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 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.```
 ```The Laplace transform usually takes 50 minutes of lecture in front of a chalkboard to explain to students who already have 2 semesters of calculus. 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.```
 ```I agree with shockandawe-ga, this would be very difficult question to answer For a somewhat more technical answer check out wikipedia: http://en.wikipedia.org/wiki/Laplace_Transform```