Abstract
The frequency-domain Prony method (FDPM) [Ando, IEEE Trans. Signal Process. 68, 3461-3470 (2020)] provides a novel and exact short-time, frequency-decomposed scheme for autoregressive model identification and sinusoidal parameter estimation with a superior statistical performance. By using it as localized estimation elements, we construct the time-frequency representation (TFR) of signals as the frequency-reassigned map of the damped sinusoidal parameters of their components. The FDPM for both single and multiple sinusoids is based on a small number of windowless Fourier coefficients of sampled sequence. Thus, a unified and flexible construction of resolution and decomposition structures including linear and log-linear frequency arrays and their combination is possible, and dense analysis along the time axis can be implemented without a significant increase in computational cost. Conditions for constructing the frequency-variant arrays are formulated. Two cooperative behaviors in the TFR are considered to find stable traces of frequencies and rapidly time-varying incidences and components. Several experiments are shown to confirm extended features and performances of the proposed TFR using musical, speech, and natural sound signals.
Highlights
Time–frequency representations (TFRs) provide a fundamental and powerful framework for various signal analyses and applications
The purpose of this study is to develop a method for constructing a TFR using the above features of the frequency-domain Prony method (FDPM)
Variations of the algorithms are indicated by the number l of sinusoids to be estimated simultaneously, the number m of Fourier coefficient (FC) used, as mFl, and the method used (R or C for the extra unknowns method and W for the windowing method)
Summary
Time–frequency representations (TFRs) provide a fundamental and powerful framework for various signal analyses and applications. Linear representations based on the spectral decomposition and quadratic ones for consistent description of the joint time–frequency energy of signals have been widely studied and applied, including extended resolutions and interference eliminations. The technique was extended to the difference equation of the autoregressive (AR) model to obtain the frequency-domain Prony method (FDPM) for AR model identification and sinusoidal parameter estimation from an arbitrarily short-duration sampled data sequence.. The purpose of this study is to develop a method for constructing a TFR using the above features of the FDPM. The obtained TFR is itself informative and can be an initial stage of a data-driven approach using multitone estimators for separating proximate sinusoids and/or adaptive time–frequency resolution for representing signal components that vary extremely widely. Several experimental evaluations are shown for some cooperative behaviors among multiple cells as well as the features and performances of the proposed TFR using musical, speech, and natural sound signals
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