2. Define convolution of two functions f,ge L'(IR) and prove that the following: (i) If f, ge L' (IR), then fge L' (IR). (ii) If f.ge L'(IR), then f g = gf Let f e L'(IR) and f denotes the Fourier transform of f, then fe L (IR) with ||||||fl|1. 3. Define Gabor transform of a function f(t) e L (IR). Let Gf denotes the Gabor transform of a function fe L (IR) and 2 be a real number. Then prove that: (i) [G(df)](w) = (Ggf)(w) (ii) [Ggf(t-a)](w) = e-law (Gg-af)(w), a e IR-{0} and we IR OR Find the Gabor transform of the following functions: (i) f(t) = e-lat,te |R, > 0 (ii) f(t) = 8(t), where 8(t) denotes the Dirac delta function.