Inverse z-transform

Discussion in 'Math' started by Peytonator, Oct 14, 2011.

  1. Peytonator

    Thread Starter Active Member

    Jun 30, 2008
    105
    3
    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 :)
     
  2. steveb

    Senior Member

    Jul 3, 2008
    2,433
    469
    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?
     
    Last edited: Oct 14, 2011
    Peytonator likes this.
  3. Peytonator

    Thread Starter Active Member

    Jun 30, 2008
    105
    3
    Thanks for your answer Steve :)
     
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