Characterisation of nonlinear and linear time-varying systems by Laplace transformation

Analysis of linear time-varying circuits by two-dimensional analog filtering

“…An overview of frequency-domain characterization of general autonomous systems is provided in [1]. The short Table I …”

“…To convert (24) into a function of single frequency, the techniques of association of variables may be used [1], [11]. Using this approach, the single-variable impulse response function, for the case when , is obtained as:…”

“…Our earlier work in this area [1][2][3] was focused on 2DLT transforms of LTV systems only. However, larger classes of 2-D analog systems are central to many applications, such as communication networks, seismic signal processing, adaptive analog systems and control.…”

Two-dimensional analog signal processing and its implications on circuit theory

“…It also serves to remind us that the mixed time and frequency analysis in the s 1 ; s ð Þ-plane or t; s 2 ð Þ-plane is a possibility. An overview of frequency-domain characterization of general autonomous systems is provided in [3]. Note that the two-dimensional time-domain impulse-response of a LTV system comprised of a single resistor rðsÞ is rðsÞd t À s ð Þ.…”

“…This approach leads to the development of the system theory based on observation of a single independent variable, which is called the time-variable, for convenience. Nevertheless, the multivariable system theory provides a more elaborate perspective and has been introduced in the system and circuit theory literature for a variety of emerging applications [1][2][3]. The multivariable system function can be defined in the original spatiotemporal domain of the input function or in the complex-frequency s-domain by the multidimensional Laplace transform (MDLT).…”