Shift-invariant system

<p>In <a href="/facts/Signal_processing/Npaja6zb">signal processing</a>, a shift invariant system is the <a href="/facts/Discrete_time_and_continuous_time/RR8wpS9e">discrete</a> equivalent of a <a href="/facts/Time-invariant_system/NpWUk0YG">time-invariant system</a>, defined such that if 
  
    
      
        y
        (
        n
        )
      
    
    {\displaystyle y(n)}
  
 is the <a href="/facts/Transient_response/m4Nr61Px">response</a> of the system to 
  
    
      
        x
        (
        n
        )
      
    
    {\displaystyle x(n)}
  
, then 
  
    
      
        y
        (
        n
        −
        k
        )
      
    
    {\displaystyle y(n-k)}
  
 is the response of the system to 
  
    
      
        x
        (
        n
        −
        k
        )
      
    
    {\displaystyle x(n-k)}
  
. That is, in a shift-invariant system, the contemporaneous  response of the output variable to a given value of the input variable does not depend on when the input occurs; time shifts are irrelevant in this regard.
</p>

Shift-invariant system open-in-new

Shift-invariant system