Data processing: measuring – calibrating – or testing – Measurement system – Measured signal processing
Reexamination Certificate
2001-12-10
2004-05-18
Hoff, Marc S. (Department: 2857)
Data processing: measuring, calibrating, or testing
Measurement system
Measured signal processing
C702S179000, C708S300000
Reexamination Certificate
active
06738734
ABSTRACT:
ORIGIN OF INVENTION
The inventor of the invention described herein is an employee of the United States Government. Therefore, the invention may be manufactured and used by or for the Government for governmental purposes without the payment of any royalties thereon or therefor.
COPYRIGHT NOTIFICATION
Portions of this patent application contain materials that are subject to copyright protection. The copyright owner has no objection to the facsimile reproduction by anyone of the patent document or the patent disclosure, as it appears in the Patent and Trademark Office patent file or records, but otherwise reserves all copyright rights whatsoever.
BACKGROUND OF THE INVENTION
1. Technical Field of the Invention
This invention generally relates to a signal analysis method, apparatus and article of manufacture. The results of processing several examples of biological signals are discussed herein to show the particular utility of the invention in that field and to further demonstrate the broad applicability of the invention.
Although the present invention finds utility in processing biological signals, it is to be understood that any signal representative of a real world phenomenon such as a signal representative of a physical process including electrical, mechanical, biological, chemical, optical, geophysical or other process(es) may be analyzed and thereby more fully understood by applying the invention thereto. The real world signals to which the invention finds utility include a wide variety of real world phenomena such as the behavior of a stock market, population growth, traffic flow, etc. Furthermore, the term “real world signal” also includes “physical signals” representative of physical processes such as the electrical, mechanical, biological, chemical, optical, geophysical process(es) mentioned above.
Although the invention is not limited to a particular type of signal processing and includes the full range of real world data representative of processes or phenomena or combinations thereof, it is most useful when such real world signals are nonlinear and nonstationary.
2. Description of Related Art
In the parent application, several examples of geophysical data signals representative of earthquakes, ocean waves, tsunamis, ocean surface elevation and wind were processed to show the invention's wide utility to a broad variety of signal types. The techniques disclosed therein and elaborated upon herein represent major advances in physical signal processing.
Previously, analyzing signals, particularly those having nonlinear and/or nonstationary properties, was a difficult problem confronting many industries. These industries have harnessed various computer implemented methods to process data signals measured or otherwise taken from various processes such as electrical, mechanical, optical, biological, and chemical processes. Unfortunately, previous methods have not yielded results which are physically meaningful.
Among the difficulties found in conventional systems is that representing physical processes with physical signals may present one or more of the following problems:
(a) The total data span is too short;
(b) The data are nonstationary; and
(c) The data represent nonlinear processes.
Although problems (a)-(c) are separate issues, the first two problems are related because a data section shorter than the longest time scale of a stationary process can appear to be nonstationary. Because many physical events are transient, the data representative of those events are nonstationary. For example, a transient event such as an earthquake will produce nonstationary data when measured.
Nevertheless, the nonstationary character of such data is ignored or the effects assumed to be negligible. This assumption may lead to inaccurate results and incorrect interpretation of the underlying physics as explained below.
A variety of techniques have been applied to nonlinear, nonstationary physical signals. For example, many computer implemented methods apply Fourier spectral analysis to examine the energy-frequency distribution of such signals.
Although the Fourier transform that is applied by these computer implemented methods is valid under extremely general conditions, there are some crucial restrictions: the system must be linear, and the data must be strictly periodic or stationary. If these conditions are not met, then the resulting spectrum will not make sense physically.
A common technique for meeting the linearity condition is to approximate the physical phenomena with at least one linear system. Although linear approximation is an adequate solution for some applications, many physical phenomena are highly nonlinear and do not admit a reasonably accurate linear approximation.
Furthermore, imperfect probes/sensors and numerical schemes may contaminate data representative of the phenomenon. For example, the interactions of imperfect probes with a perfect linear system can make the final data nonlinear.
Many recorded physical signals are of finite duration, nonstationary, and nonlinear because they are derived from physical processes that are nonlinear either intrinsically or through interactions with imperfect probes or numerical schemes. Under these conditions, computer implemented methods which apply Fourier spectral analysis are of limited use. For lack of alternatives, however, such methods still apply Fourier spectral analysis to process such data.
In summary, the indiscriminate use of Fourier spectral analysis in these methods and the adoption of the stationarity and linearity assumptions may give inaccurate results some of which are described below.
First, the Fourier spectrum defines uniform harmonic components globally. Therefore, the Fourier spectrum needs many additional harmonic components to simulate nonstationary data that are nonuniform globally. As a result, energy is spread over a wide frequency range.
For example, using a delta function to represent the flash of light from a lightning bolt will give a phase-locked wide white Fourier spectrum. Here, many Fourier components are added to simulate the nonstationary nature of the data in the time domain, but their existence diverts energy to a much wider frequency domain. Constrained by the conservation of energy principle, these spurious harmonics and the wide frequency spectrum cannot faithfully represent the true energy density of the lighting in the frequency and time space.
More seriously, the Fourier representation also requires the existence of negative light intensity so that the components can cancel out one another to give the final delta function representing the lightning. Thus, the Fourier components might make mathematical sense, but they often do not make physical sense when applied.
Although no physical process can be represented exactly by a delta function, some physical data such as the near field strong earthquake energy signals are of extremely short duration. Such earthquake energy signals almost approach a delta function, and they always give artificially wide Fourier spectra.
Second, Fourier spectral analysis uses a linear superposition of trigonometric functions to represent the data. Therefore, additional harmonic components are required to simulate deformed wave profiles. Such deformations, as will be shown later, are the direct consequence of nonlinear effects. Whenever the form of the data deviates from a pure sine or cosine function, the Fourier spectrum will contain harmonics.
Furthermore, both nonstationarity and nonlinearity can induce spurious harmonic components that cause unwanted energy spreading and artificial frequency smearing in the Fourier spectrum. In other words, the nonstationary, stochastic nature of biological data suffers from conventional signal processing techniques and makes the interpretation of the processed data quite difficult.
According to the above background, there is a need for a more accurate signal processing technique that produces results that are more physically meaningful and readily understood. Biological signals provide another example of physical si
Barbee Manuel L
Hoff Marc S.
Park Chan K.
The United States of America as represented by the Administrator
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