Estimation de la fréquence instantanée des signaux FM par opérateur d'énergie Psi_B

Psi_B energy operator is an extension of the cross Teager-Kaiser energy operator which is an non-linear energy tracking operator to deal with complex signals and its usefulness for non-stationary signals analysis has been demonstrated. In this letter two new properties of Psi_B are established. The first property is the link between Psi_B and the dynamic signal which is a generalization of the Instantaneous Frequency (IF). The second property obtained for frequency modulated signals is a simple way to estimate the IF. These properties confirm the interest of Psi_B operator to track the non-stationary of a signal. Results of IF estimation in noisy environment of a non-linear FM signal are presented and comparison to Wigner-Ville distribution and Hilbert transform-based method is provided

Densely distributed and real-time scour hole monitoring using piezoelectric rod sensors

This study aims to validate a piezoelectric driven-rod scour monitoring system that can sense changes in scour depth along the entire rod at its instrumented location. The proposed sensor is a polymeric slender rod with a thin strip of polyvinylidene fluoride that runs through its midline. Extraction of the fundamental frequency allows the direct calculation of the exposed length (or scour depth) of the slender rod undergoing fluid flow excitation. First, laboratory validation in dry conditions is presented. Second, hydrodynamic testing of the sensor system in a soil-bed flume is discussed. Each rod was installed using a three-dimensional-printed footing designed for ease of installation and stabilization during testing. The sensors were installed in a layout designed to capture symmetric scour conditions around a scaled pier. In order to analyze the system out of steady-state conditions, water velocity was increased in stages during testing to induce different degrees of scour. As ambient water flow excited the portion of the exposed rods, the embedded piezoelectric element outputted a time-varying voltage signal. Different methods were then employed to extract the fundamental frequency of each rod, and the results were compared. Further testing was also performed to characterize the relationship between frequency outputs and flow velocity, which were previously thought to be independent. In general, the proposed driven-rod scour monitoring system successfully captured changing frequencies under varied flow conditions

The estimation of geoacoustic properties from broadband acoustic data, focusing on instantaneous frequency techniques

The compressional wave velocity and attenuation of marine sediments are fundamental to marine science. In order to obtain reliable estimates of these parameters it is necessary to examine in situ acoustic data, which is generally broadband. A variety of techniques for estimating the compressional wave velocity and attenuation from broadband acoustic data are reviewed. The application of Instantaneous Frequency (IF) techniques to data collected from a normal-incidence chirp profiler is examined. For the datasets examined the best estimates of IF are obtained by dividing the chirp profile into a series of sections, estimating the IF of each trace in the section using the first moments of the Wigner Ville distribution, and stacking the resulting IF to obtain a composite IF for the section. As the datasets examined cover both gassy and saturated sediments, this is likely to be the optimum technique for chirp datasets collected from all sediment environments

On the Analytic Wavelet Transform

An exact and general expression for the analytic wavelet transform of a real-valued signal is constructed, resolving the time-dependent effects of non-negligible amplitude and frequency modulation. The analytic signal is first locally represented as a modulated oscillation, demodulated by its own instantaneous frequency, and then Taylor-expanded at each point in time. The terms in this expansion, called the instantaneous modulation functions, are time-varying functions which quantify, at increasingly higher orders, the local departures of the signal from a uniform sinusoidal oscillation. Closed-form expressions for these functions are found in terms of Bell polynomials and derivatives of the signal's instantaneous frequency and bandwidth. The analytic wavelet transform is shown to depend upon the interaction between the signal's instantaneous modulation functions and frequency-domain derivatives of the wavelet, inducing a hierarchy of departures of the transform away from a perfect representation of the signal. The form of these deviation terms suggests a set of conditions for matching the wavelet properties to suit the variability of the signal, in which case our expressions simplify considerably. One may then quantify the time-varying bias associated with signal estimation via wavelet ridge analysis, and choose wavelets to minimize this bias

Comparison of techniques for estimating the frequency selectivity of bandlimited channels

A transmission channel used in application such as telecommunications can be modeled as a bandpass filter. Measurement of the frequency selectivity of the channel is important to ensure that the information-bearing signal has minimal distortion and loss of information. A comparison is made for several methods used for estimating the frequency selectivity of the transmission. The methods presented are the correlation method, instantaneous energy and frequency estimation and the cross Wigner-Ville distribution. The theoretical foundations and assumptions are described for each method. In general, all the methods gave similar performance in terms of the frequency selectivity. Due to the shorter analysis duration, both the instantaneous energy and frequency estimation and cross Wigner-Ville distribution is ideal for estimating the frequency selectivity of time-varying channel