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Adaptive Window Zero-Crossing-Based Instantaneous Frequency Estimation

Abstract

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 local 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 intersection of confidence intervals. 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).

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Correspondence to S. Chandra Sekhar.

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Sekhar, S.C., Sreenivas, T. Adaptive Window Zero-Crossing-Based Instantaneous Frequency Estimation. EURASIP J. Adv. Signal Process. 2004, 249858 (2004). https://doi.org/10.1155/S111086570440417X

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Keywords and phrases

  • zero-crossing
  • irregular sampling
  • instantaneous frequency
  • bias-variance tradeoff
  • confidence interval
  • adaptation