Julien Huillery

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

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

Gaussian Noise Time-Varying Power Spectrum Estimation With Minimal Statistics

Given the spectrogram of an unknown signal embedded in a Gaussian noise, the Minimal Statistics Maximum Likelihood (MiniSMaL) estimator of the noise time-varying power spectrum is presented, and a method to tune one of its parameter is studied. The objective of the minimal statistics approach is to separate the signal of interest from the noise in order to estimate properly the probabilistic properties of the latter. Considering an initial time-frequency estimation neighborhood, the strategy relies on the selection of a minimal subset containing the time-frequency coefficients with the smallest values. Estimators of the noise are then sought from this minimal subset. In this work, the case of a spectrogram constructed from a finite-length discrete-time noisy signal is presented. This study extends previous works on minimal statistics on two aspects: first, the maximum likelihood estimate of the noise is formulated according to a clear analysis of the probability distribution of the time-frequency coefficients. Second, the choice of an optimal minimal subset is investigated. The signal versus noise discrimination property of the spectral kurtosis is used to select a minimal subset which ensures a fair trade-off between the bias and the variance of the estimator. The resulting performances are discussed and compared with those of other methods through numerical simulations on synthetic signals. The use of the MiniSMaL estimator in a time-frequency detection procedure is finally illustrated on a real-world signal.

Novel Design for a Rectenna to Collect Pulse Waves at 2.4 GHz

A novel rectifying circuit topology is proposed for converting electromagnetic pulse waves (PWs), that are collected by a wideband antenna, into dc voltage. The typical incident signal considered in this paper consists of 10-ns pulses modulated around 2.4 GHz with a repetition period of 100 ns. The proposed rectifying circuit topology comprises a double-current architecture with inductances that collect the energy during the pulse delivery as well as an output capacitance that maintains the dc output voltage between the pulses. Experimental results show that the efficiency of the rectifier reaches 64% for a mean available incident power of 4 dBm. Similar performances are achieved when a wideband antenna is combined with the rectifier in order to realize a rectenna. By increasing the repetition period of the incident PWs to 400 ns, the rectifier still operates with an efficiency of 52% for a mean available incident pulse power of −8 dBm. Finally, the proposed PW rectenna is tested for a wireless energy transmission application in a low-

Optimal identification experiment design for LPV systems using the local approach

Q

Time reversed pulse waves study for wireless energy transmission in a low Q cavity

cavity. The time reversal technique is applied to focus PWs around the desired rectenna. Results show that the rectenna is still efficient when noisy PW is handled.

Time-Frequency Modeling and Detection of random non-stationary signals for Monitoring Purposes

In this paper, we consider the problem of optimally designing the experimental conditions for LPV system identification with the local approach. Such an LPV system identification experiment is characterized by a number of local LTI identification experiments performed at constant values of the scheduling variable. The main contribution of this paper is to determine these constant values of the scheduling variable as well as the input spectra of the corresponding local LTI identification experiments in order to obtain a user-defined model accuracy with the least input energy.

Wireless Transmission of Electromagnetic Energy Based on a Time Reversal Approach for Indoor Applications

An original approach based on time reversal technique is studied for wireless energy transmission with electromagnetic waves. Experiments around 2.45 GHz are performed in a low-Q cavity of human size approaching real indoor environment. It is shown that, in order to increase the amplitude of the focused signals on a specific spot using time reversal technique, expanding the bandwidth of the emitted signals is needed. In addition, focused spot dimension is theoretically and experimentally illustrated. Other potential benefits of the time reversal technique are discussed and the superiority of energy performance of this technique compared to others (e.g. Inverse Filter and Continuous Wave) is demonstrated.

Design of TE-Polarized Bessel Antenna in Microwave Range Using Leaky-Wave Modes

This paper deals with the modelization and detection of non-stationary random signals in the time-frequency space. A time-frequency random model of signal is derived from a given temporal model. The time model we are interested in consists in a deterministic signal embedded in an additive centered Gaussian perturbation. This Gaussian model is characterized by two parameters, which are the mean and covariance matrix of the process. The corresponding time-frequency model depends on the time-frequency transform applied to the signal. For the spectrogram, the determinant parameters are the nature and length of the analysis window and the zero-padding. We show that for a Gaussian signal, spectrogram coecients distribution can be approximated by a chi2 law defined by three parameters. A time-frequency signal detection task inspired from a Neyman-Pearson strategy is performed on the basis of this probabilistic time-frequency model. The detector determines the time-frequency regions where signal energy is present. It thus provides a time-frequency signature of the signal. This information is used for structural health monitoring techniques. Extraction of the fundamental meshing frequency and harmonics of a gearbox under varying load conditions is presented.