Fourier Series With Spectral and Wave Number Decomposition

In this study, the generic nature of Fourier series is pointed out and the requirement of dimensional homogeneity for physical systems is emphasized. By suitable application of non-dimensional variables, both time versus frequency and spatial versus wave number decomposition of Fourier series are included properly to put the physics involved into the right physical meanings. Furthermore, the high frequency noise features through differentiation and integration are revealed nicely by the Fourier series representation of a signal including noise.