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Techniques for estimating temporal variation in the frequency content of acoustic tones based on short-time fast Fourier transforms are fundamentally limited by an inherent time-frequency trade-off. This paper presents an alternative methodology, based on Hilbert spectral analysis, that is not affected by this weakness, and applies it to the accurate estimation of mosquito wing beat frequencies. Mosquitoes are known to communicate with one another via the sounds generated by their flapping wings. Active frequency modulation between pairs of mosquitoes is thought to take place as a precursor to courtship. Studying the acoustically-based interactions of mosquitoes therefore relies on an accurate representation of flight frequency as a time-evolving property, yet conventional Fourier spectrograms are unable to capture the rapid modulations in frequency that mosquito flight tones exhibit. The algorithms introduced in this paper are able to automatically detect and extract fully temporally resolved frequency information from audio recordings. Application of the technique to experimental recordings of single tethered mosquitoes in flight reveals corroboration with previous reported findings. The advantages of the method for animal communication studies are discussed, with particular attention given to its potential utility for studying pairwise mosquito interactions.