A one-dimensional multi-frequency simulation code has been developed. Using this code, we analyze the spontaneous emission from a bunched electron beam in a FEL. With this simulation code the radiation spectral intensity and temporal profile have been evaluated for various pulse shapes of bunched electron beams. It is found that, in the case of a square electron pulse, the spontaneous emission at the edge is much stronger than the emission from numerical shot noise, and the radiation power is higher than that of a Gaussian electron pulse case.