First of all, can anyone recommend me a good signals and systems forum on the internet as it doesn't seem this one is built to deal with signals and systems specifically.

But here goes.

A continous time signal x(t) has fourier transform:
X(t) = 1 / (jw + b)
Determine the fourier transform of the signal:
v(t) = 1 / (jt - b)

Compute the generalised fourier transform of the following signals:
1.x(t) = 1/t ; -∞ <t < ∞
2.x(t) = 3cos(t) + 2sin(t); -∞ < t < ∞

 

Shortest answer: matlab.

Short answer: use a table of transform pairs as well as properties of CFT.

Long answer: plug into definition and solve integral (properties will help here too)

I'm guessing they want you to use the definition... take a stab at it and let us know where ya get.