Editing Linear system (section)

==Time-varying impulse response==
The '''time-varying impulse response''' {{math|''h''(''t''<sub>2</sub>, ''t''<sub>1</sub>)}} of a linear system is defined as the response of the system at time ''t'' = ''t''<sub>2</sub> to a single [[impulse function|impulse]] applied at time {{nowrap|{{math|1=''t'' = ''t''<sub>1</sub>}}.}}  In other words, if the input {{math|''x''(''t'')}} to a linear system is 
<math display="block">x(t) = \delta(t - t_1)</math>
where {{math|δ(''t'')}} represents the [[Dirac delta function]], and the corresponding response {{math|''y''(''t'')}} of the system is
<math display="block">y(t=t_2) = h(t_2, t_1)</math>
then the function {{math|''h''(''t''<sub>2</sub>, ''t''<sub>1</sub>)}} is the time-varying impulse response of the system. Since the system cannot respond before the input is applied the following '''causality condition''' must be satisfied:
<math display="block"> h(t_2, t_1) = 0, t_2 < t_1</math>