# Inverse z-transform

#### Peytonator

Joined Jun 30, 2008
105
Hi,

This is probably a silly question, but what is the inverse z-transform of

A/(z+B)

where A and B are constants.

Thanks

#### steveb

Joined Jul 3, 2008
2,436
It's not a silly question, but there are a few ways to get the answer. The fastest way is to use a transform table. The answer can change character depending on the values of A and B, and so you may not see that exact function in the table. You also need to use some basic principles.

First of all, delaying by one sample in the time domain is like multiplying by 1/z in the z-domain. So, you should first find the transform of Az/(z+B) and then you can delay the answer by one sample by substituting k-1 in for k.

Example transforms in a table are $$1 \Leftrightarrow {{z}\over{z-1}}$$ or $$a^k \Leftrightarrow {{z}\over{z-a}}$$. Hopefully, you know what to do with the constant A?

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