Estimating and interpreting the instantaneous frequency of a signal. II. Algorithms and applications

Abstract

The concept of instantaneous frequency (IF) is extended to discrete-time signals following a time-frequency perspective. The specific problem explored is that of estimating the IF of non-stationary signals such as frequency-modulated (FM) discrete-time signals embedded in Gaussian noise. Well-established methods for estimating the IF include differentiation of the phase and smoothing thereof, adaptive frequency estimation techniques such as the phase locked loop (PLL), and extraction of the peak from time-varying spectral representations. More recently, methods based on a modeling of the signal phase as a polynomial have been introduced. These methods are reviewed, and their performance compared on both simulated and real data. Guidelines are given as to which estimation method should be used for a given signal class and signal-to-noise ratio (SNR). The relevance to Time-Frequency Signal Processing is explored.