Analogues of the Laplace Transform and Z-Transform with Piecewise Linear Kernels
نویسندگان
چکیده
Two new transforms with piecewise linear kernels are introduced. These analogues of the classical Laplace transform and Z-transform. Properties these investigated applications to ordinary differential equations integral provided. This article is ideal for study as a foundational project in an undergraduate course and/or equations.
منابع مشابه
Laplace Transform and Z-transform: Unification and Extension
We introduce the Laplace transform for an arbitrary time scale. Two particular choices of time scales, namely the reals and the integers, yield the concepts of the classical Laplace transform and of the classical Z-transform. Other choices of time scales yield new concepts of our Laplace transform, which can be applied to find solutions of higher order linear dynamic equations with constant coe...
متن کاملIntegral Transforms with Exponential Kernels and Laplace Transform
Let X ←−fZ −→gY be a correspondence of complex manifolds. We study integral transforms associated to kernels exp(φ), with φ meromor-phic on Z, acting on formal or moderate cohomologies. Our main applicationis the Laplace transform. In this case, X is the projective compactification ofthe vector space V ' Cn, Y is its dual space, Z = X×Y and φ(z, w) = 〈z,w〉.We obt...
متن کاملLaplace Transform
We have seen before that Fourier analysis is very useful in the study of signals and linear and time invariant (LTI) systems. The main reason is that a lot of signals can be expressed as a linear combination of complex exponentials of the form e with s = jw. There are many properties that still apply when s is not restricted to be pure imaginary. That is why we introduce a generalization of the...
متن کاملthe Laplace transform.
The spherical phylon group and invariants of the Laplace transform. Abstract We introduce the spherical phylon group, a subgroup of the group of all formal diffeomorphisms of R d that fix the origin. The invariant theory of the spherical phylon group is used to understand the invariants of the Laplace transform.
متن کاملInversion of the Laplace transform
Let J% exp(-PQf(t) dt = F(P) P > 0 where b > 0 is a given number. We give a formula for f (t) in terms of F (p) , p > 0. The object of this Letter is to give a formula for the inverse Laplace transform in which the data used are given on the semi-axis p > 0 only. Let P>O where b > 0 is a fixed number. We have (1, formula 4.14.1) where Jo is a Bessel function. It follows from (1) and (2) that s,...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Foundations
سال: 2021
ISSN: ['2673-9321']
DOI: https://doi.org/10.3390/foundations1010008