Tuesday, 12 January 2016

How can we acquire the coefficients of the trigonometric series?



Actually, the trigonometric series and Fourier series are the same, right? If not, please tell me how they differ. Anyway, I want to find the coefficient of this trigonometetric series(or partial sum).



f(x)=a0+Nn=1ancos(nx)+bnsin(nx)


Answer



You need to project your function on the basis vectors using



a0=12πππf(x)dx




an=1πππf(x)cos(nx)dx,n>0



bn=1πππf(x)sin(nx)dx,n>0


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