- #1
Kambiz_Veshgini
- 2
- 0
let S be the Unit Step function
for a function with a finite jump at t0 we have:
(*) L{F'(t)}=s f(s)-F(0)-[F(t0+0)-F(t0-0)]*exp(-s t0)]
so:
L{S'(t-k)}=s exp(-s k)/s-0-[1-0]*exp(-s k) = 0 & k>0
but S'(t-k)=deltadirac(t-k) and we know that L{deltadirac(t-k)}=exp(-s k)
so why do I get ZERO when using the formula (*)
for a function with a finite jump at t0 we have:
(*) L{F'(t)}=s f(s)-F(0)-[F(t0+0)-F(t0-0)]*exp(-s t0)]
so:
L{S'(t-k)}=s exp(-s k)/s-0-[1-0]*exp(-s k) = 0 & k>0
but S'(t-k)=deltadirac(t-k) and we know that L{deltadirac(t-k)}=exp(-s k)
so why do I get ZERO when using the formula (*)