1) Let f be a function of the real variable t, absolutely integrable over R and continuous overa closed interval. Define the Fouriertransform of this function. 2) Give a physical interpretation of the...

Extracted text: 1) Let f be a function of the real variable t, absolutely integrable over R and continuous overa closed interval. Define the Fouriertransform of this function. 2) Give a physical interpretation of the Fouriertransform of a function. TF [f (t)] denotes the Fouriertransform of a function (f). 3) Show that, TF[f(t)] = 2 , f(t) cos(2nvt)dt, in the case where the function (f) is even. +0o 4) Show that, TF[f(t)] = -2 f(t) sin(2nvt)dt, in the case where the function (f) is odd. 5) The function (g) is defined by: g(t) = = t2.n(t), Where a(t), indicates the function 'door' () Define the 'door' function. (ii) Give the graphical representation of the function (g). (ii) Determine TF [g (t)]. 6) Show that, TF[f(t – a)] = e-j2nva TF[f(t)], where a E R*