# Laplace, Fourier, Z-transf

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### #1 Bj2c

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Posted 04 November 2004 - 03:00 PM

does anybody knows about programs (basic) or mcs. to solve Laplace, Fourier, Z-Transf , like in the HP 48 - 49G , or someone can help to resolve step by step , in the CP

### #2 m4x

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Posted 16 January 2005 - 04:33 PM

Hi there
I've written a program that does the Laplace transformation. Here's my idea:

Local z
InputFunc f(t),"Input the original function"
(-\$[ f(t)*e^(-s*t) ],t)|t=0 => z
PrintNatural z

where \$ is the indefinite integral

I've found out that CP isn't able to solve the definite integral of the Laplace transformation, because it can't solve the +infinity limit with the variable s. CP doesn't know it is a positive number and returns Undefined, when I tried to solve this limit. I've tried to use |s>0 right after the integral, but it didn't work. Instead I only solve an indefinite integral and put the lower limit t=0, because the value for the upper limit should be zero. And it works great
I haven't tried the Z-transformation. Maybe you have found out how to do it?

### #3 R00KIE

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Posted 17 January 2005 - 11:01 AM

For Z-Transform check
Z-Transform

For Laplace Transform Check
Laplace Transform

For Fourier Transform check
Fourier Transform

### #4 m4x

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Posted 17 January 2005 - 02:39 PM

Thanks for the info R00KIE. It's great :)

I only managed to get a Z-transformation of n^k function using the (9) pattern on:
Z-Transform

I can't find the way to solve the infinite sum ak/z^k in the main Z-transf. pattern, because CP can't solve an infinite sum with variables. It returns undefined I think because it depends on the variables if the sum is convergent or divergent. Maybe someone knows how to calculate, using Classpad, infinite sums with variables? Is CP capable of doing it at all? If not perhaps it could be improved in the new OS version. When I used the 'with' | operator to constrain variables it still doesn't work as it should be.

### #5 fiberoptik

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Posted 17 January 2005 - 09:36 PM

Hello, if you read the older posts, you'll see that i had a problem similar to yours. It seems that CP can't calculate sums with more than 260 steps
ex: sum(1/x^2, x, 0, inf). Softcalc told me that this problem is already solved, but he doesn't know if it's on OS 2 or in a later release.

Regards

fiberoptik

### #6 m4x

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Posted 17 January 2005 - 09:52 PM

It's good news that it has already been taken care of. Sure hope the fix is gonna be included in OS 2.0. Classpad seems to have some difficulties when it comes to symbolically solving something a little bit complicated.

Thanks fiberoptik

### #7 R00KIE

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Posted 19 January 2005 - 02:19 PM

My HP49 is able to solve those, at least if i make assumptions on the variables so the series is convergent, and if i'm correct, there are some cases where the z-transform doesn't exist.

### #8 Bj2c

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Posted 17 February 2005 - 06:55 PM

but you have to download a program , or is already in the calc , i see a copule of programs to download , -fourier ( series - transform) , laplace , z, ( iii think

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