Instantaneous frequency and kernel requirements for discrete time-frequency distributions

Abstract In this paper, we introduce a new definition for the in- stantaneous frequency of a discrete-time analytic signal.Unlike the existing definition which uses only two data samples around a particular time, this method utilizes all the data samples for estimating the instantaneous fre- quency. We prove that this quantity is identical to the average frequency evaluated at the particular time in thediscrete-time TFD. This property is consistent with theanalogous continuous-time property. We also derive re-quirements on the discrete-time kernel needed to satisfythis property. Using computer-generated signals and realdata, performance comparisons are made between the pro-posed approach and the existing one. 1 Introduction The mixed time-frequency distribution (TFD) has re- ceived considerable attention recently as a powerful toolfor analyzing a variety of deterministic and stochastic sig- nals [2,7,14]. A TFD is used in an attempt to localizefrequency content in time. The spectrogram has been