Digital Filters for Instantaneous Frequency Estimation
Hugh Lachlan Kennedy

TL;DR
This paper discusses digital filtering techniques for high-accuracy, low-latency frequency estimation of sinusoidal signals in noisy environments, emphasizing methods suitable for embedded systems and signals with polynomial phase.
Contribution
It introduces and analyzes various digital filtering approaches for instantaneous frequency estimation, highlighting practical solutions for real-time applications with low complexity.
Findings
Recursive filtering methods improve estimation accuracy.
Long FFTs are computationally expensive for real-time systems.
Monte-Carlo simulations validate the effectiveness of proposed filters.
Abstract
This technical note is on digital filters for the high-fidelity estimation of a sinusoidal signal's frequency in the presence of additive noise. The complex noise is assumed to be white (i.e. uncorrelated) however it need not be Gaussian. The complex signal is assumed to be of (approximately) constant magnitude and (approximately) polynomial phase such as the chirps emitted by bats, whale songs, pulse-compression radars, and frequency-modulated (FM) radios, over sufficiently short timescales. Such digital signals may be found at the end of a sequence of analogue heterodyning (i.e. mixing and low-pass filtering), down to a bandwidth that is matched to an analogue-to-digital converter (ADC), followed by digital heterodyning and sample rate reduction (optional) to match the clock frequency of the processor. The spacing of the discrete frequency bins (in cycles per sample) produced by the…
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Taxonomy
TopicsAdvanced Electrical Measurement Techniques · Structural Health Monitoring Techniques · Blind Source Separation Techniques
