Accommodating fourier transformation attenuation between transform term frequencies

• US 7,472,152 B1
• Filed: 08/02/2004
• Issued: 12/30/2008
• Est. Priority Date: 08/02/2004
• Status: Expired due to Fees

• Current Assignee: United States Of America As Represented By The Secretary Of The Air Force
• Original Assignee: United States Of America As Represented By The Secretary Of The Air Force
• Inventors: Lin, David M., Tsui, James B. Y.
• Primary Examiner(s): Ngo; Chuong D
• Application Number:
  US10/914,712
• Time in Patent Office: 1,611 Days
• Field of Search: 708/403, 708/404, 708/405
• US Class Current: 708/403
• CPC Class Codes: G06F 17/141 Discrete Fourier transforms

Abstract

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 transformation step are reduced to about 0.9 decibel each through use of the invention.

Claims

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, in a selected intermediate frequency location between two adjacent of said bin center frequencies, a substitute coefficient electrical signal determined from a combination of coefficient electrical signals relating to said exponential term located in adjacent pairs of said overlapping Fourier transformation frequency bins and to said GPS electrical input signal;

communicating electrical output signals relating to said substitute coefficient electrical signal to one of an electrical signal responsive GPS data display and a GPS data utilization device.

2. The method of recovering electrical signal amplitude loss of claim 1 wherein:

said coefficients relating to said exponential term located in adjacent pairs of said overlapping Fourier transformation frequency bins are out of phase electrical signals; and

said computed substitute coefficient electrical signal includes a vectorial combination of said out of phase electrical signals.

3. The method of recovering electrical signal amplitude loss of claim 1 wherein:

said plurality of GPS input signal Fourier transformation coefficient electrical signals and said Fourier transformation exponential terms comprise a GPS electrical output signal of said Fourier transformation and wherein said GPS electrical output signal is subjected to the additional steps of;

performing a second Fourier transformation operation on said GPS electrical output signal to obtain a plurality of GPS output signal second Fourier transformation coefficient electrical signals each relevant to a different GPS second Fourier transformation exponential term and a different band center frequency in a plurality of GPS overlapping second Fourier transformation frequency bands defined by a corresponding plurality of said second Fourier transformation exponential terms;

substituting for each GPS electrical output signal Fourier transformation coefficient relating to a second GPS Fourier transformation exponential term located in adjacent pairs of said overlapping second Fourier transformation frequency bands, in selected GPS intermediate frequency locations central between two adjacent of said band center frequencies, a substitute coefficient GPS electrical signal computed from a combination of said coefficient electrical signals relating to said exponential term located in adjacent pairs of said overlapping second Fourier transformation frequency bands and to said electrical output signal to generate a second electrical output signal;

said step of communicating electrical output signals relating to said substitute coefficient GPS electrical signal to one of an electrical signal responsive data display and data utilization device includes communicating said second electrical output signal to one of said GPS electrical signal responsive GPS data display and said data utilization device.

4. The method of recovering electrical signal amplitude loss of claim 3 wherein said frequency bin substituting steps and said frequency band substituting steps each comprise portions of GPS signal amplitude recovery of between 2.67 and 3.0 decibels of offset frequency related signal loss and between 5.34 and 6.0 decibels of total signal amplitude recovery.

5. The method of recovering electrical signal amplitude loss of claim 1 wherein said coefficients relating to said exponential term located in adjacent pairs of said overlapping Fourier transformation frequency bins are equal in magnitude and said selected intermediate frequency between two adjacent of said bin center frequencies comprise a single frequency equally disposed from each of said adjacent pairs of overlapping Fourier transformation frequency bins.

6. The method of recovering electrical signal amplitude loss of claim 1 wherein said selected intermediate frequencies between two adjacent of said bin center frequencies comprise five selected intermediate frequency locations between two adjacent of said bin center frequency locations.

7. The method of recovering electrical signal amplitude loss of claim 1 wherein:

said coefficient electrical signals relating to said exponential term located in adjacent pairs of said overlapping Fourier transformation frequency bins are out of phase electrical signals; and

said substitute coefficient electrical signal determined from a combination of coefficient electrical signals relating to said exponential term located in adjacent pairs of said overlapping Fourier transformation frequency bins includes a scalar combination of said out of phase electrical signals.

8. Fourier transformation GPS electrical input signal processing apparatus having compensated GPS electrical input signal frequency to Fourier transformation term frequency offset-induced transformation term attenuation, said apparatus comprising the combination of:

an embodied Fourier transformation filter connected to said GPS electrical input signal and determining terms of a Fourier transformation series GPS electrical output signal wherein each series term defines a bin center frequency in an array of Fourier transformation overlapping frequency bins;

each term of said Fourier transformation series including a coefficient signal of magnitude determined by said GPS electrical input signal strength and also of magnitude determined by a frequency offset responsive bin relationship between said GPS electrical input signal frequency and frequencies of a most adjacent pair of said Fourier transformation series terms; and

signal combining apparatus responsive to a coefficient portion of said Fourier transformation series terms disposed at frequencies proximate said GPS electrical input signal frequency, in two adjacent of said frequency bins;

said signal combining apparatus generating corrected replacement larger Fourier transformation coefficient GPS signals usable for enhanced accuracy transform representation of GPS electrical input signal coefficients located intermediate said most adjacent pair of Fourier transformation terms bin center frequencies;

data display apparatus responsive to said corrected replacement larger Fourier transformation coefficient GPS signals and in visual communication with a user of said GPS electrical input signal processing apparatus.

9. The Fourier transformation GPS electrical input signal processing apparatus of claim 8 wherein said input signal frequency to Fourier transformation term frequency offset-induced, periodic, transformation term attenuation has a maximum magnitude of 3.9 decibels within a single Fourier transformation filter.

10. The Fourier transformation GPS electrical input signal processing apparatus of claim 8 wherein said corrected replacement larger Fourier transformation coefficient electrical signal further includes a signal power to noise power determined magnitude correction factor.

11. The Fourier transformation GPS electrical input signal processing apparatus of claim 10 wherein said corrected replacement larger Fourier transformation coefficient electrical signal power to noise power determined magnitude correction factor includes a correction factor of square root of two magnitude.

12. The Fourier transformation GPS electrical input signal processing apparatus of claim 8 wherein said electrical signal combining apparatus includes one of a scalar and a vectorial coefficient signal combining generating said corrected replacement Fourier transformation bin frequency coefficient.

13. The Fourier transformation GPS electrical input signal processing apparatus of claim 8 wherein said coefficient portion of one of said Fourier transformation series terms is mathematically complex, including real and imaginary components and said coefficient magnitude combining apparatus includes a vectorial combining.

14. The Fourier transformation GPS electrical input signal processing apparatus of claim 8 wherein said most adjacent pair of said Fourier transformation bin frequencies comprise a bin frequency located just above said GPS electrical input signal and a bin frequency located just below said GPS electrical input signal in frequency.

15. The Fourier transformation GPS electrical input signal processing apparatus of claim 8 wherein said corrected replacement Fourier transformation bin frequency coefficient signal has a coefficient magnitude greater than either of said most adjacent Fourier transformation bin frequency coefficients.

16. The Fourier transformation electrical input signal processing apparatus of claim 8 wherein said apparatus further includes a second embodied Fourier transformation filter determining terms of a second Fourier transformation series wherein each term defines a band center frequency in an array of Fourier transformation overlapping frequency bands.

17. Fourier transformation GPS electrical input signal-processing apparatus having compensated doubly periodic GPS electrical input signal frequency to Fourier transformation term frequency offset-induced transformation term attenuation, said apparatus comprising the combination of:

a first embodied Fourier transformation filter connected to said GPS electrical input signal and determining terms of a first Fourier transformation series GPS electrical output signal wherein each series term defines a bin center frequency in an array of first Fourier transformation overlapping frequency bins;

each term of said first Fourier transformation series including a coefficient signal of magnitude determined by said GPS electrical input signal strength and also of magnitude determined by a frequency offset responsive bin waveform defining a relationship between said GPS electrical input signal and a most adjacent pair of said first Fourier transformation terms;

signal combining apparatus responsive to a coefficient portion of one of said first Fourier transformation series terms appearing at a single frequency, proximate said GPS electrical input signal frequency, in each of two adjacent of said frequency bins;

said signal combining apparatus generating a corrected replacement larger first Fourier transformation coefficient usable for enhanced accuracy transform representation of a GPS electrical input signal coefficient located intermediate said most adjacent pair of first Fourier transformation terms bin center frequencies;

a second embodied Fourier transformation filter connected to a determined GPS output signal of said embodied first Fourier transformation filter and determining terms of a second Fourier transformation series wherein each series term defines a center band frequency in an array of second Fourier transformation overlapping frequency bands;

each term of said second Fourier transformation series including a coefficient signal of magnitude determined by said first Fourier transformation determined GPS electrical output signal strength and also of magnitude determined by a frequency offset responsive band waveform defining a relationship between said first Fourier transformation determined GPS electrical output signal and a most adjacent pair of second Fourier transformation terms; and

second signal combining apparatus responsive to a coefficient portion of one of said second Fourier transformation series terms appearing at a single frequency, proximate said second Fourier transformation determined electrical output, in each of two adjacent of said second Fourier transformation overlapping frequency bands;

said second signal combining apparatus generating a corrected replacement larger second Fourier transformation coefficient usable for enhanced accuracy second transform representation of an determined output coefficient located intermediate said most adjacent pair of second Fourier transformation terms band center frequencies; and

data display apparatus connected to a GPS output signal determined by said embodied Fourier transformation filters and responsive to said corrected replacement larger transformation coefficients.

18. The Fourier transformation GPS electrical input signal processing apparatus having compensated doubly periodic input signal frequency to Fourier transformation term frequency offset-induced transformation term attenuation of claim 17 wherein said bin waveform and said band waveform each contribute to a frequency responsive input signal attenuation of between zero and 3.9 decibels magnitude.

19. Fourier transformation GPS electrical input signal processing apparatus comprising the combination of:

Fourier transformation electrical circuit means connected with said GPS electrical input signal for generating a plurality of Fourier transformation coefficient signals each relating to a GPS Fourier transformation output frequency and each responsive to both said electrical input signal and to frequency offset between said GPS electrical input signal frequency and frequency of adjacent respective GPS Fourier transformation output frequency signals;

Fourier transformation signal correction electrical circuit means for computing replacement coefficients for Fourier transformation coefficients related to Fourier transformation output frequencies adjacent but offset in frequency from said GPS electrical input signal frequency;

said replacement coefficients each having a magnitude determined by a mathematical combination of adjacent but offset in frequency Fourier transformation coefficient magnitudes;

data utilization apparatus responsive to a generated, said replacement coefficient inclusive, output signal of said Fourier transformation electrical circuit means.

20. The Fourier transformation GPS electrical input signal processing apparatus of claim 19 wherein said mathematical combination comprises a vectorial summation of complex Fourier transformation coefficients.

21. The method of recovering electrical signal amplitude loss arising from frequency offset between a noise inclusive GPS system electrical input signal and a bin center coefficient frequency of an electrical signal Fourier transformation frequency filtering operation applied to said input signal, said method comprising the steps of:

performing an electrical signal Fourier transformation operation on said noise inclusive GPS system electrical input signal to obtain a plurality of 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;

substituting for a selected input signal Fourier transformation coefficient electrical signal relating to an exponential term located in adjacent pairs of said overlapping Fourier transformation frequency bins, in a selected intermediate frequency location between two adjacent of said bin center frequencies, a substitute coefficient electrical signal determined from a combination of coefficient electrical signals relating to said exponential term located in adjacent pairs of said overlapping Fourier transformation frequency bins and to said electrical input signal; and

said substituting step including a noise correction mathematical operation performed on said computed substitute coefficient electrical signal.

22. 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, in a selected intermediate frequency location between two adjacent of said bin center frequencies, a substitute coefficient electrical signal determined from a combination of coefficient electrical signals relating to said exponential term located in adjacent pairs of said overlapping Fourier transformation frequency bins and to said GPS electrical input signal;

communicating electrical output signals relating to said substitute coefficient electrical signal to one of an electrical signal responsive GPS data display and a GPS data utilization device;

said one of an electrical signal responsive GPS data determined display and a GPS data utilization device being a selected one of a radio receiver GPS output signal determined display and an aircraft mounted GPS signal determined display.