Robust adaptive Lomb periodogram for time-frequency analysis of signals with sinusoidal and transient components

This article introduces a robust adaptive Lomb periodogram (RALP) for time-frequency (TF) analysis of time series with sinusoidal and transient components, which are possibly non-uniformly sampled. It extends the conventional Lomb spectrum by windowing the observation data and adaptively selects the window lengths by the intersection of confidence intervals (ICI) rule. The influence of transient components to conventional time-frequency representation can be moderated using M-estimation of robust statistics. Instead of treating the transient components as impulsive noise and removing them, the proposed RALP TF distribution yields separately a time domain representation of the transient components and a conventional TF representation of the sinusoidal components, which greatly improves the visualization and detection of these components. Simulation results show that the proposed RALP differentiates the two kinds of components well, and offers better time and frequency resolutions than the conventional Lomb periodogram. © 2005 IEEE.published_or_final_versio

An Efficient Algorithm for Instantaneous Frequency Estimation of Nonstationary Multicomponent Signals in Low SNR

A method for components instantaneous frequency (IF) estimation of multicomponent signals in low signal-to-noise ratio (SNR) is proposed. The method combines a new proposed modification of a blind source separation (BSS) algorithm for components separation, with the improved adaptive IF estimation procedure based on the modified sliding pairwise intersection of confidence intervals (ICI) rule. The obtained results are compared to the multicomponent signal ICI-based IF estimation method for various window types and SNRs, showing the estimation accuracy improvement in terms of the mean squared error (MSE) by up to 23%. Furthermore, the highest improvement is achieved for low SNRs values, when many of the existing methods fail.Scopu

A time-frequency based method for the detection and tracking of multiple non-linearly modulated components with births and deaths

International audienceThe estimation of the components which contain the characteristics of a signal attracts great attention in many real world applications. In this paper, we address the problem of the tracking of multiple signal components over discrete time series. We propose an algorithm to first detect the components from a given time-frequency distribution and then to track them automatically. In the first place, the peaks corresponding to the signal components are detected using the statistical properties of the spectral estimator. Then, an original classifier is proposed to automatically track the detected peaks in order to build components over time. This classifier is based on a total divergence matrix computed from a peak-component divergence matrix that takes account of both amplitude and frequency information. The peak-component pairs are matched automatically from this divergence matrix. We propose a stochastic discrimination rule to decide upon the acceptance of the peak-component pairs. In this way, the algorithm can estimate the number, the amplitude and frequency modulation functions, and the births and the deaths of the components without any limitation on the number of components. The performance of the proposed method, a post-processing of a time-frequency distribution is validated on simulated signals under different parameter sets. The method is also applied to 4 real-world signals as a proof of its applicability. Index Terms—Time-frequency domain, multicomponent, peak detection, component tracking, amplitude and frequency modulation , nonlinear, nonstationary, births and death

Linear and synchrosqueezed time–frequency representations revisited:overview, standards of use, resolution, reconstruction, concentration, and algorithms

Time–frequency representations (TFRs) of signals, such as the windowed Fourier transform (WFT), wavelet transform (WT) and their synchrosqueezed versions (SWFT, SWT), provide powerful analysis tools. Here we present a thorough review of these TFRs, summarizing all practically relevant aspects of their use, reconsidering some conventions and introducing new concepts and procedures to advance their applicability and value. Furthermore, a detailed numerical and theoretical study of three specific questions is provided, relevant to the application of these methods, namely: the effects of the window/wavelet parameters on the resultant TFR; the relative performance of different approaches for estimating parameters of the components present in the signal from its TFR; and the advantages/drawbacks of synchrosqueezing. In particular, we show that the higher concentration of the synchrosqueezed transforms does not seem to imply better resolution properties, so that the SWFT and SWT do not appear to provide any significant advantages over the original WFT and WT apart from a more visually appealing pictures. The algorithms and Matlab codes used in this work, e.g. those for calculating (S)WFT and (S)WT, are freely available for download

Estimación de la frecuencia respiratoria mediante análisis tiempo-frecuencia de la señal de variabilidad del ritmo cardiaco en condiciones no estacionarias

La influencia de la respiración sobre la señal electrocardiográfica (ECG) se manifiesta tanto en variaciones morfológicas de la misma como en una modulación del ritmo cardíaco, conocida como arritmia sinusal respiratoria (RSA), por lo que medidas basadas en el ECG pueden, de forma indirecta, proveer información de la respiración, que resulta de especial interés cuando el registro de la señal respiratoria es inviable o incómodo para el paciente. El objetivo de este trabajo fin de máster (TFM) es estimar la frecuencia respiratoria a partir del estudio tiempo-frecuencia (TF) de la señal de variabilidad del ritmo cardíaco (HRV) en condiciones no estacionarias. La recuencia respiratoria se estima como la componente de alta frecuencia (HF) de la HRV, que, a su vez es estimada mediante la localización para cada instante de tiempo del pico máximo de la distribución pseudo Wigner-Ville suavizada (SPWVD) de la HRV en la banda de HF. El método desarrollado en éste TFM utilizada para el cálculo de la SPWVD ventanas de filtrado frecuencial de longitud variable con el fin de minimizar el error cuadrático medio (MSE) de estimación de la frecuencia, en especial cuando las variaciones de ésta son no lineales. La longitud óptima de la ventana de filtrado frecuencial para cada instante de tiempo depende tanto de las variaciones de la frecuencia a estimar, como de la amplitud la componente de HF y del ruido presente en la señal, que es necesario estimar. En condiciones no estacionarias, no solo la frecuencia sino también la amplitud de la componente HF y el ruido pueden variar, por lo que se ha desarrollado un estimador de la amplitud instantánea de la componente HF a partir de la SPWVD con eliminación de la influencia de los filtrados temporal y frecuencial. También se ha desarrollado un estimador de la potencia instantánea del ruido presente en la señal que incluye los errores de estimación de la amplitud instantánea. Para el cálculo de la SPWVD se han utilizado diferentes kernels de filtrado tiempo-frecuencia formados por tres tipos de ventanas, rectangular, Hamming y exponencial, tanto en tiempo como en frecuencia. La evaluación del método se ha realizado tanto a través de un estudio de simulación, en el que se han generado señales con características tiempo-frecuencia similares a las de la HRV, variaciones no lineales de frecuencia y amplitudes variantes en el tiempo, como a través del análisis de una base de datos, que consta del registro simultáneo de la señales ECG y respiratorias de 58 sujetos sometidos a la escucha de diferentes estímulos musicales. El método propuesto en este TFM estima la amplitud instantánea de la componente de HF de la HRV sobre la señales simuladas con un error medio de 0.324±2.294% y su frecuencia con un error medio de -0.239±2.041% (-0.008±6.026 mHz). La estimación de la frecuencia respiratoria en señales reales presenta un error mediano de -1.525±4.557% (1.953±4.883 mHz) en los segmentos musicales y de -0.919±6.542% (11.465±43.477 mHz) en las transiciones entre segmentos musicales. Finalmente el método desarrollado en este TFM ha sido comparado con otros existentes en la literatura, basados en ventanas de filtrado frecuencial tanto de longitud fija como variable para amplitudes constantes

Detection Schemes for Multi-Antenna FH/MFSK Systems in the Presence of Multiple Follower Jamming

Ph.DDOCTOR OF PHILOSOPH

Phase Gradient Estimation Techniques in Fringe Analysis

The thesis introduces novel techniques in the field of fringe analysis for direct estimation of phase gradients or derivatives. A pseudo Wigner-Ville distribution based method is proposed to reliably estimate the phase derivatives from a single fringe pattern. The method's ability for estimating rapidly varying phase derivatives is enhanced by developing an adaptive windowing technique. Further, the two-dimensional extension of the method is presented to handle fringe patterns with severe noise. In addition, a generalized approach is described to enable direct estimation of arbitrary order phase derivatives. Subsequently, methods based on digital holographic moiré and multi-component polynomial phase formulation are introduced to measure the in-plane and out-of-plane displacements and their derivatives for a deformed object in digital holographic interferometry. These methods permit the simultaneous estimation of multiple phases and their derivatives without the need of multiple fringe patterns and complex experimental configurations, which is hitherto not possible with the current state-of-the-art fringe analysis methods. The major advantages of the developed techniques are the ability to directly estimate phase derivatives without relying on complex unwrapping, filtering and numerical differentiation operations, high computational efficiency and strong robustness against noise. In addition, the requirement of a single fringe pattern makes these techniques less error-prone in the presence of vibrations and external disturbances and enhances their applicability for dynamic measurements. Further, the developed techniques offer a potential solution to the challenging problem of simultaneous multi-dimensional deformation analysis in digital holographic interferometry. The reliable performance of these techniques is validated by numerical simulation and their practical applicability is demonstrated in digital holographic interferometry and fringe projection for slope and curvature measurement, defect detection, surface slope evolution studies and measurement of in-plane and out-of-plane displacements and their derivatives. These techniques offer substantial advancements in fringe analysis and exhibit significant application potential in areas such as non-destructive testing, biomechanics, reliability analysis, material characterization and experimental mechanics