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In network analysis, rather than use the differential equations directly, it is usual practice to carry out a Laplace transform on them first and then express the result in terms of the Laplace parameter s, which in general is complex. This is described as working in the s-domain. Working with the equations directly would be described as ...
The tuning application, for instance, is an example of band-pass filtering. The RLC filter is described as a second-order circuit, meaning that any voltage or current in the circuit can be described by a second-order differential equation in circuit analysis. The three circuit elements, R, L and C, can be combined in a number of different ...
In mathematics, the Laplace transform, named after Pierre-Simon Laplace (/ l ə ˈ p l ɑː s /), is an integral transform that converts a function of a real variable (usually , in the time domain) to a function of a complex variable (in the complex-valued frequency domain, also known as s-domain, or s-plane).
The Laplace transform is a frequency-domain approach for continuous time signals irrespective of whether the system is stable or unstable. The Laplace transform of a function f ( t ) , defined for all real numbers t ≥ 0 , is the function F ( s ) , which is a unilateral transform defined by
The following is a list of Laplace transforms for many common functions of a single variable. [1] The Laplace transform is an integral transform that takes a function of a positive real variable t (often time) to a function of a complex variable s (complex angular frequency ).
where I 1 is a modified Bessel function of the first kind, [9] obtained by using Laplace transforms and inverting the solution. [10] The Laplace transform of the M/M/1 busy period is given by [11] [12] [13]: 215
The term "transfer function" is also used in the frequency domain analysis of systems using transform methods, such as the Laplace transform; it is the amplitude of the output as a function of the frequency of the input signal.
Bode, Hendrik, Network Analysis and Feedback Amplifier Design, pp. 360–371, D. Van Nostrand Company, 1945 OCLC 1078811368. Brune, Otto , "Synthesis of a finite two-terminal network whose driving-point impedance is a prescribed function of frequency" , MIT Journal of Mathematics and Physics , vol. 10, pp. 191–236, April 1931.