Recognition of signals with time-varying spectrum using time-frequency transformation with non-uniform sampling

This paper presents the efficient algorithm for estimation of parameters of signals with a polynomial phase. The multilinear method with uniform sampling of an analyzed signal is replaced by the multilinear method with non-uniform sampling. By sampling the signal at none-equidistant time instants, the procedure lowers the nonlinearity of the estimator function and allows to get lower thresholds of SNR ratios. The time-frequency distribution with square root-based sampling within the kernel is presented. It is shown that a fourth-order kernel can be successively used for estimation of the fifth and fourth phase parameters of phase polynomial signals (PPS). The presented distribution can be implemented with Fast Fourier Transform (FFT), what decreases the computational load. In this paper the linear interpolation is proposed for computation of the square root-based sampling kernel instead of the formula known in literature. Using the additional cubic phase (CP) function allows estimation of remaining parameters in an efficient manner. The presented algorithm requires only one-dimensional optimization in every step of computation. This approach substantially outperforms known multilinear functions for estimation of parameters of a phase polynomial.