8 15-2 The unit-impulse function We define the unit impulse as a function of time which is zero when its argument, generally(t-to), is less than zero; which is also zero when argument is greater than zero; which is infinite when its argument is zero; and which has unit area (t-t0) 6(t-t)=0t≠t0 ayt-4)=10m8(-4)M=1 (t) δ(t)=0t≠0§15-2 The unit-impulse function We define the unit impulse as a function of time which is zero when its argument, generally (t-t0 ), is less than zero; which is also zero when argument is greater than zero; which is infinite when its argument is zero; and which has unit area.     = = =    + − + − 0 0 ( ) 1 ( ) 1 ( ) 0 0 and t dt or t dt t t    0 t t 1 ( ) 0  t − t 0 t 1  (t) 0     − = − = − =    + − + − 0 0 ( ) 1 ( ) 1 ( ) 0 0 0 0 0 t t and t t dt or t t dt t t t t   