Need information on transforms

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checkmate

Joined: 25 Feb 2004
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01 Aug 2004 18:37 Need information on transforms

Can anyone give a brief description on the various types of transforms, and their main applications? Would also appreciate if anyone could recommend good sites. Thanks.

eltonjohn

Joined: 22 Feb 2002
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01 Aug 2004 20:01 Re: Need information on transforms

Ok First .What is a TRANSFORM .A transform is a mathematical( founded on a mathematical theory) operation that allows to change the form of a calculation . This is called a DOMAIN conversion .. The transform converts the calculation from one DOMAIN to another ,.Once its equivalent form in this new domain is obtained .very often new mathematical properties of this OTHER DOMAIN make THE CALCULATION much more SIMPLER .. and efficient .Then you REVERT to the ORIGINAL DOMAIN .and you have solved YOUR CALCULATION ..for example with LAPLACE transform an Integral calculation can be coverted to a simple Arithmetic Operation
Now you anderstand why COMPUTERS can use this shortcut and why now FOURIER and LAPLACE are so IMPORTANT .
Ok one more example so you can understand the DOMAIN conversion
Imagine any point P in a CARTESIAN plane ..this plane has only TRIGONOMETRICAL PROPERTIES .But by means of a MATHEMATICAL function is possible to correspond another point P' on a complex plane . This plane has nice properties that are not only TRIGONOMETRICAL but also EXPONENTIAL and some calculation can be worked out muy easier
then KNOWING the inverse of the function that you used to calculate point P' f P-> P' and f ^-1 P' -> P is posible to return to your CARTSESIAN plane or DOMAIN
Actually all this has been worked out for you ,and you only need to get TRANSFORM tables and use those FORMULAS without any PAIN

cheers

cesardelahoz

Joined: 24 Jul 2004
Posts: 28

02 Aug 2004 2:02 Re: Need information on transforms

this is a link that may help you:

http://documents.wolfram.com/applications/signals/MathematicalTransforms.html

fasaghandis

Joined: 10 Jul 2002
Posts: 164
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02 Aug 2004 5:42 Re: Need information on transforms

you may find valualble information on several Transforms on
"The Transforms and Applications Handbook" by by Alexander D. Poularikas .
which can be download on mcu(ebook_old/electronic )
yours

checkmate

Joined: 25 Feb 2004
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Location: Toilet Seat

02 Aug 2004 10:09 Re: Need information on transforms

Thanks for all your help. Actually, I already have knowledge of the common transforms such as the various deviations of FT, ZT and LT. I need information on some of the more advanced and uncommon transforms. I've glanced through the Transforms and Application Handbook. It helps alot. But I need just a short primer to the various types of transforms available.

To eltonjohn, i think transforms does not necessarily imply domain conversion. An example is the hilbert transform.