Finding Z-Transform of a piecewise function.

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?

Answer 1

[Arnav]

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.

[Astitva]

It helped. Thanks @Arnav!!

Answer 2

[Paul]

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.