Time-Frequency Analysis Using Warped-Based High-Order Phase Modeling

The high-order ambiguity function (HAF) was introduced for the estimation of polynomial-phase signals (PPS) embedded in noise. Since the HAF is a nonlinear operator, it suffers from noise-masking effects and from the appearance of undesired cross-terms when multicomponents PPS are analyzed. In order to improve the performances of the HAF, the multi-lag HAF concept was proposed. Based on this approach, several advanced methods (e.g., product high-order ambiguity function (PHAF)) have been recently proposed. Nevertheless, performances of these new methods are affected by the error propagation effect which drastically limits the order of the polynomial approximation. This phenomenon acts especially when a high-order polynomial modeling is needed: representation of the digital modulation signals or the acoustic transient signals. This effect is caused by the technique used for polynomial order reduction, common for existing approaches: signal multiplication with the complex conjugated exponentials formed with the estimated coefficients. In this paper, we introduce an alternative method to reduce the polynomial order, based on the successive unitary signal transformation, according to each polynomial order. We will prove that this method reduces considerably the effect of error propagation. Namely, with this order reduction method, the estimation error at a given order will depend only on the performances of the estimation method.