A review on machinery diagnostics and prognostics implementing condition-based maintenance

to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

Information Theory and Reliable Communication

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Statistical Parametric Mapping The Analysis Of Functional Brain Images

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Methods Of Modern Mathematical Physics

Upright stance in humans is inherently unstable, requiring corrective action based on spatial-orientation information from sensory systems. One might logically predict that environments providing a...

Dynamic regulation of sensorimotor integration in human postural control.

A general method for constructing nonnegative definite, joint time-frequency distributions (TFDs) satisfying the marginals of time |s(t)|/sup 2/ and frequency |S(f)|/sup 2/ is presented. As nonnegative-definite distributions with the correct marginals, these TFDs are members of the Cohen-Posch class. Several examples illustrating properties of these TFDs are presented for both synthetic and real signals. >

Construction of positive time-frequency distributions

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.

On the amplitude‐ and frequency‐modulation decomposition of signals

Instantaneous frequency, taken as the derivative of the phase of the signal, is interpreted in the time-frequency literature as the average frequency of the signal at each time. We point out some difficulties with this interpretation, and show that for a generic two-component AM-FM signal, the interpretation holds only when the components are of equal strength. We conclude that instantaneous frequency and the average frequency at each time are generally two different quantities. One possible interpretation of the difference between these two quantities is suggested.

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Comments on the interpretation of instantaneous frequency

The invention relates to an anesthesia ventilating apparatus having a breathing circuit and a plurality of control loops for the anesthesia gas, the anesthesia agent and the carbon dioxide exhaled by a patient. A disconnect switch is provided for opening and closing the control loop for adjusting the anesthesia agent. When this control loop is opened, a control unit changes the desired value of the anesthetic agent to a desired flushing value thereof. The control unit includes a processor which monitors the time-dependent course of the concentration of the anesthetic agent to determine breathing circuit system parameters and then computes the adjusting parameters of a controller in the control loop for adjusting the anesthetic agent. A method of operating the apparatus is also disclosed.

Patrick J. Loughlin

Papers

Dynamic regulation of sensorimotor integration in human postural control.

Construction of positive time-frequency distributions

On the amplitude‐ and frequency‐modulation decomposition of signals

Comments on the interpretation of instantaneous frequency

Anesthesia ventilating apparatus having a breathing circuit and control loops for anesthetic gas components