I want to get the expression of signal in time domain by using inverse fourier transform. The signal in frequency domain is a little special: H(jw) is 1/(a+jw) only when |w|< W; and when |w|> W H(jw)=0. Can we use inverse fourier formula to get h(t)? In other words, can we get the expression of h(t) by calculating the integral below? $$ h(t) = \frac{1}{2π}\int_{-W}^W \frac{e^{jwt}}{a+jw}dw\,. $$
Please help me! Thanks a lot.