(a) Define the Fourier transform of a function f(t) e L'(IR) and find the Fourier transform of the following function- f(t) = {e ; t0 0 ; t <0 (b) Define Dirac delta function 8(t) and find the value of the following integrals: (i) (ii) e(t+zt) s(t)dt (t+3t+4) 8(t 1)dt (c) Define support of a function f(t) e 1 (IR). Find the support of the following functions: (i) f(t) = {1 ; te (0,1) lo; otherwise 1 (ii) g(t): = V telR 2|t|+1 Where IR be the set of all real numbers. (d) Define window function. Show that the function f(t) defined by (1 ; te (0,2) 10 ; otherwise f(t) = {1 function. is a window