Question

State and prove first shifting theorem

Answer 1

Step-by-step explanation:

A Laplace transform which is a constant multiplied by a function has an inverse of the constant multiplied by the inverse of the function. First shift theorem: L − 1 { F ( s − a ) } = e a t f ( t ) , where f(t) is the inverse transform of F(s).

Ancos(nω)u(n): z(z−a cos ω)z2−2az cos ω+a2

Cos(nω)u(n): z(z−cosω)z2−2zcosω+1

U(n): zz−1

Anu(n): zz−a