Computer graphics processing and selective visual display system – Computer graphics processing – Graph generating
Reexamination Certificate
2000-01-24
2002-04-23
Luu, Matthew (Department: 2672)
Computer graphics processing and selective visual display system
Computer graphics processing
Graph generating
C345S094000, C345S208000, C073S465000
Reexamination Certificate
active
06377260
ABSTRACT:
FIELD OF THE INVENTION
The present invention relates, in general, to computer graphics processing, operator interface processing, and selective visual display systems and, in particular, to waveform display (e.g., oscilloscope type).
BACKGROUND OF THE INVENTION
Signals are often described as complex numbers. A complex number is a number in the form of a+bi, where a and b are real numbers, and where i is the square root of −1. The first part of the complex number (i.e., a) is referred to as the real component, and the second part of the complex number (i.e., bi) is referred to as the imaginary component. The magnitude and phase of a signal are each derived from both the real and imaginary components of the complex number that represents the signal. The equations for finding the magnitude and phase of a signal described by a complex number may be found on page 39 of a 1995 book by Robert W. Ramirez, entitled “The FFT Fundamentals and Concepts.” The magnitude of such a signal may be found by squaring the real component, squaring the imaginary component, summing the two squared terms, and finding the square root of the sum. The result of the square root is the magnitude. The phase is found by dividing the imaginary component by the real component and finding the inverse tangent of the quotient. The result of the inverse tangent is the phase. As you can see, both the real component and the imaginary component contribute to both the magnitude and the phase of the signal. Typical oscilloscopes display the magnitude or phase of a signal versus time, but not the real and imaginary components separately. By combining the real and imaginary components of a waveform on a single axis, the user is forced to mentally integrate the real and imaginary components from the combined information to get a sense of how the complex waveform evolves over time.
Where the phase of a signal is plotted versus time, the range of the phase is often artificially restrained to +/−180 degrees. Such a restriction complicates the phase depiction near these limits by causing abrupt shifts from +180 degrees to −180 degrees or vice versa. Such a distortion does not give the user a true sense of the phase history at these limits.
U.S. Pat. No. 5,739,807, entitled “METHOD FOR PRESENTING COMPLEX NUMBER WAVEFORMS,” displays a complex waveform by (1) graphing the magnitude of the signal versus time while representing the phase of the signal by color or area under the curve or (2) graphing the phase of the signal versus time while representing the magnitude of the signal by color or area under the curve. To separate the real component from the imaginary component, a user must integrate the two different display forms of U.S. Pat. No. 5,739,807. Also, U.S. Pat. No. 5,739,807 does not disclose a method of displaying a signal represented by a complex number where the real and imaginary components are displayed separately as does the present invention. U.S. Pat. No. 5,739,807 is hereby incorporated by reference into the specification of the present invention.
Plotting a single set of the real and imaginary components is disclosed on page 76-77 of a book entitled “The Prentice Hall Encyclopedia of Mathematics which was published in 1982. However, this book does not disclose a method of displaying numerous sets of such plots with additional display features as does the present invention.
SUMMARY OF THE INVENTION
It is an object of the present invention to obtain a time history of a signal without having to integrate information on magnitude versus time and phase versus time.
It is another object of the present invention to obtain a time history of a signal by separately displaying sets of the real and imaginary components of a signal versus time.
The present invention is a method of obtaining a time history of a signal without having to integrate information on magnitude versus time and phase versus time by separately displaying sets of the real and imaginary components of a signal verses time.
The first step of the method is sampling a signal in time.
The second step of the method is selecting a user-definable size of a display.
The third step of the method is determining the real and imaginary components for each time sample of the signal.
The fourth step of the method is selecting a user-definable number of samples to be displayed at any one instance.
The fifth step of the method is displaying each sample to be displayed according to its real component along the X-axis, the imaginary component along the Y-axis, and the time associated with the sample along the Z-axis.
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Beverley Henderson West et al., “The Prentice-Hall Encyclopedia of Mathematics”, 1982, pp. 76-77, Prentice-Hall Inc., Englewood Cliffs, New Jersey, U.S.A.
Robert W. Ramirez, “The FFT Fundamentals and Concepts,” 1985, pp. 38-39, Prentice Hall Inc., Englewood Cliffs, New Jersey U.S.A.
Havan Thu-Thao
Luu Matthew
Morelli Robert D.
The United States of America as represented by the National Secu
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