A Fast Algorithm for the Quasi-Synchronous Window

A fast algorithm based on the central limit theorem is proposed for the quasi-synchronous window in this paper. Based on analysis of the quasi-synchronous window, a probability model is established for the purpose of obtaining the window coefficients. By the means of applying the central limit theorem to the model, it has been proved theoretically that a specific Gaussian window is capable of approximating the quasi-synchronous window accurately while the number of signal cycles is sufficiently large. Parameters of the Gaussian window are analyzed in detail, and some important formulas are given. By approximating the quasi-synchronous window with the specific Gaussian window, computational burden is decreased significantly. Computer simulations demonstrate that the algorithm outperforms both the current FFT based algorithm and the convolution based algorithm remarkably in terms of computational speed, especially when the number of signal cycles is large. In addition, it has been verified that precision of the fast algorithm is perfect