The document demonstrates the proof of a solution using the shifting property of the unit impulse function. It involves defining a function and applying the shifting property to show the relationship between integrals. The final assertion confirms that the derived equation holds true, completing the proof.

1. Using the Shifting property of unit impulse, prove that
Solution
given the function
(at)
by shifting property
f(t)(td)dt=f(d)
so by using the shifting property
let f(t) = (at)
integral ( - infinty to + infinty ) (at) (td)dt
let at = P
a dt = dP
integral ( - infinty to + infinty ) (P) (td)dP / |a|
= (P) /|a|
= (t) / |a|
hence proved