Adaptive Window Zero-Crossing-Based Instantaneous Frequency Estimation

Abstract

<p/> <p>We address the problem of estimating instantaneous frequency (IF) of a real-valued constant amplitude time-varying sinusoid. Estimation of polynomial IF is formulated using the zero-crossings of the signal. We propose an algorithm to estimate nonpolynomial IF by <it>local</it> approximation using a low-order polynomial, over a short segment of the signal. This involves the choice of window length to minimize the mean square error (MSE). The optimal window length found by directly minimizing the MSE is a function of the higher-order derivatives of the IF which are not available a priori. However, an optimum solution is formulated using an adaptive window technique based on the concept of <it>intersection of confidence intervals</it>. The adaptive algorithm enables minimum MSE-IF (MMSE-IF) estimation without requiring a priori information about the IF. Simulation results show that the adaptive window zero-crossing-based IF estimation method is superior to fixed window methods and is also better than adaptive spectrogram and adaptive Wigner-Ville distribution (WVD)-based IF estimators for different signal-to-noise ratio (SNR).</p

Event-triggered sampling using signal extrema for instantaneous amplitude and instantaneous frequency estimation

“…This is a classic bandwidth selection (relating to window-size) problem for LPR fitting in statistics [22] and a full treatment of it is beyond the scope of this paper. A work in this direction using ZCs for IF estimation of phase only signals is proposed in [35].…”

An Adaptive Resolution Computationally Efficient Short‐Time Fourier Transform

“…According to [6], the sampling instants of a nonuniformly sampled signal obtained with the level crossing sampling scheme (LCSS) are defined by (1). Where t n is the current sampling instant, t n−1 is the previous one, and dt n is the time delay between the current and the previous sampling instants (cf.…”

“…The spectral contents of these signals vary with time, which is a direct consequence of the signal generation process [1]. The STFT is a classical tool for characterizing such signals [2].…”

Auditory motivated level-crossing approach to instantaneous frequency estimation

“…We assume that the nature of the underlying IF variation is known a priori so that the appropriate model is employed. Estimating the IF when the underlying model is not known a priori is reported separately [20]. The ZC-IF and LC-IF estimates (corresponding to an arbitrarily chosen level value of 0.25) are shown in Fig.…”