Effects of Cauchy Integral Formula Discretization on the Precision of IF Estimation: Unified Approach to Complex-Lag Distribution and its Counterpart L-Form

Effects of Cauchy integral formula discretization on the concentration of time-frequency (TF) distribution are analyzed. As a result of this discretization, new forms of distributions are produced. In order to increase the accuracy of instantaneous frequency (IF) estimation, two solutions are considered: increasing the number of integration points and multiple successive integrations using the same number of points (it corresponds to the L-form of the TF distribution). In practical applications, the L-form of the fourth-order complex-lag distribution produces very efficient representation. In this case, the analysis of noise influence is also provided.