Question: Fourier Transforms

Problems: Calculate Fourier Transforms of:
>
> f(t)=1 for (1<=|t|<=2) and 0 otherwise
>
> f(t)=cos wt[H(t+1/2T)-H(t-1/2t]
>
> f(t)=exp(at) (t<=0), (a>a) and exp(-at) (t>0)
>
> f(t)=exp(-at) sin wt H(t)
>
> note: w is omega and T is Tau, H is Heaviside
 

Not sure how to do these problems with maple.

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