The coefficients of the Fourier series are
a0 = 2/T∫f(t) dt
an= 2/T∫cos(nx) f(t) dt
bn = 2/T∫sin(nx) f(t) dt
This simulation demonstrates the calculation of the coefficients of the fundamental (n = 1) and the next 9 harmonics (n = 2 to 10) of a set of predefined functions.
The operation scheme is the same as with e-Fourier_1, under different assignment of parameters.
The ComboBox stores the following functions, whose fourier coefficients are to be determined:
When a function is selected, it will be aligned symmetrically in the interval 0 < x < 2π. As default the calculation of the 10th harmonic is chosen, because with it the outline of the function f(x) (envelope of the periodic function) is best recognized.
Slider a defines the amplitude, slider n the harmonic order
Slider b shifts the symmetry point of the function, slider c determines the width of the Gaussian and, together with b, the width of the rectangle pulse. The significance of the parameters can be seen in the formulas.
Activating Integral starts the integration process. As long as this field is activated, integration will start automatically after every change of parameters or functions. The final value of the integral curve is the coefficient of the selected harmonic, except for a factor of π.