A linear time-invariant system is an input-output system that is both linear and unchanged by a shift in time. If inputs 
and 
produce outputs 
and 
, linearity means that the input 
produces 
. Time invariance means that delaying an input by an
amount 
delays its output by the same amount.
Under the zero-state condition, a continuous-time linear time-invariant system is completely characterized by its impulse
response function 
, and the output corresponding to an input 
is the convolution
 |
The analogous discrete-time formula is 
.
