Instantaneous frequency estimation and localization

Abstract

In many applications, a critical feature of a non-stationary signal is provided by its instantaneous frequency (IF), which accounts for the signal spectral variations as a function of time. This chapter presents methods and algorithms for the localization and estimation of the signal IF using time-frequency (t,f) based methods. The topic is covered in seven sections with appropriate internal cross-referencing to this and other chapters.

In addition to filter banks and zero-crossings, one of the first conventional approaches for IF estimation used the spectrogram. To account for its major limitations related to accuracy, resolution, window dependence, and sensitivity, improvements were made by introducing iterative methodologies on the estimate provided by the first moment of the spectrogram (Section 10.1). Another approach uses an adaptive algorithm for IF estimation using the peak of suitable TFDs with adaptive window length (Section 10.2). This method was extended to the case of multicomponent signals using high-resolution TFDs such as the modified B-distribution (Section 10.3). When the signals considered have polynomial FM characteristics, both the peak of the polynomial WVD and higher-order ambiguity functions can be used as IF estimators (Section 10.4). In the special case when the signals are subject to random amplitude modulation (or multiplicative noise), IF estimation procedures are described using the peak of the WVD for linear FM signals, and the peak of the PWVD for nonlinear FM signals (Section 10.5). Then, a comparison of multicomponent IF estimation algorithms is provided (Section 10.6); and methods for IF and polynomial phase parameters estimation using linear (t,f) representations are presented (Section 10.7). Next, linear (t,f) methods are described for IF and polynomial phase parameter estimation. Finally, the concept of particle filtering is used for sequential Bayesian estimation of the IF (Section 10.8).