A pde-Based Analysis of the Spectrogram Image for Instantaneous Frequency Estimation

Vittoria Bruni, Michela Tartaglione and Domenico Vitulano
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Vittoria Bruni: Department of Basic and Applied Sciences for Engineering, Sapienza University of Rome, via Antonio Scarpa 16, 00161 Rome, Italy
Michela Tartaglione: Department of Basic and Applied Sciences for Engineering, Sapienza University of Rome, via Antonio Scarpa 16, 00161 Rome, Italy
Domenico Vitulano: Department of Basic and Applied Sciences for Engineering, Sapienza University of Rome, via Antonio Scarpa 16, 00161 Rome, Italy

Mathematics, 2021, vol. 9, issue 3, 1-26

Abstract: Instantaneous frequency (IF) is a fundamental feature in multicomponent signals analysis and its estimation is required in many practical applications. This goal can be successfully reached for well separated components, while it still is an open problem in case of interfering modes. Most of the methods addressing this issue are parametric, that is, they apply to a specific IF class. Alternative approaches consist of non-parametric time filtering-based procedures, which do not show robustness to destructive interference—the most critical scenario in crossing modes. In this paper, a method for IF curves estimation is proposed. The case of amplitude and frequency modulated two-component signals is addressed by introducing a spectrogram time-frequency evolution law, whose coefficients depend on signal IFs time derivatives, that is, the chirp rates. The problem is then turned into the resolution of a two-dimensional linear system which provides signal chirp rates; IF curves are then obtained by a simple integration. The method is non-parametric and it results quite robust to destructive interference. An estimate of the estimation error, as well as a numerical study concerning method sensitivity and robustness to noise are also provided in the paper.

Keywords: partial differential equations; multicomponent signals; instantaneous frequency estimation; chirp rate estimation; ridge curves recovery; interfering AM-FM signals; non-separable modes; overlapping components (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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