Showing papers by "Patrick J. Loughlin published in 1996"

On the amplitude‐ and frequency‐modulation decomposition of signals

Abstract: In general, the problem of determining the amplitude and frequency modulations (AM and FM) of a signal is ill posed because there is an unlimited number of combinations of AM and FM that will generate a given signal. Although Gabor proposed a method for uniquely defining the AM and FM of a signal, namely via the analytic signal, the results obtained are sometimes physically paradoxical. In this paper, four reasonable physical conditions that the calculated AM and FM of a signal should satisfy are proposed. The analytic signal method generally fails to satisfy two of the four conditions. A method utilizing the positive (Cohen–Posch) time‐frequency distribution and time‐varying coherent demodulation of the signal is given for obtaining an AM and FM that satisfy the four proposed conditions. Contrary to the accepted definition, the instantaneous frequency (i.e., the FM) that satisfies these conditions is generally not the derivative of the phase of the signal. Rather, the phase is separated into two parts, one which gives the instantaneous frequency via differentiation, and the other which can be interpreted either as phase modulation or quadrature amplitude modulation of the signal. Examples are given for synthetic signals and speech, with comparisons to the analytic signal method.

Time-varying characteristics of visually induced postural sway

Abstract: To study potential time-varying dynamics of postural sway as measured via center-of-pressure (COP) under the feet, the authors applied time-frequency analysis to COP data from ten vestibularly impaired subjects and 13 nonimpaired controls, during quiet stance and in response to visual perturbation. This analysis revealed that 1) the spectral characteristics of COP change over time; 2) there are time-dependent and frequency-dependent differences in COP between impaired and nonimpaired populations during visual perturbation; and 3) there is no difference in COP during quiet stance (eyes open) between impaired and nonimpaired populations for the parameters investigated. A novel finding of this research is that controls appear to adapt to constant frequency visual perturbation, while vestibularly impaired subjects do not. This difference could not have been observed with conventional Fourier analysis, which is commonly used in COP data analysis, because time is not a parameter of the spectrum and adaptation is, by nature, a time-varying process. These results suggest that time-frequency analysis of COP data is useful for studying temporal dynamics of postural control, and in particular the differences between vestibularly impaired subjects and healthy controls during visual perturbation.

What are the joint time-frequency moments of a signal?

Abstract: We investigate the question of what the joint moments of a signal are by considering the joint moments of the spectrogram for limiting cases of the window. Operator methods are also explored. Expressions for the joint moments are derived, which reveal the distorting effects of the spectrogram window. Knowledge of the joint moments of a signal may be useful in estimating positive time-frequency distributions, or in signal classification of nonstationary signals.

Time-frequency-based classification

Abstract: We propose a time-frequency based pattern classification method which utilizes the joint moments of time-frequency distributions (TFDs) for features The method is applied to a biomedical data set, and compared to a template matching scheme and to methods utilizing only temporal moments or spectral moments Our results show that a classification algorithm which utilizes joint time-frequency information, as quantified by the joint moments of the TFD, can potentially improve performance over time or frequency-based methods alone, for classification of nonstationary time series

Time-scale energy density functions

Abstract: Scale, like frequency, is a physical characteristic of a signal. To measure the scale content of a signal, the signal must be appropriately transformed. A theory for joint time-scale energy density functions is presented, and a method for generating such functions for any signal is given. Examples for synthetic signals and real data are presented. The theory and method can be extended to arbitrary joint densities of any variables, for example, frequency and scale.

Time-varying characteristics of postural sway differ between balance impaired and unimpaired populations

Abstract: To study potential time-varying dynamics of postural sway as measured via center-of-pressure (COP), the authors applied time-frequency analysis to COP data from ten vestibularly impaired subjects and thirteen unimpaired controls, during quiet stance and in response to visual perturbation. This analysis revealed that: (1) the spectral characteristics of the COP change over time; (2) there are time-dependent and frequency-dependent differences in the COP between impaired and unimpaired populations during visual perturbation; and (3) there is no difference in the COP during quiet stance (eyes open) between impaired and unimpaired populations for the parameters investigated. A novel finding of this research is that controls appear to adapt to constant frequency visual perturbation, while vestibularly impaired subjects do not.