Using two-dimensional fast Fourier transform for estimating spectral correlation function

Abstract

The paper presents the algorithm for estimating spectral correlation function (SCF) of a wide-sense cyclostationary random process. SCF provides the quantitative representation of the correlation in frequency domain and relates to cyclic autocorrelation function via Fourier transform. The algorithm is based on two-dimensional Fourier transform, which is being applied to the discrete diadic correlation function weighted by a two-dimensional windowing function, chosen rectangular in the direction orthogonal to the current-time axis. This transform can be implemented by means of the fast Fourier transform (FFT) algorithm, which is built-in in a variety of modern mathematical platforms. A pulse-amplitude modulated process masked by the additive stationary Gaussian noise was considered as an example of a random process exhibiting strong cyclostationarity. The numerical simulation where the estimation of spectral correlation function of such process is conducted, and it proved the effectiveness of the proposed algorithm.