The Fourier series (FS) applies to a periodic non-sinusoidal function satisfying 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 iterati on algorithm, and an optimal iterati on algorithm. The direct calculation algorithm correctly calculate s its Fourier coefficients (FCs) when is periodic and satisf ies the Dirichlet conditions . B oth the constant iterati on algorithm and the optimal iterati on algorithm provide an idea of determining the states of . From the idea , we obtain an algorithm for determining the states of based on the optimal iterati on algorithm. In the algorithm, the variable iterati on step is introduced ; t hus , we present an algorithm for determining the states of based on the variable iterati on step. The presented algorithm accurately determine s the states of . On the basis of the se algorithms, we build a biproportional construction theory . The theory consists of a first and a second proportional construction theory . The former correctly calcula te s the FCs of at the present samp ling time
KeywordsFourier Coefficients (FCs)Fourier Series (FS)Iteration AlgorithmAperiodic Non-Sinusoidal Signal
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