ABSTRACT
The Fourier coefficients a0,an and bn all require functions to be integrated, i.e.
a0 = 12π ∫ π −π
f (x)dx = 1 2π
f (x)dx
= mean value of f (x) in the range −π to π or 0 to 2π
an = 1 π
f (x)cosnx dx = 1 π
f (x)cosnx dx
= twice the mean value of f (x)cosnx in the range 0 to 2π
bn = 1 π
f (x)sinnx dx = 1 π
f (x)sinnx dx
= twice the mean value of f (x)sinnx in the range 0 to 2π
However, irregular waveforms are not usually defined by mathematical expressions and thus the Fourier coefficients cannot be determinedby using calculus. In these cases, approximate methods, such as the trapezoidal rule, can be used to evaluate the Fourier coefficients. Most practicalwaveforms to be analysed are periodic.
