A new general optimal approach is presented, for those cases where one and multi-dimensional Fourier transforms are used for pattern recognition. It consists in using both the real and imaginary components of Fourier transforms as features. The use of the power spectral density and phase spectrum is shown to be a specific case of this general approach. Specific examples demonstrating the proposed approach are presented. This dealt with the recognition of Gaussian stationary zero mean signal. A specific case using the short-time Fourier transform, where a different feature vector is optimal is presented. The gain of usage optimal feature vector is shown by using Fisher's criterion.