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<p>This paper presents an important digital signal-processing application – instantaneous phase and frequency estimation of a complex signal – where recursive Infinite Impulse Response (IIR) filters have a much lower complexity than standard non-recursive Finite Impulse Response (FIR) filters of comparable precision and accuracy. For unbiased estimates and a low variance at high SNR (greater than 10–12 dB), the conventional requirements of (FIR or IIR) filters for this problem are specified. For improved performance and the attainment of the Cramer-Rao lower-bound at low SNR (less than 3–6 dB) a further unconventional requirement on the frequency response, i.e. a one-sample lead for improved phase unwrapping, is specified and shown to yield improved performance in Monte Carlo simulations. A simple but novel procedure that solves for recursive IIR solutions with an arbitrary or optimal group delay and good passband phase-linearity is described. The novelty of this work lies in both the improved phase-unwrapping technique for estimating instantaneous phase and frequency at low SNR in digital receivers using FIR or IIR predictors, and in the procedure used to design low-pass digital IIR filters for smoothing and prediction of uniformly sampled time-series data, e.g. phase measurements.</p>

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Recursive Optimal Filters for Smoothing and Prediction with Instantaneous Phase and Frequency Estimation Applications

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年7月9日

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  • Hugh Lachlan Kennedy

摘要

This paper presents an important digital signal-processing application – instantaneous phase and frequency estimation of a complex signal – where recursive Infinite Impulse Response (IIR) filters have a much lower complexity than standard non-recursive Finite Impulse Response (FIR) filters of comparable precision and accuracy. For unbiased estimates and a low variance at high SNR (greater than 10–12 dB), the conventional requirements of (FIR or IIR) filters for this problem are specified. For improved performance and the attainment of the Cramer-Rao lower-bound at low SNR (less than 3–6 dB) a further unconventional requirement on the frequency response, i.e. a one-sample lead for improved phase unwrapping, is specified and shown to yield improved performance in Monte Carlo simulations. A simple but novel procedure that solves for recursive IIR solutions with an arbitrary or optimal group delay and good passband phase-linearity is described. The novelty of this work lies in both the improved phase-unwrapping technique for estimating instantaneous phase and frequency at low SNR in digital receivers using FIR or IIR predictors, and in the procedure used to design low-pass digital IIR filters for smoothing and prediction of uniformly sampled time-series data, e.g. phase measurements.