Showing papers on "Time–frequency analysis published in 2004"

Algorithms for computing the time-corrected instantaneous frequency (reassigned) spectrogram, with applications.

Abstract: A modification of the spectrogram (log magnitude of the short-time Fourier transform) to more accurately show the instantaneous frequencies of signal components was first proposed in 1976 [Kodera et al., Phys. Earth Planet. Inter. 12, 142-150 (1976)], and has been considered or reinvented a few times since but never widely adopted. This paper presents a unified theoretical picture of this time-frequency analysis method, the time-corrected instantaneous frequency spectrogram, together with detailed implementable algorithms comparing three published techniques for its computation. The new representation is evaluated against the conventional spectrogram for its superior ability to track signal components. The lack of a uniform framework for either mathematics or implementation details which has characterized the disparate literature on the schemes has been remedied here. Fruitful application of the method is shown in the realms of speech phonation analysis, whale song pitch tracking, and additive sound modeling.

Bayesian variable selection and regularization for time-frequency surface estimation

Abstract: Summary. We describe novel Bayesian models for time–frequency inverse modelling of non-stationary signals. These models are based on the idea of a Gabor regression, in which a time series is represented as a superposition of translated, modulated versions of a window function exhibiting good time–frequency concentration. As a necessary consequence, the resultant set of potential predictors is in general overcomplete—constituting a frame rather than a basis—and hence the resultant models require careful regularization through appropriate choices of variable selection schemes and prior distributions. We introduce prior specifications that are tailored to representative time series, and we develop effective Markov chain Monte Carlo methods for inference. To highlight the potential applications of such methods, we provide examples using two of the most distinctive time–frequency surfaces—speech and music signals—as well as standard test functions from the wavelet regression literature.

A novel time–frequency-based 3D Lissajous figure method and its application to the determination of oxygen saturation from the photoplethysmogram

Abstract: We present a novel time–frequency method for the measurement of oxygen saturation using the photoplethysmogram (PPG) signals from a standard pulse oximeter machine. The method utilizes the time–frequency transformation of the red and infrared PPGs to derive a 3D Lissajous figure. By selecting the optimal Lissajous, the method provides an inherently robust basis for the determination of oxygen saturation as regions of the time–frequency plane where high- and low-frequency signal artefacts are to be found are automatically avoided.

Detection of a manoeuvring air target in sea-clutter using joint time-frequency analysis techniques

Abstract: Traditionally, radar signals have been analysed in either the time or the frequency domain. Joint time-frequency representations characterise signals over a time-frequency plane. They thus combine time-domain and frequency-domain analyses to yield a potentially more revealing picture of the temporal localisation of a signal's spectral components. Therefore, for air target returns with time-vary ing frequency content, joint time-frequency representations offer a powerful analysis tool. A concise review of time-frequency transforms is provided as background and is needed to appreciate how time-frequency processing methods can improve conventional time or frequency processing methods. The authors use time-frequency analysis techniques for the detection of a manoeuvring aircraft using high frequency (HF) radar in heavily cluttered regions. They compare the ability of different time-frequency transforms to resolve several experimental aircraft returns. The relative speeds of the different transforms are also quantitatively studied. The results clearly demonstrate that time-frequency analysis techniques can significantly improve the detection performance of the HF radar and add considerable physical insight over what can be achieved by conventional Fourier transform methods currently used by HF radars.

Time‒Frequency and Time‒Scale Methods: Adaptive Decompositions, Uncertainty Principles, and Sampling

Abstract: Preface Wavelets: Basic properties, parametrizations and sampling Derivatives and multiwavelets Sampling in Fourier and wavelet analysis Bases for time--frequency analysis Fourier uncertainty principles Function spaces and operator theory Uncertainty principles in mathematical physics Appendix References Index

The application of the conditional moments analysis to gearbox fault detection—a comparative study using the spectrogram and scalogram

Abstract: Time–frequency methods, which can lead to the clear identification of the nature of faults, are widely used to describe machine condition. Capabilities of time–frequency distributions in the detection of any abnormality can further be improved when their low-order frequency moments (or time-dependent parameters), which characterise dynamic behaviour of the observed signal with few parameters, are considered. This paper presents the applications of four time-dependent parameters (e.g. the instantaneous energy, mean and median frequencies, and bandwidth) based upon the use of spectrogram and scalogram, and compares their abilities in the detection and diagnosis of localised and wear gear failures. It has been found that scalogram based parameters are superior to those of a spectrogram in the detection and location of a local tooth defect even when the gear load is small, as they result in equally useful parameters in the revelation of gear wear. Moreover, the global values of these time-dependent parameters are found to be very useful and provide a very good basis for reflecting not only the presence of gear damage, but also any change in operating gear load.

Time-frequency based newborn EEG seizure detection using low and high frequency signatures.

Abstract: The nonstationary and multicomponent nature of newborn EEG seizures tend to increase the complexity of the seizure detection problem. In dealing with this type of problem, time–frequency based techniques were shown to outperform classical techniques. Neonatal EEG seizures have signatures in both low frequency (lower than 10 Hz) and high frequency (higher than 70 Hz) areas. Seizure detection techniques have been proposed that concentrate on either low frequency or high frequency signatures of seizures. They, however, tend to miss seizures that reveal themselves only in one of the frequency areas. To overcome this problem, we propose a detection method that uses time–frequency seizure features extracted from both low and high frequency areas. Results of applying the proposed method on five newborn EEGs are very encouraging.

Identification of otoacoustic emissions components by means of adaptive approximations.

Abstract: Clicks and a set of tone bursts covering the same frequency band were applied as a stimuli evoking otoacoustic emissions (OAE). Recorded otoacoustic emissions were decomposed into the basic waveforms by means of high-resolution adaptive time–frequency approximation method based on the matching pursuit algorithm. The method allows for description of the signal components in terms of frequencies, time occurrences, time spans, and energy. The analysis of OAE’s energy density distributions in time–frequency space revealed that click responses can be considered as linear superpositions of responses to tone bursts. The frequency–latency relationship was studied and compared with earlier works. The method made possible the exhaustive description of the resonant modes specific for given subject/ear. They were characterized not only by the close frequencies appearing for different tones, but they usually had similar latencies and time spans. Short-time and long-time resonant modes were identified. The second ones ...

Dilating Gabor transform for the fringe analysis of 3-D shape measurement

Abstract: In order to overcome the limitations of conventional Fourier transform and Gabor transform analyzing nonstationary signals, dilating Gabor transform is applied to analyze the optical fringes of 3-D shape measurement. The dilating Gabor transformation is introduced by using a changeable window of Gaussian function in a conventional Gabor transform. This phase analysis method provides more accurate results than Fourier transform and Gabor transform. Simulation and experimental results are presented that demonstrate the validity of the principle.

Ultrasonic flaw detection using discrete wavelet transform for NDE applications

Abstract: In this work, we analyze signal decomposition properties of discrete wavelet transform (DWT) for enhanced ultrasonic flaw detection. In wavelet signal decomposition, a collection of time-frequency representations of the signal with different resolutions is obtained. DWT allows to utilize both time and frequency domain information for compacting and decorrelating the flaw echo from clutter echoes. In this paper, we present the performance analysis of different wavelet kernels with respect to ultrasonic NDE applications and develop the wavelet selection criteria for optimal flaw detection. Experimental results indicate that DWT based flaw detection algorithms offer flaw-to-clutter ratio enhancement of 5-12 dB when the measured flaw-to-clutter ratio is 0 dB or less. DWT flaw detection system can be implemented efficiently for real time applications using reconfigurable architecture and lifting scheme.

On some spectrum estimation methods for analysis of nonstationary signals in power systems. Part I. Theoretical aspects

Abstract: Frequency power converters and arc furnaces generate a wide spectrum of harmonic components and interharmonics. Representation of signals in time and frequency domain has been of interest in signal processing areas for many years, especially taking in the limelight time-varying nonstationary signals. Standard tools of harmonic analysis based on the Fourier transform assume that only harmonics are present and the periodicity intervals are fixed, while periodicity intervals in the presence of interharmonics are variable and very long. In this paper the Prony method was tested for this purpose and a novel approach for the analysis of power nonstationary signals, based on the "subspace" methods, is proposed: the "rootMusic" harmonic retrieval method which is an example of high-resolution eigenstructure-based methods. Both methods can allow an accurate and useful estimation of power quality indices as well as of the interharmonic frequencies with their changes in time. This paper, which reports the theoretical aspects of these methods, is a companion paper to a paper of the same title, Part II, in which the numerical aspects of the proposed spectrum estimation methods are analysed using nonstationary voltage and current waveforms in a supply system of a DC arc furnace.

Approximation of matrices by Gabor multipliers

Abstract: We present a fast Fourier transform based algorithm which allows to obtain the best approximation of a given time-variant linear system by approximating its matrix (in the Hilbert-Schmidt sense) by a Gabor multiplier, using a given tight Gabor frame. We illustrate the approach by approximating the inverse of a slowly time variant filter.

Steady-motion-based Dopplerlet transform: application to the estimation of range and speed of a moving sound source

Abstract: New results on the recently introduced steady-motion-based Dopplerlet transform is presented and an estimation scheme for both range and speed of moving sound source using Dopplerlet transform is considered. First, we derive the real, discrete, and real discrete Dopplerlet transforms from their complex counterpart. Second, we reformulate some of the existing integral transformations within the framework of the Dopplerlet transform. Finally, we provide the application results. Experimental results with real underwater acoustic data and land acoustic data, as well as Monte Carlo simulation results with computer-generated data, have confirmed the veracity and practical usefulness of the estimation scheme advocated.

Time–frequency analysis of the restricted three-body problem: transport and resonance transitions

Abstract: A method of time–frequency analysis based on wavelets is applied to the problem of transport between different regions of the solar system, using the model of the circular restricted three-body problem in both the planar and the spatial versions of the problem. The method is based on the extraction of instantaneous frequencies from the wavelet transform of numerical solutions. Time-varying frequencies provide a good diagnostic tool to discern chaotic trajectories from regular ones, and we can identify resonance islands that greatly affect the dynamics. Good accuracy in the calculation of time-varying frequencies allows us to determine resonance trappings of chaotic trajectories and resonance transitions. We show the relation between resonance transitions and transport in different regions of the phase space.

Time–frequency analysis of nonstationary fusion plasma signals: A comparison between the Choi–Williams distribution and wavelets

Abstract: The continuous wavelet transform scalogram, and recently the Choi–Williams distribution, have both been used to improve upon the short-time Fourier transform spectrogram in the analysis of some nonstationary phenomena in fusion plasmas. Here, a comparison is made with real fusion plasma signals that shows the advantages of the Choi–Williams distribution over wavelets as a complementary tool to the spectrogram.

Method and system for the denoising of large-amplitude artifacts in electrograms using time-frequency transforms

Abstract: The present invention relates to a method of signal processing of electrograms for use in medical devices, preferably by time-frequency transforms. The present invention additionally relates to a system for receiving and analyzing such signals. The present invention preferably is a method utilizing the time-frequency transforms, such as wavelet transforms, for the purpose of artifact removal from EGs. These transforms decompose a signal in both time and frequency domains, and therefore, are well suited for non-stationary signal analysis. As a result, dissimilar signal features are well localized both in time and frequency, which potentially provides a good separation between the signal of interest and artifacts. This particularly applies to large-amplitude artifacts corrupting EGs.

Hyperbolic wavelet family

Abstract: This article reports early results on digital implementation of first- and nth-order hyperbolic wavelets whose important parameters are explicitly expressed and numerically estimated. The first-order hyperbolic, Morlet and Choi–Williams wavelets are compared in detail by numerically calculating their band-peak frequencies, minimum numbers of sampling points, scale resolutions, and maximum numbers of scales. One of the main aims is to show that there exists a strong link among time–frequency kernels and wavelets. This relationship helps to expand and link time–frequency and wavelet approaches to signal analysis. One example of using the hyperbolic wavelet for speech recognition is also given.

Multi-resolution time-frequency analysis for detection of rhythms of EEG signals

Abstract: In recent years, various time-frequency methods have been applied widely For detecting all kinds of feature waves and abnormal waves in EEG signals. But because of their nature and some inherent limitations, their application in EEG analysis has been limited. Considering the excellence and shortcomings of STFT (short time Fourier transform) and wavelets, in the "virtual EEG recording and analysis instrumentation", the multi-resolution time-frequency analysis method, based on STFT and wavelet packet transform, has been introduced to advance the self-adaptive ability for signals, so more flexible division of frequency bands in EEG can be obtained and the basic rhythms in EEG signals can be detected efficiently.

Short-time fourier transform analysis of the phonocardiogram signal

Abstract: Heart sound is a highly nonstationary signal, and the Short-time Fourier Transform ation(STFT) is an effective method for this kind of signal to be analysed. Because of the nonstationarity of the phonocardiogram, it is important to maintain an analysing time window as short as possible to guaranty the stationarity hypothesis over small analysed segments. This will reduce the frequency resolution of the resulting spectrogram. However by adjusting the sliding time window, we can reach an acceptable result. The spectrogram is caculated by using first, short length sliding window to generate a temporal representation of the PCG, then longer length sliding window in order to generate a spectral representation of the PCG power. The resolution in such representations depend directly on the sliding window length. The temporal representation allows heart sounds and cardiac cycle durations to be measured. Whereas the spectrum, assuming a good frequency resolution, allows spectral characterization of each heart sound. The results we obtained on normal PCG signal show that the STFT analysis with different scale basis provides a clear comprehension of the cardiac events in both time and frequency domain.

Comparative study of three time-frequency representations with applications to a novel correlation method

Abstract: The effect of three time-frequency representations on a novel correlation algorithm is studied. By representing a signal in the time-frequency domain, a redundant representation of the signal is obtained. The algorithm presented relies on such redundancies to extrapolate some significant features of the signal. The developed scheme has been applied to heart sound analysis using real recordings from patients, where the opening snap (OS) is distinguished from the third heart sound (S3). The results for the three time-frequency transforms are compared and very encouraging results have been obtained with S-transform.

Design of frequency modulated waveforms via the Zak transform

Abstract: This paper introduces a new technique for designing frequency modulated waveforms that have ambiguity functions with desirable properties, such as strong peaking at the origin and low sidelobes. The methods employed involve signal design in the Zak transform space, as well as the use of stationary phase arguments in the analysis of ambiguity functions.

Instantaneous frequency estimate for non-stationary signal

Abstract: Instantaneous frequency (IF) estimate has important physical meaning for non-stationary signal. Traditional IF estimate methods were investigated, their features were compared and each technique had certain weaknesses. On the basis of these, the newly-emerged Hilbert-Huang transform (HHT) method was introduced. The theories and features of HHT were discussed. Its application in IF estimate was presented. It gives accurately the IF estimate for non-stationary signal. The better performance is illustrated by the simulated signal. The results indicate that this method provides an efficient tool for the IF estimation of non-stationary signal.