Fourier analysis

The Fourier Series is a series of partial sums of periodic trigonometric functions (sine and cosine) with harmonic frequencies ωp = nω0 , (n  = 1, 2, 3...) .ω0 is the "fundamental harmonic" frequency; the higher indices characterize the "higher harmonics".

Fourier analysis is a very useful mathematical tool as the nth member of a Fourier series can serve as nth approximations of arbitrary periodical functions with period T =1 / ν. The coefficients (amplitudes) of the harmonics define a spectrum of sine and cosine function that describe the function in "frequency space". With constant coefficients a0, am and bm

f(x)=a0 /2+(amcos(mx)+bmsin(mx))

approximation fn(x)   with m <= n

In the simulation x = ω0 t = 2πνt = 2πt/T, with ω angular frequency , ν frequency , T period of the fundamental , t time. The x coordinate duration of 1 period (t = T) is 2π.