Frequency analysis based on general periodic functions

Following the sine-cosine function, the sawtooth wave, square wave, triangu lar wave, trapezoidal wave, and so on become new easily generated periodic functions in modern electronics. Similar to Fourier's idea, a natural quest ion is whether a signal can be considered as a superposition of easily gene rated functions with different frequencies. Therefore it is necessary to ge neralize Fourier analysis based on sine-cosine functions into frequency ana lysis based on general periodic functions. In this paper, we introduce the frequency series and frequency transformation based on general periodic fun ctions. We discuss when a frequency system is a complete system or an uncon ditional basis in L-2[-pi,pi], and when a frequency transformation can be c arried out in L-2(-infinity,+infinity). For practical convenience almost al l easily generated functions in electronics are considered carefully as exa mples. As a new and practical generalization of classical Fourier analysis, these results will become a theoretical foundation for the technique of ea sily generated function analysis in signal processing. (C) 1999 American In stitute of Physics. [S0022-2488(99)02706-1].