Implementing Unilateral Z-Transform of a^n

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Gennaro Arguzzi
Gennaro Arguzzi 2017-7-27
回答： Star Strider 2017-7-27
Hello everyone, I wrote the following lines to implement the unilateral Z-transform of a^n:
close all
clear all
syms n a z
assume(a>0)
S=symsum(a^n*z^-n,n,0,+Inf)
the result is:
piecewise([a == z, Inf], [a ~= z, -(z - z*limit(a^n/z^n, n == Inf))/(a - z)])
The result should be z/(z-a). How can I get it?
Thank you in advance.

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采纳的回答

Star Strider
Star Strider 2017-7-27
It is necessary to add assumptions, then a simplify call:
syms a n z
assume(a > 0)
assumeAlso(a < 1)
assumeAlso(a < z)
S = symsum((a/z)^n, n, 0, Inf);
S = simplify(S, 'Steps',20)
S =
-z/(a - z)

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