8/20/2019 A Simple Laplace Transform is Conducted While Sending Signals Over Any Two

1/2

A simple Laplace Transform is conducted while sending signals over any two-way communication medium (FM/AM

stereo, 2-way radio sets, cellular phones).

When information is sent over medium such as cellular phones, they are first converted into time-varying wave, and then

it is super-imposed on the medium.

In this way, the information propagates. Now, at the receiving end, to decipher the information being sent, medium

wave’s time functions are converted to frequency functions.

This is a simple real life application of Laplace Transform.

Laplace transform is crucial for the study of control systems, hence they are used for the analysis of HVAC (Heating,

Ventilation and Air Conditioning) control systems, which are used in all modern buildings and constructions.

Laplace transform has several applications in almost all Engineering disciplines.

1) System Modelling

Laplace transform is used to simplify calculations in system modelling, where large differential equations are used.

2) Analysis of Electrical Circuits

In electrical circuits, a Laplace transform is used for the analysis of linear time-invariant systems.

3) Analysis of Electronic Circuits

Laplace transform is widely used by Electronics engineers to quickly solve

dierential equations occurring in the analysis of electronic circuits

!) "igital #ignal $rocessing

%ne cannot imagine solving "#$ &"igital #ignal processing) problems without

employing Laplace transform

') (uclear $hysics

n order to get the true form of radioactive decay* a Laplace transform is used t

makes studying analytic part of (uclear $hysics possible

+) $rocess Controls

8/20/2019 A Simple Laplace Transform is Conducted While Sending Signals Over Any Two

2/2

Laplace transforms are critical for process controls t helps analy,e the

variables* which when altered* produces desired manipulations in the result -or

e.ample* while study heat e.periments* Laplace transform is used to /nd out to

what e.tent the given input can be altered by changing temperature* hence one

can alter temperature to get desired output for a while 0his is an e1cient and

easier way to control processes that are guided by dierential equations

 $E22E #%( LA$LACE

 0he Laplace transform is a simple way of converting functions in one domain tofunctions of another domain

4ere5s an e.ample 6

#uppose we have a function of time* such as cos&w7t) 8ith the Laplace

transform* we can convert this to a function of frequency* which is

cos&w7t) 9999L:;99999< w = &s>? @ w>?)

 0his is useful for a very simple reason6 it makes solving dierential equations

much easier

 0he development of the logarithm was considered the most important

development in studying astronomy n much the same way* the Laplace

transform makes it much easier to solve dierential equations

#ince the Laplace transform of a derivative becomes a multiple of the domain

variable* the Laplace transform turns a complicated n9th order dierential

equation to a corresponding nth degree polynomial #ince polynomials are much

easier to solve* we would rather deal with them 0his occurs all the time

n brief* the Laplace transform is really ust a shortcut for comple. calculations t

may seem troublesome* but it bypasses some of the most di1cult mathematics

Laplace transform is a technique mainly utili,ed in engineering purposes for

system modeling in which a large dierential equation must be solved

 0he Laplace transform can also be used to solve dierential equations and is

used e.tensively in electrical engineering

Laplace 0ransform is used in electrical circuits for the analysis of linear time9

invariant systems