5. Description of Partly Correlated Random Sequences: Replacement of Random Sequences by the Generalised Prony Spectrum

Any young researcher is accustomed to the conventional Fourier transform (F-transform). However, it would be useful to think about the meaning of this transformation and its purpose. Is it just for detecting the harmonic components in the input signal? This chapter tries to answer this question, such that the reader will be acquainted with not only periodic signals but also a different class of signals defined as quasi-periodic. Based on this information, one can enter another world of processes that can be used in practical applications. In this chapter, a general algorithm to describe these processes is provided along the methods to detect them from real, available data. Two nontrivial examples should confirm that this “quasi-periodic world” exists, and keen students could use the newly introduced tools and methods to find quasi-periodic processes from data at his/her disposal. This chapter also illustrates some open problems that can encourage and invite the reader to a new way of thinking and modelling. This way should increase the limits of the conventional F-transform and should probably set on thinking about the physical meaning of Laplace-transform (L-transform), which is a powerful tool from the mathematical point of view, but with a still uncertain physical meaning.