Adaptive multimode signal reconstruction from time–frequency representations

Abstract

This paper discusses methods for the adaptive reconstruction of the modes of multicomponent AM–FM signals by their time–frequency (TF) representation derived from their short-time Fourier transform (STFT). The STFT of an AM–FM component or mode spreads the information relative to that mode in the TF plane around curves commonly called ridges. An alternative view is to consider a mode as a particular TF domain termed a basin of attraction. Here we discuss two new approaches to mode reconstruction. The first determines the ridge associated with a mode by considering the location where the direction of the reassignment vector sharply changes, the technique used to determine the basin of attraction being directly derived from that used for ridge extraction. A second uses the fact that the STFT of a signal is fully characterized by its zeros (and then the particular distribution of these zeros for Gaussian noise) to deduce an algorithm to compute the mode domains. For both techniques, mode reconstruction is then carried out by simply integrating the information inside these basins of attraction or domains.

Assessment of musical noise using localization of isolated peaks in time-frequency domain

“…Unlike signals considered in [16,21], audio signals are too complex to be easily described as the combination of simple modulated components, and then do not exhibit isolated areas of interest. One notable exception is precisely the spots that appear in audio signals with a lot of musical noise, as described in Section 2.…”

“…Step 4: Group adjacent triangles in domains components using this approach has been proven to be of interest in tasks such as mode extraction [21] or filtering [16].…”

An Adaptive Computation of Contour Representations for Mode Decomposition

“…This section introduces a new adaptive algorithm that uses a criterion based on a local rather than punctual orientation of RV r to define a direction of projection. More precisely, the direction of projection for each RV r is defined by considering a squared neighborhood centered at the point of study instead of considering only one single grid point as introduced [17], [18]. This results in a much more robust estimation of the TF signature of modes like Dirac impulses, even at high noise level, while maintaining a good behavior for AM/FM modes.…”

“…Note that the direction of projection θ being fixed a priori, the technique does not adapt well to the determination of CPs corresponding to varying orientations. To deal with this problem, an improved technique to compute CPs was proposed in [17], [18]. It first consisted in remarking that, due to the discrete nature of the studied signals, RV should be viewed as a displacement on a grid not a vector of with real coordinates.…”

Adaptive data analysis: theory and applications

“…The authors for the articles in this theme issue stem from many different fields, including applied mathematics (with articles on new theoretical developments by Cicone et al [1]; Daubechies et al [2]; Hou & Shi [3]; Joliffe & Cadima [4]; and Mallat [5]), physics (Meignen et al [6]), physiology (Yeh et al [7]), general science and data analysis (Huang et al [8]), meteorology and climate (Qiao et al [9] and Wu et al [10]) and biomedical research (Hemakom et al [11]). …”