Abstract

Electrical waveforms may have various shapes, and therefore it is necessary to study the frequency analysis based on general periodic functions. In this chapter, we introduce the frequency series and frequency transform based on general periodic functions. Considering the fact that the theory for Fourier series in L2[−π,π] and the theory for Fourier transform in L2(−∞, +∞) are both simple and elegant, we shall develop a theory for general frequency series in L2[−π,π] and a theory for general frequency transform in L2(−∞,+∞). In the following, we shall discuss when a frequency system is a complete system or an unconditional basis in L2[−π,π], and when a frequency transform can be carried out in L2(−∞, +∞). We present a number of complete systems and unconditional bases formed by common waveforms. Almost every common waveform is considered as an example

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