Relationship to Laplace Transform to other transform by tutorcircleteam


									   Relationship to Laplace Transform to other transform
Relationship to Laplace Transform to other transform

Laplace transform rechecks a function into its instance. Relationship of Laplace
transform to other transform can be given as: Laplace transform performs on
the density of function of measure while Laplace stieltjes transform do work on
its cumulative distribution function.

The relationship between Fourier and Laplace transform can be used to find
dynamical system or frequency spectrum of a signal.

Mellin transform is related to two sided Laplace transform or bilateral transform
by a simple change of variables and z-transform is related to one sided or
unilateral transform of an ideally sampled signal. Borel transform is used for
entire function of exponential type.

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Fourier Transform

Fourier transform is a function of mathematics that is used in various fields like
engineering and physics. Fourier transform is a function of time that is related to
the frequency known as frequency spectrum. F^ is the common convention that
is an integral function f: R->C.

Fourier transform is basically described by the study of the Fourier series that
are related with the study of the waves that are defined in form of sin and
cosine waves.

Sin and Cosine waves contain the property of the sum of its amplitude so it is
defined by the integration of these waves. In the world everything is defined in
the form of wave forms so Fourier transform is the method of representing this
wave form into the sinusoid.

TV signals, mobile signals or voice of a person is come into the continuous form
not in a discrete manner but the Fourier transform is makes it possible to
generate the discrete constructs that represent in the sinusoid form.

Fourier transform has some basic properties as follows: Fourier transform has

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the linear property as if two waves g(t),h(t) then with Fourier transform G(t) and
H(t) are defined as f(c1g(t)+c2h(t))=c1G(f)+c2H(f) Fourier transform also have
the shift property it is related to the time shifting.

Fourier transforms also show the scaling property that is defined as fgc(t=gf(c)/|
c|. It also shows some property as modulation property it is defined as the
modulated function by another function.
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