0.2 Circuits, Signals and 2023-2024 The Fourier transform of a function f(t) is defined by - F(w) = De-Just dt a) Using the above definition, find the Fourier transform F(w) of

the following high pass filter that is applied for removing the high-frequency noise in a mobile communication device; and simplify as much as possible: f(t) = 8(t)- e-t 0st<∞0 (7 marks) b) Write down expressions for the modulus and the phase of F(w). (6 marks) c) Find the values for the modulus and phase of F(w) at w = 0,1,3,00. (7 marks) d) Using the time shift theorem (no proof is needed) and the result of Q.2 (a), find the Fourier transform of the function 8(t-2) - -e-3t+6 for 2 St< (5 marks) (Total 25 marks)