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Patent Number: |
7472152 |
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Case ID: |
0 |
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Patent Title:
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Accommodating fourier transformation attenuation between transform term
frequencies
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Status: |
ACTIVE |
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Status Date: |
2/3/2010 11:00:29 AM |
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Issue Date:
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12/30/2008 |
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Filed Date:
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8/2/2004 |
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Serial #:
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0/914,712 |
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Assignee Name:
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The United States of America as represented by the Secretary of the Air Force
(Washington,
DC)
N/A
(
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Inventor(s):
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Tsui, James B. Y. , Lin, David M. |
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BACKGROUND OF THE INVENTION
When computing the Fourier transformation of a mathematical function or of the waveform representing an electrical signal it is necessary to select the number of "points" or locations in the waveform at which the Fourier transformation
coefficients will be determined. Alternately this selection may be expressed as a need to determine in advance the number of terms to be included in the Fourier series used to represent the waveform or the signal in the transform output. Thus it is
common practice to speak of for example a ten point or a one hundred point or a two hundred fifty six point Fourier transformation. Each such point of the achieved Fourier transformation includes a coefficient magnitude for a component frequency in the
sought-after Fourier series representing the mathematical function or the waveform.
The Fourier transformation accomplished in this manner has in effect performed the function of filtering the input signal of the re . . . . More |
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A Fourier transformation algorithm implementation in which accommodation
is provided for the output attenuation occurring when an input signal
falls intermediate two terms of the transformation output series in its
frequency. Corrected Fourier transformation terms, achieved by combining
the magnitudes of attenuated Fourier transformation terms generated by
the input signal at Fourier transformation frequencies distant to the
input signal frequency, in either a vectorial or a scalar combination,
are substituted for an attenuated Fourier transformation term according
to the invention. Noise correction of the substitute Fourier
transformation terms is also provided. The invention is disclosed through
use of a global position system signal example that is subjected to a
double Fourier transformation filtering process to enhance the incoming
signal to noise ratio. Normally occurring 3.9 decibel attenuations in
each Fourier tra . . . . More |
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We claim:
1. The method of recovering electrical signal amplitude loss arising from frequency offset between a GPS electrical input signal and a bin center coefficient frequency of an electrical
signal Fourier transformation frequency filtering operation applied to said GPS electrical input signal, said method comprising the steps of: performing an electrical signal Fourier transformation operation on said GPS electrical input signal to obtain a
plurality of GPS input signal Fourier transformation coefficient electrical signals each relevant to a different Fourier transformation exponential term and a different bin center frequency in a plurality of overlapping Fourier transformation frequency
bins defined by a corresponding plurality of said exponential terms; and substituting for a selected GPS input signal Fourier transformation coefficient electrical signal relating to an exponential term located in adjacent pairs of said overlapping
Fourier transformation frequency bins, . . . . More |
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