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\iteman{io-port 01471228}
\itemau{Wei, Yuchuan}
\itemti{Dirichlet multiplication and easily-generated function analysis.}
\itemso{Comput. Math. Appl. 39, No.9-10, 173-199 (2000).}
\itemab
Summary: Following sine-cosine functions, sawtooth wave, square wave, triangular wave, and trapezoidal wave become new easily-generated periodic functions. Can a signal be considered to be a superposition of easily-generated functions with different frequencies? In order to answer this question, we generalize Fourier analysis to easily-generated function analysis including easily-generated function series, easily-generated function transformation, and discrete transformation for easily-generated functions. The results in this paper make it possible to represent a signal by use of easily-generated functions. A lot of techniques based on sine-cosine functions can be translated into techniques based on easily-generated functions. Because Dirichlet multiplication in number theory plays a basic role in easily-generated function analysis, we briefly introduce this concept and present a related formula. The main contents of this paper include Dirichlet multplication and a related formula, relations between basic waveforms in electronics, easily-generated function series, easily-generated function transformation, and discrete transformation for easily-generated function analysis.
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\itemut{signal; Fourier analysis; easily-generated function analysis; Dirichlet multiplication; waveforms}
\itemli{doi:10.1016/S0898-1221(00)00095-X}
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