A fast time-frequency multi-window analysis using a tuning directional kernel
Résumé
In this paper, a novel approach for time-frequency analysis and detection, based on the chirplet transform and dedicated to non-stationary as well as multi-component signals, is presented. Its main purpose is the estimation of spectral energy, instantaneous frequency (IF), spectral delay (SD), and chirp rate (CR) with a high time-frequency resolution (separation ability) achieved by adaptive fitting of the transform kernel. We propose two efficient implementations of this idea, which allow to use the fast Fourier transform (FFT). In the first one, referred to as “self-tuning”, a previously proposed CR estimation is used for a local fitting of the chirplet kernel over time. For this purpose, we use the CR associated with the dominant (prominent) component. In the second one, we define a new measure for evaluating at each time-frequency point, how the used analyzing window is matched to the signal. This measure is defined as the absolute difference between the estimated CR and the CR parameter associated to the used analysis window. Our method is able to produce combined time-frequency distributions of the spectral energy, IF, SD, and CR. They are obtained using several classical chirplet transforms with analysis windows of various CRs. The compositions are made by finding the lowest fitting measure for every time-frequency points over all transforms. Finally, we assess the robustness of the methods by a detection application and time-frequency localization, both in the presence of high additive white Gaussian noise (additive white Gaussian noise (AWGN)) as well as we present many time-frequency (TF) images of synthetic and real-world signals.