The Fourier series (FS) applies to a periodic non-sinusoidal functionsatisfying the Dirichlet conditions, whereas the being-processed function in practical applications is usually an aperiodic
non-sinusoidal signal. When is aperiodic, its
calculated FS is not correct, which is still
a challenging problem. To overcome the problem, we derive a direct calculation algorithm, a constant iteration algorithm,
and an optimal iteration algorithm. The direct calculation
algorithm correctly calculates its Fourier coefficients (FCs) when is periodic and satisfiesthe Dirichlet conditions
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