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[✓] Calculate the inverse Z transform with exact precision?

Posted 7 months ago
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Hello All. I hope you are doing well.

I need to perform an inverse Z transform

enter image description here

As you can see I dont get a clean output. what are that dots there?

For example

6.-5n Whats that?

5 Replies
 In[1]  = 10/3.
Out[1] = 0.3333

By adding a decimal point to a number, you force Mathematica to treat it as approximate. These approximate numbers will be machine precision by default. If the expression contains a decimal number,then the result is also a decimal number.

I refer to the book for more information:1.Mathematica Cookbook and 2.Mathematica Navigator

Try:

InverseZTransform[-0.9568/(z - 4.321*10^-2), z, n] // Rationalize

(* -299 2^(6 - 5 n) 5^(1 - 5 n) 4321^(-1 + n) UnitStep[-1 + n] *)

or:

InverseZTransform[-(598/625)/(z - 4321/100000), z, n]

(* -299 2^(6 - 5 n) 5^(1 - 5 n) 4321^(-1 + n) UnitStep[-1 + n] *)
Posted 7 months ago

Thanks a lot

There are dots in the input so is it really a surprise to see them in the output?

Posted 7 months ago

But what number its 6.?? It suppose to be 6.0? and .5 it suppose to be 0.5?

Yes, these follow the usual rules and conventions of decimal notation. That is to say, there are equivalent ways to display these, and the one in use as default output form in the Wolfram Language displays with the fewest digits possible.

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