Finding Z-Transform of a piecewise function.

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Astitva Ranjan
Astitva Ranjan 2024-9-20
回答： Paul 2024-9-20
I am trying to find the Z-transform of the piecewise function:
using the inbuilt function ztrans().
Here is the code I wrote:
syms n z
f = piecewise(n < 0, (1/2).^(-n), n >= 0, (1/3).^(n));
Z_f = ztrans(f);
disp(Z_f);
But the command window is giving the result:
>> untitled
ztrans(piecewise(n < 0, 1/(1/2)^n, 0 <= n, (1/3)^n), n, z)
I dont know what I am doing wrong. Is there another way to do this?

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采纳的回答

Arnav
Arnav 2024-9-20
编辑：Arnav 2024-9-20
Hi @Astitva Ranjan,
I understand that you are trying to find the Z-Transform of a piecewise function and are not getting a simplified explicit value of the result.
You can rewrite the piecewise function using heaviside function as:
syms n z
f = (1/2).^(-n) * heaviside(-n) + (1/3).^(n) * heaviside(n); % Define the piecewise function
Z_f = ztrans(f, n, z); % Compute the Z-transform
Z_f
You may refer to the documentation of heaviside function to learn more:
https://www.mathworks.com/help/symbolic/sym.heaviside.html
Hope it helps.

更多回答（1 个）

Paul
Paul 2024-9-20
Based on the context of the question, it is quite likely that the problem is to solve for the bilateral z-transform of f(n). However, ztrans finds the unilateral z-transform.
To solve this problem in Matlab one has to define the f(n) as the sum of a causal signal and a non-causal signal. The z-transform of each can be found using ztrans and application of z-transform properties. Those results can be summed to find F(z) as long as their regions of convergence overlap.

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