a) Determine the Fourier transform. Integrate from -Infinity to 0 with e^x plus from 0 to +Infinity with e^-x. 

b) Find the inverse Fourier transform of f(w)= (Pi/2)^0.5 for -1

c) Calculate the energy in both the time and frequency domain versions of f in 11.9-6 to show that they are equal. For the time domain integral use the identity (a^b)^c=a^(bc) and double the integral from 0 to +infinity. For the frequency domain integral, use: IntegralOf[1/(1+w^2)^2]=0.5[w/(1+w^2) + arctan(w)]. Ans: 1 joule.

d) Calculate the Fourier transform of the first and second derivative of the function in 11.9-6 using the derivative identities.

e) Given that f(x)=e^-1x and g(x)=3e^-4x where both functions are zero for x<0. Use the table of Fourier transforms to a) Find Fourier Transform of f(x)+g(x) and b) Find the Fourier transform of the convolution of f(x) and g(x).

Answer rating: 100% (QA)

aThe Fourier transform is 12exex The Fourier transform of a function fx is defined as Fsfxe2isxdx Th... View the full answer