Joint Time-frequency Analysis Research Articles

Quantitative SNR analysis for ISAR imaging using joint time-frequency analysis-Short time Fourier transform

V.C. Chen recently presented an inverse synthetic aperture radar (ISAR) imaging technique using the joint time-frequency analysis (JTFA), which has been shown having a better performance for maneuvering targets over the conventional Fourier transform method. The main reason is because the frequencies of the radar returns of the maneuvering targets are time varying and a JTFA is a technique that is suitable for such signals, in particular a JTFA may concentrate a wideband signal, such as a chirp, while it spreads noise. We quantitatively study the signal-to-noise ratio (SNR) in the ISAR imaging using one of the typical JTFA techniques, namely the short time Fourier transform (STFT). We show that the SNR increases in the joint time-frequency (TF) domain over the one in the time or the frequency domain alone both theoretically and numerically. This quantitatively shows the advantage of the JTFA technique for the ISAR imaging.

Simulations of non‐stationary frequency content and its importance to seismic assessment of structures

AbstractTo verify the importance of the non‐stationary frequency characteristic of seismic ground motion, a joint time–frequency analysis technique of time signals, called chirplet‐based signal approximation, is developed to extract the non‐stationary frequency information from the recorded data. The chirplet‐based signal approximation is clear in concept, similar to Fourier Transform in mathematical expressions but with different base functions. Case studies show that the chirplet‐based signal approximation can represent the joint time–frequency variation of seismic ground motion quite well. Both the random models of uniform modulating process and evolutionary process are employed to generate artificial seismic waves. The joint time–frequency modulating function in the random model of evolutionary process is determined by chirplet‐based signal approximation. Finally, non‐linear response analysis of a SODF system and a frame structure is performed based on the generated artificial seismic waves. The results show that the non‐stationary frequency characteristic of seismic ground motion can significantly change the non‐linear response characteristics of structures, particularly when a structure goes into collapse phase under seismic action. It is concluded that non‐stationary frequency characteristic of seismic ground motion should be considered for the assessment of seismic capacity of structures. Copyright © 2002 John Wiley & Sons, Ltd.

Vibration Measurements by Tracking Laser Doppler Vibrometer on Automotive Components

This paper describes the application of a Tracking Laser Doppler Vibrometer (TLDV) to the measurement of vibration of some typical automotive component.After a presentation and discussion of the measurement technique, the attention is focused on the development of specific version optimised for each application.The first component analysed is the sidewall of a tire during its rotation in a typical drum test‐bench. An optimised version of the TLDV was developed for the specific application adding a trajectory assessment tool based on image analysis, in order to fulfil the accuracy specifications imposed by tire manufacturer.The second automotive component is a timing belt.This application presents problems related to the high‐speed linear motion and to data processing for noise rejection. The third application is on windscreen wipers. In this case the tracking approach fully demonstrate his capabilities, representing the only technique able to give information in the time domain on the dynamic behaviour of the rubber blade in operative conditions.All the application shows as the TLDV allows to obtain realistic results on the dynamic characteristics under simulated operative conditions.A Lagrangian approach was adopted: data were acquired with the target in continuously changing conditions and that impose a not traditional approach on LDV data such as a joint time‐frequency analysis.

伝熱管伝播音に基づく流動層ボイラの流動状態監視

The newly developed monitor watches the fluidized condition of FBC (Fluidized Bed Combustor), referring to acoustic signals which are collected by heating tubes in the beds and passing to tube acceleration sensors outside the fluidized Beds. The monitor, without any observation hole or special probes, not only detects the bad-fluidized region, which requires proper operations for preventing from agglomeration, but also diagnoses conditions of the boiler equipment. The monitor adopts the joint time-frequency analysis technique to the acoustic signals as well as considers non-Gaussian properties, on decision making procedure, including skewness and excess of parameter distributions which are the resulting characteristics through the analyses on the time-frequency plain. The monitor has been applied to an 350MWe FBC for testing, and validated through one and a half year operation

WAVELET ANALYSIS OF VIBRATION SIGNALS OF AN OVERHANG ROTOR WITH A PROPAGATING TRANSVERSE CRACK

This paper presents an experimental study of the dynamic response of an overhang rotor with a propagating transverse crack using the discrete wavelet transform (DWT)—a joint time frequency analysis technique. Start-up and steady state vibration signatures are analyzed using Daubechies (Db6) mother wavelet and the results are presented in the form of scalograms and space-scale energy distribution graphs. The start-up results showed that crack reduces the critical speed of the rotor system. The steady state results showed that propagating crack produces changes in vibration amplitudes of frequency scale levels corresponding to 1 X, 2 X and 4 X harmonics. The vibration amplitude of frequency scale level corresponding to 1 X may increase or decrease depending on the location of the crack and side load. However, the amplitude of frequency scale level corresponding to 2 X increases continuously as the crack propagates.

Joint time–frequency analysis of electrochemical noise

Results have been presented for regular Fourier transformation of results of electrochemical noise measurements. The variability of the frequency composition and the averaging character of the classical Fourier analysis have been shown for the example electrochemical noise records. Loss of information concerning the time evolution of the signal has been indicated. These inconveniences render difficult or even make impossible the drawing of conclusions on the basis of a noise signal spectrum of non-stationary character. Two types of transformation have been presented belonging to the class of joint time–frequency analysis methods. The first one, short-time Fourier transformation (STFT) is based on application of a time window, determining the localisation of the spectrum in the time domain. The second, (wavelet transformation) is based on analysis of a signal on the basis of a family of functions formed through translation and scaling of an appropriately chosen localised mother function. Spectrograms obtained by the above methods have been presented, for electrochemical noise recordings.

ADC testing using joint time–frequency analysis

Analog-to-digital converter (ADC) characterization is usually performed using stationary stimuli like sine waves. However, the use of a non-stationary stimulus, besides providing testing conditions closer to those found in real applications, can lead to interesting improvements in ADC testing speed. This kind of signal needs proper processing techniques in order to extract useful information. In this paper we propose the use of joint time–frequency analysis (JTFA) for this purpose. The basic principles of the technique, and how it can be used in ADC testing are presented. In particular, a method for characterising an ADC on its entire bandwidth using a single stimulus is described.

Fundamental frequency estimation based on the joint time-frequency analysis of harmonic spectral structure

In this paper, we propose a new scheme to analyze the spectral structure of speech signals for fundamental frequency estimation. First, we propose a pitch measure to detect the harmonic characteristics of voiced sounds on the spectrum of a speech signal. This measure utilizes the properties that there are distinct impulses located at the positions of fundamental frequency and its harmonics, and the energy of voiced sound is dominated by the energy of these distinct harmonic impulses. The spectrum can be obtained by the fast Fourier transform (FFT) however, it may be destroyed when the speech is interfered with by additive noise. To enhance the robustness of the proposed scheme in noisy environments, we apply the joint time-frequency analysis (JTFA) technique to obtain the adaptive representation of the spectrum of speech signals. The adaptive representation can accurately extract important harmonic structure of noisy speech signals at the expense of high computation cost. To solve this problem, we further propose a fast adaptive representation (FAR) algorithm, which reduces the computation complexity of the original algorithm by 50%. The performance of the proposed fundamental-frequency estimation scheme is evaluated on a large database with or without additive noise. The performance is compared to that of other approaches on the same database. The experimental results show that the proposed scheme performs well on clean speech and is robust in noisy environments.

Identification of nonlinear dynamic systems: Time-frequency filtering and skeleton curves

The nonlinear behavior varying with the instantaneous response was analyzed through the joint time-frequency analysis method for a class of S. D. O. F nonlinear system. A masking operator on definite regions is defined and two theorems are presented. Based on these, the nonlinear system is modeled with a special time-varying linear one, called the generalized skeleton linear system (GSLS). The frequency skeleton curve and the damping skeleton curve are defined to describe the main feature of the non-linearity as well. Moreover, an identification method is proposed through the skeleton curves and the time-frequency filtering technique.

Laser–ultrasonic absorption measurements in low carbon steels

We have refined the contactless laser–ultrasound reverberation technique to measure ultrasonic absorption on small metallic samples. In this technique, a sample is supported by a holder which is ultrasonically decoupled from the sample. A pulsed laser is used to generate an acoustic pulse. After the pulse has mode converted and scattered sufficiently to fully insonify the sample, the decrease in the noise-like ultrasonic signal is recorded as a function of time using a laser-interferometer. A joint time–frequency analysis technique is used to extract an absorption spectrum from the signal. In this paper, the technique is demonstrated in a frequency bandwidth ranging from 1 to 7 MHz, and in a dynamic range of 0.003 to 0.3 dB μs −1. Measurements made on samples of three low-carbon steel grades, namely ultra low carbon (ULC), low carbon (LC), and high strength, low-alloy steels (HSLA), clearly show that ultrasonic absorption varies with steel grade. The technique was utilized to study the effect of a magnetic field on the ultrasonic absorption of an annealed ultra low carbon steel sample. It was found that magnetoelastic effects are responsible for a large fraction of the total absorption.

Iterative algorithm for direction of arrival estimation with wideband chirp signals

A time–frequency MUSIC algorithm with narrowband models for the estimation of direction of arrival (DOA) when the source signals are chirps has been developed by Amin et al. (1998, 1999). The present authors consider wideband models. The joint time–frequency analysis is first used to estimate the chirp rates of the source signals, and then the DOA is estimated by the MUSIC algorithm with an interative approach.

Joint time-frequency analysis on neuronal reverberation

Joint time-frequency analysis on neuronal reverberation

Instabilities in a laser-diode-pumped microchip solid-state laser with feedback

Random chaotic relaxation oscillation burst generations have been observed in laser-diode-pumped microchip multimode lasers coupled to a single-mode optical ber. Dynamical characterizations have been carried out by the singular value decomposition method and the joint time-frequency analysis, and the observed instability has been identi ed to be a random switching between stable and chaotic operation. @S1050-2947~99!50511-8#

Joint time-frequency analysis

It has been well understood that a given signal can be represented in an infinite number of different ways. Different signal representations can be used for different applications. For example, signals obtained from most engineering applications are usually functions of time. But when studying or designing the system, we often like to study signals and systems in the frequency domain. Although the frequency content of the majority of signals in the real world evolves over time, the classical power spectrum does not reveal such important information. In order to overcome this problem, many alternatives, such as the Gabor (1946) expansion, wavelets, and time-dependent spectra, have been developed and widely studied. In contrast to the classical time and frequency analysis, we name these new techniques joint time-frequency analysis. We introduce the basic concepts and well-tested algorithms for joint time-frequency analysis. Analogous to the classical Fourier analysis, we roughly partition this article into two parts: the linear (e.g., short-time Fourier transform, Gabor expansion) and the quadratic transforms (e.g., Wigner-Ville (1932, 1948) distribution). Finally, we introduce the so-called model-based (or parametric) time-frequency analysis method.

Joint time-frequency analysis for radar signal and image processing

The Fourier transform has been widely used in radar signal and image processing. When the radar signals exhibit time- or frequency-varying behavior, an analysis that can represent the intensity or energy distribution of signals in the joint time-frequency (JTF) domain is most desirable. In this article, we showed that JTF analysis is a useful tool for improving radar signal and image processing for time- and frequency-varying cases. We applied JTF analysis to radar backscattering and feature extraction; we also examined its application to radar imaging of moving targets. Most methods of JTF analysis are non-parametric. However, parametric or model-based methods of time-frequency analysis, such as adaptive Gaussian and chirplets, are more suitable for radar signals and images.

Aseismic designs based on artificial simulations

It is commonly believed that the time-varying frequency characteristics are important for the inelastic response of structures. Design code modification means structural cost changes; therefore any change must be based on solid evidence. Although the significance of time-varying frequency characteristics to ground motion has been recognized for a while, much more in-depth research is necessary before any meaningful engineering design conclusions can be reached. We apply joint time-frequency analysis techniques to a fully non-stationary ground motion model, with both intensity and frequency being non-stationary. The chirplet-based signal approximation is used to extract the time-varying frequencies from seismic ground-motion data samples. Based on that information, we compute the frequency-dependent modulating function in the stochastic model of the evolutionary random process. We generate and compare the artificial waves based on stochastic models of a uniform modulating random process and an evolutionary random process, separately. We also investigate the importance of the time-varying frequency characteristics of earthquake ground motion through an oscillator, with a single degree of freedom and elastic-plastic material behavior.

Wavelet and chaos analysis of flow induced vibration of a single cylinder in cross-flow

This paper attempts to shed some light on the characteristics of the flow induced vibration of an elastically mounted single cylinder in a cross flow using the newly developed joint time–frequency analysis techniques (JTFA) and in particular the modulated Gaussian wavelet. More specifically, the modulated Gaussian wavelet is chosen in the current work, since it was shown in [1]to be more effective than other well known wavelets in analysing the flow induced vibrations of a single cylinder similar to the one under consideration. In the current work, this wavelet shows good evidence that the flow induced vibration process, in the range of system parameters considered, is most likely to undergo nonstationary, nonlinear and chaotic dynamics. It is found that for certain values of system parameters the nonlinearity may lead the system into chaos. Phase plane portraits, Poincaré maps and fractal dimensions have been used to confirm the chaotic behavior of the response of the system under investigation.

Determination of layer ordering using sliding-window Fourier transform of x-ray reflectivity data

X-ray reflectometry allows the determination of the thickness, density and roughness of thin layers on a substrate from several Angstroms to some hundred nanometres. The thickness is determined by simulation with trial-and-error methods after extracting initial values of the layer thicknesses from the result of a classical Fast Fourier Transform (FFT) of the reflectivity data. However, the order information of the layers is lost during classical FFT. The order of the layers has then to be known a priori. In this paper, it will be shown that the order of the layers can be obtained by a sliding-window Fourier transform, the so-called Gabor representation. This joint time-frequency analysis allows the direct determination of the order of the layers and, therefore, the use of a more appropriate starting model for refining simulations. A simulated and a measured example show the interest of this method.

In vivo bidirectional color Doppler flow imaging of picoliter blood volumes using optical coherence tomography

We describe a novel optical system for bidirectional color Doppler imaging of flow in biological tissues with micrometer-scale resolution and demonstrate its use for in vivo imaging of blood flow in an animal model. Our technique, color Doppler optical coherence tomography (CDOCT), performs spatially localized optical Doppler velocimetry by use of scanning low-coherence interferometry. CDOCT is an extension of optical coherence tomography (OCT), employing coherent signal-acquisition electronics and joint time-frequency analysis algorithms to perform flow imaging simultaneous with conventional OCT imaging. Cross-sectional maps of blood flow velocity with <50-microm spatial resolution and <0.6-mm/s velocity precision were obtained through intact skin in living hamster subdermal tissue. This technology has several potential medical applications.

COHEN–POSCH (POSITIVE) TIME–FREQUENCY DISTRIBUTIONS AND THEIR APPLICATION TO MACHINE VIBRATION ANALYSIS

Recent developments in the theory and methods of joint time–frequency analysis, coupled with limitations of separate time and frequency domain analyses, have sparked interest in the application of modern time–frequency methods for methods for machine monitoring. An overview of the theory and methods for Cohen–Posch time–frequency distributions (TFDs), and their applications to machine vibration analysis are presented. These TFDs clearly reveal time–frequency structure in machine vibrations that is related to the ‘health’ of the machine and which is difficult or impossible to discern with conventional methods.