Nadine Martin

Spectrogram segmentation by means of statistical features for non-stationary signal interpretation

Time-frequency representations (TFRs) are suitable tools for nonstationary signal analysis, but their reading is not straightforward for a signal interpretation task. This paper investigates the use of TFR statistical properties for classification or recognition purposes, focusing on a particular TFR: the spectrogram. From the properties of a stationary process periodogram, we derive the properties of a nonstationary process spectrogram. It leads to transform the TFR to a local statistical features space from which we propose a method of segmentation. We illustrate our matter with first- and second-order statistics and identify the information they, respectively, provide. The segmentation is operated by a region growing algorithm, which does not require any prior knowledge on the nonstationary signal. The result is an automatic extraction of informative subsets from the TFR, which is relevant for the signal understanding. Examples are presented concerning synthetic and real signals.

Circularity of the STFT and Spectral Kurtosis for Time-Frequency Segmentation in Gaussian Environment

This paper investigates the circularity of short time Fourier transform (STFT) coefficients noise only, and proposes a modified STFT such that all coefficients coming from white Gaussian noise are circular. In order to use the spectral kurtosis (SK) as a Gaussianity test to check if signal points are present in a set of STFT points, we consider the SK of complex circular random variables, and its link with the kurtosis of the real and imaginary parts. We show that the variance of the SK is smaller than the variance of the kurtosis estimated from both real and imaginary parts. The effect of the noncircularity of Gaussian variables upon the spectral kurtosis of STFT coefficients is studied, as well as the effect of signal presence. Finally, a time-frequency segmentation algorithm based on successive iterations of noise variance estimation and time-frequency coefficients detection is proposed. The iterations are stopped when the spectral kurtosis on nondetected points reaches zero. Examples of segmented time-frequency space are presented on a dolphin whistle and on a simulated signal in nonwhite and nonstationary Gaussian noise.

Three-component signal recognition using time, time-frequency, and polarization information-application to seismic detection of avalanches

A method for automatic signal recognition, applied to seismic signals classification, is presented. It is based on the fusion of data derived from the analysis of the signal in three domains: time, time-frequency, and polarization. In the time domain, two techniques are used for envelope shape parametrization. In the time-frequency domain, the autoregressive and Capon (ARCAP) time-frequency method is used on a gliding time-window to estimate the spectral components of the signal versus time. For each window, the frequencies are estimated using AR modelization. The power at each frequency and the corresponding filtered signal are estimated using Capons (1969) method. A comparison with Fouriers narrow-bandpass filtering shows that Capons method produces a better filtering. In the polarization domain, two original methods are proposed: one for checking the linear polarization of a signal and one for localizing the linear waves in the time-frequency plane. A system for automatic recognition of seismic signals associated with avalanches is then presented as an application. Signal features are derived from the analysis to sum up the characteristics of the signal in each domain. These features are combined using fuzzy logic and credibility factors, according to rules derived from physical knowledge (generating processes and propagation rules), in order to decide whether a signal comes from an avalanche or not. The global rate of correct recognition is over 90% for that first version of the system.

Estimation of the instantaneous amplitude and frequency of non-stationary short-time signals

We consider the modeling of non-stationary discrete signals whose amplitude and frequency are assumed to be nonlinearly modulated over very short-time duration. We investigate the case where both instantaneous amplitude (IA) and instantaneous frequency (IF) can be approximated by orthonormal polynomials. Previous works dealing with polynomial approximations refer to orthonormal bases built from a discretization of continuous-time orthonormal polynomials. As this leads to a loss of the orthonormal property, we propose to use discrete orthonormal polynomial bases: the discrete orthonormal Legendre polynomials and a discrete base we have derived using Gram-Schmidt procedure. We show that in the context of short-time signals the use of these discrete bases leads to a significant improvement in the estimation accuracy. We manage the model parameter estimation by applying two approaches. The first is maximization of the likelihood function. This function being highly nonlinear, we propose to apply a stochastic optimization technique based on the simulated annealing algorithm. The problem can also be considered as a Bayesian estimation which leads us to apply another stochastic technique based on Monte Carlo Markov Chains. We propose to use a Metropolis Hastings (MH) algorithm. Both approaches need an algorithm parameter tuning that we discuss according our application context. Monte Carlo simulations show that the results obtained are close to the Cramer-Rao bounds we have derived. We show that the first approach is less biased than the second one. We also compared our results with the higher ambiguity function-based method. The methods proposed outperform this method at low signal to noise ratios (SNR) in terms of estimation accuracy and robustness. Both proposed approaches are of a great utility when scenarios in which signals having a small sample size are non-stationary at low SNRs. They provide accurate system descriptions which are achieved with only a reduced number of basis functions.

A New Flexible Approach to Estimate the IA and IF of Nonstationary Signals of Long-Time Duration

In this paper, we propose an original strategy for estimating and reconstructing monocomponent signals having a high nonstationarity and long-time duration. We locally apply to short-time duration intervals the strategy developed in our previous work about nonstationary short-time signals. This paper describes a nonsequential time segmentation that provides segments whose lengths are suitable for modeling both the instantaneous amplitude and frequency locally with low-order polynomials. Parameter estimation is done independently for each segment by maximizing the likelihood function by means of the simulated annealing technique. The signal is then reconstructed by merging the estimated segments. The strategy proposed is sufficiently flexible for estimating a large variety of nonstationarity and specifically applicable to high-order polynomial phase signals. The estimation of a high-order model is not necessary. The error propagation phenomenon occurring with the known approach, the higher ambiguity function (HAF)-based method, is avoided. The proposed strategy is evaluated using Monte Carlo noise simulations and compared with the Cramer-Rao bounds (CRBs). The signal of a songbird is used as a real example of its applicability.

Estimation of a white Gaussian noise in the Short Time Fourier Transform based on the spectral kurtosis of the minimal statistics: Application to underwater noise

In this paper we present a noise level estimator using minimal values of the Short Time Fourier Transform of a signal embedded in a white Gaussian noise. The spectral kurtosis of the smallest values is used to estimate the variance of the noise without any a priori knowledge on the signal. This estimation is illustrated on both a synthetic and speech signal. A dolphin whistle detection in underwater noise is given as an application.

Short Time Fourier Transform Probability Distribution for Time-Frequency Segmentation

Taking as signal model the sum of a non-stationary deterministic part embedded in a white Gaussian noise, this paper presents the distribution of the coefficients of the short time Fourier transform (STFT), which is used to determine the maximum likelihood estimator of the noise level. We then propose an automatic segmentation algorithm of the real and imaginary parts of the STFT based on statistical features, which is an alternative to the spectrogram segmentations considered as image segmentations. Examples of segmented time-frequency space are presented on a simulated signal and on a dolphin whistle

Time-Frequency Tracking of Spectral Structures Estimated by a Data-Driven Method

The installation of a condition monitoring system (CMS) aims to reduce the operating costs of the monitored system by applying a predictive maintenance strategy. However, a system-driven configuration of the CMS requires the knowledge of the system kinematics and could induce a lot of false alarms because of predefined thresholds. The purpose of this paper is to propose a complete data-driven method to automatically generate system health indicators without any a priori on the monitored system or the acquired signals. This method is composed of two steps. First, every acquired signal is analyzed: the spectral peaks are detected and then grouped in a more complex structure as harmonic series or modulation sidebands. Then, a time-frequency tracking operation is applied on all available signals: the spectral peaks and the spectral structures are tracked over time and grouped in trajectories, which will be used to generate the system health indicators. The proposed method is tested on real-world signals coming from a wind turbine test rig. The detection of a harmonic series and a modulation sideband reports the birth of a fault on the main bearing inner ring. The evolution of the fault severity is characterized by three automatically generated health indicators and is confirmed by experts.

Maximum likelihood noise estimation for spectrogram segmentation control

This communication is composed of two related parts. First we propose an approximation to the Maximum Likelihood estimator of the γ distribution parameters. We show that it leads to build an efficient estimator of a white Gaussian process variance by noting that γ distribution admits sufficient statistics. Second we describe an application of this result to a non-stationary signal spectrogram segmentation that we proposed recently. Examples of segmented spectrograms are presented on a synthetic signal and on an acoustical recording of a dolphin whistle.

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

In time-frequency analysis, Capons 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 Capons 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 Capons 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. >