Need step-by-step answer in detail so that i can understand how to solve each question. I need it for my test. HW has alredy been submitted. Thank you. Please if you can write in form of steps. As in, STEP1 - ....., STEP2 - ..... and so on

1. (1 pt) Consider f(x) =xe""\"7 c > 0 The Fourier transform of f is If [f] (z) = Note that the transformed variable z is used. 2. (1 pt) The most general form of the Gaussian or normal density function is f( > 1 ' (\"3'2 x = e 2: V 21ts2 where m is the mean and s is the standard deviation. The Fourier transform of f is IT lf](z) = Note that the transformed variable z is used. 3. (1 pt) Consider x f (X) = (1+x2)2 The Fourier transform of f is 5F [f] (z) = Note that the transformed variable z is used. The absolute value function abs(z) is available, should you need it