Dominique Fourer

Recursive versions of the Levenberg-Marquardt reassigned spectrogram and of the synchrosqueezed STFT

In this paper, we first present a recursive implementation of a recently proposed reassignment process called the Levenberg Marquardt reassignment, which allows a user to adjust the slimness of the signal components localization in the time-frequency plane. Thanks to a generalization of the signal reconstruction formula, we also present a recursive implementation of the synchrosqueezed short-time Fourier transform. This approach paves the way for a real-time computation of a reversible and adjustable almost-ideal time-frequency representation.

The ASTRES toolbox for mode extraction of non-stationary multicomponent signals

In this paper, we introduce the ASTRES∗ toolbox which offers a set of Matlab functions for non-stationary multi-component signal processing. The main purposes of this proposal is to offer efficient tools for analysis, synthesis and transformation of any signal made of physically meaningful components (e.g. sinusoid, trend or noise). The proposed techniques contain some recent and new contributions, which are now unified and theoretically strengthened. They can provide efficient time-frequency or time-scale representations and they allow elementary components extraction. Usage and description of each method are then detailed and numerically illustrated.

The Sliding Singular Spectrum Analysis: A Data-Driven Nonstationary Signal Decomposition Tool

Singular spectrum analysis (SSA) is a signal decomposition technique that aims at expanding signals into interpretable and physically meaningful components (e.g., sinusoids, noise, etc.). This paper presents new theoretical and practical results about the separability of the SSA and introduces a new method called sliding SSA. First, the SSA is combined with an unsupervised classification algorithm to provide a fully automatic data-driven component extraction method for which we investigate the limitations for components separation in a theoretical study. Second, the detailed automatic SSA method is used to design an approach based on a sliding analysis window, which provides better results than the classical SSA method when analyzing nonstationary signals with a time-varying number of components. Finally, the proposed sliding SSA method is compared to the empirical mode decomposition and to the synchrosqueezed short-time Fourier transform, applied on both synthetic and real-world signals.

A fast time-frequency multi-window analysis using a tuning directional kernel

Abstract 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.

Objective characterization of audio signal quality: Applications to music collection description

In this paper, we propose a set of audio features to describe the quality of an audio signal. Audio quality is here considered as being modified by the chain of processes/effects applied to the individual instrument tracks to obtain the final mix of a musical piece. Thus, the quality also depends on the mastering processes applied to the final mix or the signal degradation caused by MP3 compression. To evaluate our proposal, we created a large set of artificial mixes and also used real-world studio mixes. Using unsupervised and supervised classification methods, we show that our proposed audio features can detect the processing chain. Since this processing chain applied in professional studio has evolved over the years, we use our audio features to directly predict the decade during which a music track was recorded.

Recursive versions of the reassigned scalogram anc of the synchrosqueezed wavelet transform

This paper introduces a new class of mother wavelet functions, based on a specific analysis window which allows a recursive implementation of the Continuous Wavelet Transform (CWT). Using this new transform, we propose to compute a sharpened time-frequency representation by rewording the reassigned scalogram and the (first and second-order) synchrosqueezed CWT. We also propose an extension of the CWT reassignment operators, using the Levenberg-Marquardt algorithm, which can control the energy concentration of a reassigned scalogram through a damping parameter. Thus, our methods provide tools which pave the way of the real-time computation of reversible and almost-ideal time-frequency representations.

Estimation of time-frequency complex phase-based speech attributes using narrow band filter banks

In this paper, we present nonlinear estimators of nonstationary and multicomponent signal attributes (parameters, properties) which are instantaneous frequency, spectral (or group) delay, and chirp-rate (also known as instantaneous frequency slope). We estimate all of these distributions in the time-frequency domain using both finite and infinite impulse response (FIR and IIR) narrow band filers for speech analysis. Then, we present few examples including a novel type of imaging joining energy and phase acceleration in a single picture. Finally, we provide an open-source project — ccROJ — Time-Frequency C++ Framework of which we are authors and that is used for computing the presented figures.