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Theoretical and practical comparisons of the reassignment method and the derivative method for the estimation of the frequency slope

In the context of non-stationary sinusoidal analysis, the theoretical comparison of the reassignment method (RM) and the derivative method (DM) for the estimation of the frequency slope is investigated. It is shown that for the estimation of the frequency slope the DM differs from the RM in that it does not consider the group delay. Theoretical equivalence is shown to be possible with a refinement of the DM. This refinement is evaluated on synthetic signals and shown to improve the estimation of the frequency slope. The differences between the two methods in terms of window and signal constraints are discussed to show when each method is more appropriate to use.