Dirichlet multiplication and easily-generated function analysis

Following sine-cosine functions, sawtooth wave, square wave, triangular wav e, 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 generaliz e Fourier analysis to easily-generated function analysis including easily-g enerated function series, easily-generated function transformation, and dis crete transformation for easily-generated functions. The results in this pa per make it possible to represent a signal by use of easily-generated funct ions. A lot of techniques based on sine-cosine functions can be translated into techniques based on easily-generated functions. Because Dirichlet mult iplication 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 multiplication and a rel ated formula, relations between basic waveforms in electronics, easily-gene rated function series, easily-generated function transformation, discrete t ransformation for easily-generated functions, and techniques of easily-gene rated function analysis. (C) 2000 Elsevier Science Ltd. All rights reserved .