Abstract: The major signal in protein coding regions of genomic sequence is three-base periodicity. We use Fourier transform as a spectral analysis tool for genes detection, all that is required is a spot Fourier coefficient at M/3, and the complete Fourier spectrum is not required. An algorithm for computing spot Fourier coefficients is presented. Thereby, a method is developed to recognize the protein coding region of genomic sequence quickly. An important feature of the method is that its computational speed is very fast. Furthermore, this method is independent of training sets or existing datebase information and thus can find general applications.