Auto Spectral Density Research Articles

Cross-correlation analysis of multi-unit EMG recordings in man

This paper discusses the measurement of synchrony between 2 multi-unit EMG recordings. The suitability of a number of previously described indices of synchrony is reviewed. A new index of synchronisation is proposed. This index is independent of the number of units contributing to the correlogram but is dependent upon their firing frequency and upon the bin width of the correlogram. The autospectral density function calculated from each multi-unit record is used to estimate motor unit firing rates. The relationship between the frequency of firing and the chosen index of synchronisation is reciprocal such that if the firing rate is doubled, the index is halved. This may be explained if the proportion of events that is synchronized remains constant and is independent of the firing rate. It is argued that this in turn indicates that the proportion of common and non-common sources driving the neurons also remains unchanged in these experiments. In these circumstances, and to take into account changes in unit firing that may be present in different recordings, it is convenient to normalize an experimentally determined index E/M at a frequency f to some standard frequency f s. The problem of superimposition of spikes that occurs as the contraction strength is increased is discussed.

Time-dependent behaviour of the liquid film in horizontal annular flow

A crucial point still to be established in the prediction of the film thickness distribution in horizontal annular two-phase flow is the mechanism(s) for transporting liquid from the bottom to the top part of the tube. To resolve this issue, the time-dependent behaviour of the liquid film is studied. Wave characteristics such as velocity and frequency are measured around the circumference. It is inferred from the autospectral density functions of film thickness variation that disturbance waves play an important, but as yet unclear, role in the formation of a liquid film in the top part of the tube. A new mechanism, based on the shape of disturbance waves is proposed.

Shock absorption of below-knee prostheses: A comparison between the SACH and the Multiflex foot

Shock waves were measured during walking on a treadmill on the metal tube of a below-knee KBM prosthesis, provided either with a SACH foot or with a Multiflex foot. Accelerations were measured in the axial direction and the dorso-ventral direction, about 160 mm proximal to the sole of the shoe. The accelerations had comparable amplitudes to those measured on normal legs. Dorso-ventral amplitudes (order of magnitude 4 g) were generally higher than the axial amplitudes. For some patients, the SACH foot gave much higher axial accelerations than the Multitlex foot did. In the dorso-ventral direction, the SACH foot showed a moderate resonance phenomenon in the autospectral density function in the range of 40–50 Hz. The Multiflex foot showed a more variable behaviour. For both types of feet, components above 65 Hz were negligible.

Correlation and spectral analysis of relations between single unit discharge and muscle activities

Correlation and spectral analysis was used to study functional linkages between single-cell discharge in the magnocellular red nucleus and the electromyographic activity of several limb muscles. Long sequences of unit discharge and EMG activity were recorded while feline subjects performed a food retrieval task. Unit discharge and muscle activity were patterned in bursts that corresponded in different phases of the task. There was sufficient variability in the parameters of these bursts to regard the signals as pseudorandom variables, thus facilitating a correlation analysis. Cross-correlation functions computed between unit discharge and each muscle EMG served to characterize the strength and reliability of linkages between a single unit and various limb muscles. Auto-correlation and auto-spectral density functions provided summary measures of the temporal and frequency characteristics of the signals. Power in the signals was concentrated in a behaviorally relevant range (0.2–8 Hz). Coherence functions showed peaks that indicated which frequency components were well correlated with unit discharge. Two-sided impulse responses served to characterize the dynamic properties of the linkages. These methods are shown to be valuable in characterizing noncausal, as well as causal, linkages through multisynaptic pathways in the nervous system.

Fluctuation Phenomena Studies in Chemically Sensitive Field Effect Transistors: I . Corrosion of Aluminum

It is shown that chemically sensitive field effect transistors can be used to study stochastic processes at the solution/solid interface which is not at equilibrium. Auto spectral densities and coherence functions for corrosion of aluminum‐silicon alloy at zero‐net current conditions have been obtained.

On the statistical accuracy in nuclear reactor noise analysis

The statistical accuracy of the interesting parameters in nuclear reactor noise measurements is theoretically studied. The minimum variance error estimation is applied to the one and two detector measurements. The error analysis carried out for periodogram estimators can be applied to both spectral density measurements and covariance function measurements. A comparison between the cross- and autospectral density measurements is made, adjusting and extending previous results. The error is also estimated for the Rossi-a and related measurements. These results can be applied in other branches of nuclear physics, e.g. in half-life measurements when there is significant background radiation present. The interpretation is primarily given in terms of a zero-power point reactor model. The results of the present analysis may be utilized in comparing various methods and in planning and optimizing an experiment.

Phase and Amplitude Fluctuations in Propagating through a Layered Ocean

A propagation experiment was conducted over a 25-mile wholly refracted (RRR) path for 48 h in October 1967. The data recorded during the experiment consisted of both the arrival time and the amplitude of acoustic pulses at 11 vertically spaced hydrophones. The source and the receivers were fixed, and the medium was sampled every tenth of an hour with a 10-msec pulse at 800 Hz. The propagation path between source and receiver was purely refractive and amounted to a complete cycle of RRR type of propagation. The means, variances, autocorrelation, autospectral density, cross correlation, and coherence function were estimated for both the amplitude and phase data. The probability distribution function for both amplitude and phase is demonstrated to be nearly Gaussian. An interrelationship between the time and space characteristics of the random inhomogeneities of the medium is illustrated. Wherever possible, the measured results are compared with the theoretical values of Chernov (1960). A comparison of the theory, which is based on a statistically homogeneous medium, with the measured values, obtained in a layered medium, is discussed.