1 is the case for n = 1 for a quadratic wave. Parameters
T1 to T4 can be adjusted to give the least error.
Fn = 2 shows the error is a minimum when the amplitude is
1.03204919 compared with the correct value of 1.03204910186.
The accuracy of the applet is limited by the simple
numerical integration algorithm used.
Fn = 3 is the case of n = 3 for a quadratic wave and Fn = 4
shows the minimum error case.
Fn = 5 and 6 shows the n = 5 case.
Fn = 7 and 8 shows the n = 1 case for the triangular wave.
Fn = 9 and 10 shows the n = 3 case for the triangular wave.
Fn = 11 and 12 shows the n = 5 case for the triangular wave.
Fn = 13 and 14 shows the n = 1 case for the rectangular wave.
The other cases Fn = 15 to 30 shows n = 2, 3, 5, 6, 7, 9, 10
and 11 for the
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COPYRIGHT © 1996, 2012 Cuthbert Nyack.