Data processing: measuring – calibrating – or testing – Measurement system in a specific environment – Electrical signal parameter measurement system
Reexamination Certificate
2002-05-28
2004-06-15
Bui, Bryan (Department: 2863)
Data processing: measuring, calibrating, or testing
Measurement system in a specific environment
Electrical signal parameter measurement system
C702S070000, C702S077000
Reexamination Certificate
active
06751564
ABSTRACT:
FIELD OF THE INVENTION
The present invention is generally directed to a method of analyzing signals. More particularly, the invention is directed to a method for extracting parameter information from a time-varying signal.
BACKGROUND OF THE INVENTION
It is well known that sounds and other mechanical vibration signals typically have actual frequency spectra, especially if the sound persists for even a few cycles of the frequencies involved. A vibrating object will normally produce a fundamental frequency and a sequence of overtones that relate in some manner to the fundamental, often as integer or near-integer multiples. Almost any mechanical system can be described as a collection of such vibrating objects, whether it is a violin string, a human vocal cord, or even a bridge or tall building. If the characteristics of a mechanical system are known well enough, the exact frequency spectrum that it produces can be determined through mechanical modeling. A simple system is shown in FIG.
1
.
As shown in
FIG. 1
, the fundamental frequency is 10.21 Hz and it produces a series of overtones at frequency multiples of 2, 3, 4, 5, and 6. When this mechanical system operates it produces a vibrational signal—in effect a weighted sum of these frequencies and overtones—which is conventionally analyzed using conventional spectrum analysis.
FIGS. 2 and 3
illustrate two of the many possibilities for the vibrational signal as a function of time that might be expected from this example system. Both versions are equally valid, differing only in the phase relationships between the different overtone components.
Conventional spectrum analysis as applied to a sound signal or a recording of a sound signal typically makes use of the Fourier Transform, typically some form of a Discrete Fourier Transform (DFT), often the Fast Fourier Transform (FFT), which is a specific manner of implementing a DFT. The DFT requires that a signal be digitized, that is, that a series of samples of the amplitude of the signal be taken at successive increments of time over a short length of time called the sample time or the sample interval. This series of amplitudes over the sample interval is transformed into a corresponding representation which is called the frequency spectrum.
Typical spectrum analysis applies some form or modification of the DFT to a digitized form of the signal sampled over a time interval. The modification of the basic DFT almost invariably includes some form of windowing. Windowing is a process of pre-multiplying the digitized sample by a set of weights in order to improve the amplitude and frequency resolution of the DFT and has been a central part of spectrum analysis during nearly the entire history of using the method on digital computers.
The lowest frequency represented in the spectrum is (1/sample interval), e.g., if the sample interval is 1 second the lowest frequency is 1 Hz. For a DFT, if the increments of time are evenly spaced, then the frequencies in the spectrum that results from the DFT will also be evenly spaced. In the above example 1 Hz is the first frequency represented, so the frequencies will be 1 Hz apart and the frequency spectrum will have entries for 1 Hz, 2 Hz, 3 Hz, 4 Hz, etc. The number of frequencies thus represented will be one-half the number of points in the sample interval. The DFT frequency spectrum resulting from this operation is shown in FIG.
4
.
FIG. 4
is computed directly from the real system spectrum shown in
FIGS. 1-3
and is an accurate representation of the spectrum for an evenly spaced DFT. The example chosen is far from being a worst case. There is only a superficial resemblance of the so-called DFT frequency spectrum to the actual frequency spectrum of the simple mechanical system (FIG.
1
), with considerable “leakage” of the pure frequencies into adjacent frequencies. The visually apparent amplitudes differ substantially and seemingly randomly from the true spectrum. This problem is obvious and serious and was recognized by the early practitioners of digital spectrum analysis.
A single frequency vibrational tone typically causes amplitudes to be detected in several nearby frequencies of the DFT spectrum rather than in just the one or two nearest, due to a phenomenon called sideband leakage. The detected amplitude can vary considerably from that of a known test signal and it is customary—almost universal—to use windowing to minimize this and force the frequency spectrum peak to be sharper and to more nearly approximate the true amplitude. Windowing usually entails multiplying the sampled values by a sequence of numbers chosen so that the result tapers to zero at either end of the sample interval and is the unaltered signal near the middle of the sample interval.
Windowing does offer considerable improvement in comparison to the above graph, and produces a graph intermediate in appearance between the real spectrum and the DFT spectrum, but leakage and consequent seemingly random variations of amplitude remain. While amplitude information can be partially regained by windowing, phase information is essentially completely lost in conventional spectrum analysis.
To obtain higher precision in the frequency of components, conventional spectrum analysis requires a longer sample interval—the signal must be sampled for a longer period of time. A longer sample interval does not necessarily improve the estimates of amplitude, however, and phase information is still lost in the analysis. The requirement for longer sample times in order to obtain greater accuracy of frequency determination is a fact of life in the current state of the art. To get approximately 1 Hz accuracy requires a one second sample time, with ½ second giving approximate 2 Hz accuracy and 0.1 second sample time giving 10 Hz accuracy. Alternative methods of frequency determination such as the various forms of autocorrelation also require comparatively long sample times and tend to work only in situations where the signal is fairly simple, with a single frequency component or with components spaced well apart in frequency.
Time domain analysis has been used to estimate the frequency, amplitude, and phase of some frequency components of real signals. Here a conventional spectrum analysis is customarily used to provide an initial guess at the frequencies of the various components and the sine/cosine pairs for each frequency are fit to the actual time series data using an iterative scheme to converge to better estimates of the individual components. This approach requires a long sample time for accuracy. Time domain analysis falls apart at short sample times or if there are closely spaced frequencies or if there are frequencies which are not included in the analysis for other reasons.
Several techniques can be made to work when signals are stable enough so that long sample times are not a problem. For example, radio and television transmission signals are designed to be stable and can be very accurately detected by many different methods. The difficulty is that mechanical vibrations and sounds in particular are often very unstable. Only over very short intervals is the signal stable enough to be approximated by a combination of pure frequency tones. We as humans very often recognize sounds as having a particular pitch, a particular color resulting from overtone frequency combinations, and a particular loudness. Yet we also track these qualities as they change—sometimes very rapidly—with time. No current state of the art technique can even approximate this.
Therefore, a new method of analyzing signals and extracting information from the signals is needed.
SUMMARY OF THE INVENTION
Advanced frequency domain methods determine the precise frequency, amplitude, and phase of many components over an interval of time that is short enough to permit the tracking of changing signals. In the case of sound, tracking speed is on the same order as that of a human listener. Tracking is the ability to determine a complete and precise actual, nearly instantaneous spectrum based on a very short time interva
Bui Bryan
Luedeka Neely & Graham P.C.
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