ABSTRACT
This chapter spectrally analyses the delayed signals with the non-zero initial time. It shows that the whole spectral analysis on regular, non-delayed time signals can be extended directly to delayed signals solely via a formal replacement of the old amplitudes by the new ones. By definition, the Padé approximant becomes the exact theory if the input function is a rational function given as a quotient of two polynomials (a rational polynomial). For example, by solely plotting a given signal, an experienced practitioner with time sequences could qualitatively discern certain oscillatory patterns pointing at a harmonic-type structure. Such structures could often become more pronounced by viewing the corresponding derivative of the time signal. Of course, the Fourier shape spectrum in the frequency domain would give a more definitive indication of an underlying structure through a clearer display of peaks.
