François Auger

Improving the readability of time-frequency and time-scale representations by the reassignment method

In this paper, the use of the reassignment method, first applied by Kodera, Gendrin, and de Villedary (1976) to the spectrogram, is generalized to any bilinear time-frequency or time-scale distribution. This method creates a modified version of a representation by moving its values away from where they are computed, so as to produce a better localization of the signal components. We first propose a new formulation of this method, followed by a thorough theoretical study of its characteristics. Its practical use for a large variety of known time-frequency and time-scale distributions is then addressed. Finally, some experimental results are reported to demonstrate the performance of this method. >

Industrial Applications of the Kalman Filter: A Review

The Kalman filter (KF) has received a huge interest from the industrial electronics community and has played a key role in many engineering fields since the 1970s, ranging, without being exhaustive, trajectory estimation, state and parameter estimation for control or diagnosis, data merging, signal processing, and so on. This paper provides a brief overview of the industrial applications and implementation issues of the KF in six topics of the industrial electronics community, highlighting some relevant reference papers and giving future research trends.

Time-Frequency Reassignment and Synchrosqueezing: An Overview

This article provides a general overview of time-frequency (T-F) reassignment and synchrosqueezing techniques applied to multicomponent signals, covering the theoretical background and applications. We explain how synchrosqueezing can be viewed as a special case of reassignment enabling mode reconstruction and place emphasis on the interest of using such T-F distributions throughout with illustrative examples.

Speed and rotor flux estimation of induction machines using a two-stage extended Kalman filter

This paper presents an effective implementation of an extended Kalman filter used for the estimation of both rotor flux and rotor velocity of an induction motor. An algorithm proposed by Hsieh and Chen in [Hsieh, C.S., & Chen, F.C. (1999). Optimal solution of the two-stage Kalman estimator. IEEE Transactions on automatic control, 44(1), 194-199] for linear parameter estimation is extended to non-linear estimation, where parameters such as the velocity of an induction machine are present in the transition matrix and in the augmented state space. Compared to a straightforward implementation of an extended Kalman filter, our modified optimal two-stage Kalman estimator reduces the number of arithmetic operations by 25%, allowing higher sampling rate or the use of a cheaper microcontroller.

Two efficient Kalman filters for flux and velocity estimation of induction motors

This paper first presents an efficient implementation of the linear Kalman filter used for the rotor flux estimation of an induction motor. This estimator has three parameters which are tuned by an optimization procedure, so as to obtain a good flux estimation in spite of an underestimated rotor resistance. Our approach is then applied to the extended Kalman filter used for the estimation of both the rotor flux and the rotor velocity. Compared with straightforward implementations of these Kalman filters, our algorithms reduce the number of arithmetic operations by a factor 4.7 in the first case and a factor 2.7 in the second case, allowing higher sampling rates and/or cheaper microcontrollers.

Making reassignment adjustable: The Levenberg-Marquardt approach

This paper presents a new time-frequency reassignment process for the spectrogram, called the Levenberg-Marquardt reassignment. Compared to the classical one, this new reassignment process uses the second-order derivatives of the phase of the short-time Fourier transform, and provides the user with a setting parameter. This parameter allows him to produce either a weaker or a stronger localization of the signal components in the time-frequency plane.

Time-Frequency/Time-Scale Reassignment

This chapter reviews the reassignment principle, which aims at “sharpening” time-frequency and time-scale representations in order to improve their readability.

Generalization of the reassignment method to all bilinear time-frequency and time-scale representations

Reassigning each value of a time-frequency representation to a different location in the plane can produce a better localization of the signal components. This idea, pioneered by Kodera et al. (1976, 1978), was only applied to the sole spectrogram. We present a new formulation of this method which allows a generalization of its use for any bilinear time-frequency or time-scale representation. The resulting reassigned distributions are easily computable versatile tools which highlight the signal features and preserve many theoretical properties.<<ETX>>

On Phase-Magnitude Relationships in the Short-Time Fourier Transform

A complete evaluation of first-order, second-order and mixed derivatives is proposed for both the (log-)magnitude and the phase of a given Short-Time Fourier Transform (STFT), leading to equivalent expressions based on additional STFTs with specific windows. Consequences are drawn in terms of phase-magnitude relationships, resulting in new formulations of time-frequency techniques such as reassignment, as well as new insights in the structure of admissible STFTs in some special cases.

H/sub /spl infin// control for a single-phase active power filter: a systematic approach

This paper shows the efficiency of the H/sub /spl infin// control design methodology for the case of the active filtering of single phase power networks. At first, a continuous time H/sub /spl infin// controller is designed which achieves all performances and robustness properties required. In particular, this approach allows one to choose the attenuation of each harmonic frequency independently of each other. Finally an effective 18th order discrete regulator is derived from the continuous one in an original way.