HW5.3 (Dilation, Contraction, and Time-Reversal Properties) Show that scaling the argument of the Dirac delta affects its strength (area) in the following manner: 8 ( at ) = 1 8(t ) , VaER. (1) Equation (1)-which denotes an operational equivalence, not a point-wise equality- is sometimes referred to as thetime-scaling property, even though the argument of the Dirac delta need not be "time." To verify the time-scaling property, place each side of Equation1( inside an inte- gral with a test functiong that is continuous att = 0, and verify that both sides produce the same result. That is, show that too 1 S(at) g(t) dt = too Tal 8(t) g(t) dt . (2) Hint: Use the change of variabler = at in the left-hand side of Equation ?). Show that the Dirac deltabehaves like an even function, namely,(-t) = 8(t). Note that this is true even if the function that the Dirac delta idealizes is not even