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Q: mathematical transforms ( No Answer,   2 Comments )
Subject: mathematical transforms
Category: Computers > Algorithms
Asked by: smn-ga
List Price: $3.00
Posted: 24 Aug 2005 13:32 PDT
Expires: 23 Sep 2005 13:32 PDT
Question ID: 559905
What are mathematical transforms? Explain the concept of Z and
La-place mathematical transforms and their applications with very
simple examples.
There is no answer at this time.

Subject: Re: mathematical transforms
From: shockandawe-ga on 27 Aug 2005 19:41 PDT
The Laplace transform usually takes 50 minutes of lecture in front of
a chalkboard to explain to students who already have 2 semesters of

There won't be many takers on this for $3.

I'll say a little in the hopes that it helps a little. 

The Laplace transform takes a continuous function and maps it in a
special way to a different function. Any continuous function that does
not grow faster then an exponential function has a Laplace transform
(whether or not you can compute it is another question.) . If f(t) was
our original function then let F(s) represent its laplace transform. A
thing that teachers say, is that you are bringing the function from
the "t domain" to the "s domain." The function won't look anything
like it used to, but there is a procedure for mapping them back and
forth. Ok, so the definition of the laplace transform of f(t) is
L{f(t)} = F(s) = integral ( f(t)*exp(-st) dt from 0 to infinity) Like
I said, so long as the f(t) doesnt grow faster then an exponential
function, this integral will converge.

SO, very simple example

Laplace Transform of f(t) = 1 (a constant function) is 
integral ( 1*exp(-st) from 0 to infinity) = 1/s  (I am presuming you
have 2 semesters equivalent of calculus.)

other simple ones can be computed, 
L{t^n} = n!/(s^(n+1)) 
L{sin(bt)} = b / (s^2+b^2)
L{cos(bt)} = s / (s^2+b^2)

Laplace transforms are good for differential equations, because...
basically, you can transform the functions in a given differential
equation with the laplace transform, and certain families of really
hard to calculate things become much easier to calculate.. and then
you can transform them back.

The z-transform is very simmilar to the laplace transform, except it
transforms discrete functions (also called sequences) in a very
simmilar manner.

let f_n (written f subscript n) be a sequence, 
then its z-tranform is sum f_n * z^n from 0, infinity. 

So any sequence that grows no faster then geometric can be tranformed. 

Who cares about z-transforms?, MOSTLY electrical engineering students
who are taking  classes in signals and systems; also people studiyng
advanced probability although they would call it "a generating
function" of a discrete random variable.
Subject: Re: mathematical transforms
From: shad2-ga on 02 Oct 2005 22:33 PDT
I agree with shockandawe-ga, this would be very difficult question to answer
For a somewhat more technical answer check out wikipedia:

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