A Capon´s time-octave representation application in room acoustics

In time-frequency analysis, Capon´s estimator has proven its efficiency in precise applications. In a context where a time-octave representation is also necessary, the authors propose a new method combining both Capon´s estimator and a time-octave representation. The main objective is to obtain legibility in the time frequency plane using a variable frequency resolution with a fixed time resolution. This fixed time resolution is possible owing to the good resolution properties of Capon´s estimator compared to the Fourier transform. This choice leads to a particular repartition of basic cells in the time-frequency plane that seems more adapted to a physical interpretation in the application presented. Nevertheless, a parallel with the wavelet transform is displayed: the constructed wavelet is adapted to the signal at each octave or at each fraction of octave. The proposed method is presented both in continuous and discrete formulations. Its structure is studied and a simplification is proposed when precise hypotheses are verified. Simulations and comparisons with classical representations (spectrogram, scalogram) are discussed. The contribution of each method, essentially in the duality of time-frequency and time-scale, are shown up in relation to the analyzed signal. Lastly, the proposed method and classical ones are applied on rear signals issued from room acoustics where the aim is the time-frequency characterization of concert halls from impulse responses