Real-Time Procedure for Development of an Optimal Time-Frequency Filter Suitable for Non-Linear Highly Nonstationary FM Signals Estimation

Estimation of nonstationary one-dimensional and two-dimensional signals represents very challenging problem that has efficiently been solved by using time-frequency and space/spatial-frequency analysis tools, respectively. However, these solutions provide high quality results only in the cases of linear frequency modulated (FM) signals. To this end, regions of support of the developed solutions correspond to the instantaneous frequency (IF) of the estimated signals, whereas the filtering problem is reduced to the IF estimation. Contrarily, non-linear signals occupy certain ranges of frequencies in a time instant, so that the IF estimation-based solutions cannon produce high quality results in this case. Therefore, in this paper the time-frequency filtering solution suitable for the non-linear FM signal estimation is considered.

I. Introduction

Estimation of highly nonstationary signals, problem widely considered during last two decades, can be resolved by using tools of the time-frequency (TF) analysis (the case of one-dimensional (1D) signals) and of the space/spatial-frequency analysis (the case of two-dimensional (2D) signals). These solutions result in nonstationary, TF and space/spatial-frequency filters, [1]–[7], respectively. Most of them belong to the linear filters, [1], since they include either only linear steps within their explicit designing (the classical Zadeh and Weyl filters) or their regions of support are estimated based on linear TF transforms (the STFT and Gabor filters). Contrarily, regions of support of non-linear filters, within their implicit designing, are estimated based on quadratic (non-linear) TF distributions (TFDs). The non-linear TF filters improve performances and estimation quality of linear TF filters, but at the expense of their complexity.