The Development of the Algorithm for Estimating the Spectral Correlation Function Based on Two-Dimensional Fast Fourier Transform

P. 75–86.

Shevgunov T., Efimov E., Kirdyashkin V., Kravchenko T.

This chapter presents the algorithm for estimating spectral correlation
function of a random process that is a valid bi-frequency description of the probabilistic
properties of any wide-sense cyclostationary process and relates to its cyclic
autocorrelation function via Fourier transform. The key point of the algorithm is that
it is based on the two-dimensional discrete Fourier transform of the sample dyadic
correlation function weighted by the two-dimensional windowing function, which
is rectangular in the direction orthogonal to the current-time axis shape. The dedicated
mathematical software libraries implementing fast Fourier transform, which
is typically used for image processing, achieve higher performance in comparison
with other algorithms involving spectra accumulation. The signal containing a pulse
sequence with random amplitudes masked by the additive stationary white Gaussian
noise is used in numerical simulation to provide an example of the spectral correlation
function estimation procedure and obtain results demonstrating the effectiveness
of the proposed algorithm.

Keywords: Fast Fourier Transform, Cyclostationarity, spectral correlation density, spectral correlation function, Cyclic frequency, Two-dimensional FFT, Pseudo-power

In book

Intelligent Systems Reference Library

Vol. 184: Advances in Signal Processing: Theories, Algorithms, and System Control. , Springer, 2020.