Advanced z-transform

In <a href="/facts/Mathematics/pxTouaz4">mathematics</a> and <a href="/facts/Signal_processing/Npaja6zb">signal processing</a>, the advanced z-transform is an extension of the <a href="/facts/Z-transform/ERNvDJqt">z-transform</a>, to incorporate ideal delays that are not multiples of the <a href="/facts/Sampling_rate/xxck7aLN">sampling time</a>. The advanced z-transform is widely applied, for example, to accurately model processing delays in <a href="/facts/Digital_control/NrHWPB6w">digital control</a>. It is also known as the modified z-transform. 
It takes the form

F
        (
        z
        ,
        m
        )
        =
        
          ∑
          
            k
            =
            0
          
          
            ∞
          
        
        f
        (
        k
        T
        +
        m
        )
        
          z
          
            −
            k
          
        
      
    
    {\displaystyle F(z,m)=\sum _{k=0}^{\infty }f(kT+m)z^{-k}}

where

<ul><li>T is the sampling period</li>
<li>m (the "delay parameter") is a fraction of the sampling period 
 
 
 
 [
 0
 ,
 T
 ]
 .
 
 
 {\displaystyle [0,T].}
 
</li></ul>

Advanced z-transform open-in-new

Advanced z-transform