Refining the ambiguity domain characteristics of non-stationary signals for improved time-frequency analysis: Test case of multidirectional and multicomponent piecewise LFM and HFM signals

摘要

This paper aims at providing a more accurate description of the ambiguity domain characteristics of a piecewise multicomponent non-stationary signals with focus on piece-wise linear frequency modulated (LFM) (PW-LFM) signal and a mixed LFM and hyperbolic FM (HFM). The main motivation comes from the observed PW-LFM nature of several real life signals. It is essential that the characteristics of these types of signals be taken into account for the design of high resolution Time-Frequency Distributions (TFDs) and therefore to improve the application and interpretation of time-frequency signal analysis and processing. In this paper the ambiguity function (AF) of a general PW LFM signal is derived exactly and then analyzed to deduce important properties. The precise location and behavior of both auto-terms and cross-terms of a general piecewise LFM signal can be deduced from its AF. Numerical simulations using different types of test signals confirm the analytical derivations. An extension of the PW-LFM test signal is also presented by using HFM signals. For such signals, the exact analytical expression of auto-terms is given as well as the expression of cross-terms between HFM and LFM. The results obtained can be used in future studies to design more advanced quadratic time-frequency distributions (QTFDs) that exhibit improved properties in terms of resolution and accuracy. (C) 2018 Elsevier Inc. All rights reserved.