One Fast Discrete Correlation Algorithm in the Frequency Domain

Correlation algorithm in the frequency domain is now in widespread use due to Fast Fourier Transform Algorithm. However, its calculating speed and accuracy need to be further studied for the limited length sequence. A kind of discrete correlation algorithm in the frequency domain was derived based on analyzing the correlation theorem and vectors in the frequency domain. As is shown from the simulation experiments for two periodic signals and the composite signals of mixing the stochastic signal, the error of correlation values obtained by using the correlation algorithm in the frequency domain and the classic correlation algorithm in the time domain was lower than 10^-6. Moreover, by contrast with the classic correlation algorithm in the time domain, the correlation algorithm in the frequency domain has higher accuracy and can enhance the calculation speed due to leave out the inverse FFT calculation step. It will play a significant role in removing the correlation components and solving the coherence components in composite signals.