Fabien Millioz

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.

Sparse Detection in the Chirplet Transform: Application to FMCW Radar Signals

This paper aims to detect and characterize a signal coming from frequency modulation continuous wave radars. The radar signals are made of piecewise linear frequency modulations. The maximum chirplet transform (MCT), a simplification of the chirplet transform is proposed. A detection of the relevant maximum chirplets is proposed based on iterative masking, an iterative detection followed by window subtraction that does not require the recomputation of the spectrum. This detection is designed to provide a sparse subset of maximum chirplet coefficients. The chirplets are then gathered into linear chirps whose starting time, length, and chirprate are estimated. These chirps are then gathered again back into the different frequency modulation continuous wave signals, ready to be classified. An illustration is provided on synthetic data.

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 and time-scale analysis of Barkhausen noise signals

Abstract Carrying out information about the microstructure and stress behaviour of ferromagnetic steels, magnetic Barkhausen noise (MBN) has been used as a basis for effective non-destructive testing methods, opening new areas in industrial applications. One of the factors that determines the quality and reliability of the MBN analysis is the way information is extracted from the signal. Commonly, simple scalar parameters are used to characterize the information content, such as amplitude maxima and signal root mean square. This paper presents a new approach based on the time—frequency analysis. The experimental test case relates the use of MBN signals to characterize hardness gradients in a AISI4140 steel. To that purpose different time—frequency (TFR) and time-scale (TSR) representations such as the spectrogram, the Wigner-Ville distribution, the Capongram, the ARgram obtained from an AutoRegressive model, the scalogram, and the Mellingram obtained from a Mellin transform are assessed. It is shown that, due to nonstationary characteristics of the MBN, TFRs can provide a rich and new panorama of these signals. Extraction techniques of some time—frequency parameters are used to allow a diagnostic process. Comparison with results obtained by the classical method highlights the improvement on the diagnosis provided by the method proposed.

On the Probability Distributions of Spectrogram Coefficients for Correlated Gaussian Process

This paper deals with the probability distribution of spectrogram coefficients related to a correlated centered Gaussian process. It is shown that the windowing operation and the presence of correlation between input samples may introduce heteroscedaticity and correlation between the real and imaginary parts of the short time Fourier transform. The impact of this phenomenon on spectrogram distribution is evaluated in terms of deviation from the chi-square distribution. A numerical method is provided to calculate the probability density function of the spectrogram coefficients and deviation from the chi-square distribution is evaluated using the Kullback-Liebler divergence. This measure of deviation is used to control the validity of a chi-square approximation

Detection and segmentation of fmcw radar signals based on the chirplet transform

In this paper we present a algorithm designed to detect and characterise the signal coming from Frequency Modulation Continuous Wave radars. The signals are made of linear frequency modulations. A few relevant coefficients of the chirplet transform are selected, and then gathered into chirps whose starting time, length, and chirprate are estimated. An example is provided on a synthetic signal.