Interference reduction by step function removal
First Claim
Patent Images
1. A method comprising:
- observing a finite duration signal yn having N samples that comprises a representation of a mixture of a desired signal and an undesired signal, in which the desired signal is a function of at least one unknown signal parameter θ and
the undesired signal comprises an offset component based on interference of an external interference source;
modeling the offset component of the undesired signal as comprising a step function u defined by unknown step function parameters that include a first parameter c1 indicative of a first amplitude of the step function, a second parameter c2 indicative of a second amplitude of the step function, and a third parameter α
indicative of a point at which the step function transitions from the first amplitude to the second amplitude;
estimating jointly the unknown signal parameter θ and
the unknown step function parameters c1, c2, and α
(0≦
α
<
N) based on a non-linear optimization method; and
adjusting yn based on the estimated step function parameters.
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Abstract
Correcting a signal offset may include observing a finite duration signal yn that comprises a representation of a mixture of a desired signal that may include data of interest, and an undesired signal based on interference of an external interference source. The undesired signal may include an offset component which may be modeled as comprising a step function u defined by unknown step function parameters. The unknown step function parameters may be estimated using, for example, a maximum likelihood method. Thereafter, yn may be corrected based on the estimated step function parameters.
14 Citations
43 Claims
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1. A method comprising:
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observing a finite duration signal yn having N samples that comprises a representation of a mixture of a desired signal and an undesired signal, in which the desired signal is a function of at least one unknown signal parameter θ and
the undesired signal comprises an offset component based on interference of an external interference source;
modeling the offset component of the undesired signal as comprising a step function u defined by unknown step function parameters that include a first parameter c1 indicative of a first amplitude of the step function, a second parameter c2 indicative of a second amplitude of the step function, and a third parameter α
indicative of a point at which the step function transitions from the first amplitude to the second amplitude;
estimating jointly the unknown signal parameter θ and
the unknown step function parameters c1, c2, and α
(0≦
α
<
N) based on a non-linear optimization method; and
adjusting yn based on the estimated step function parameters.
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2. A system comprising:
-
an observation circuit structured and arranged to observe a finite duration signal yn having N samples that comprises a discrete representation of a mixture of a desired signal and an undesired signal, in which the desired signal is a function of at least one unknown signal parameter θ and
the undesired signal comprises an offset component based on interference of an external interference source;
a modeling circuit structured and arranged to model the offset component of the undesired signal as comprising a step function u defined by unknown step function parameters that include a first parameter c1 indicative of a first amplitude of the step function, a second parameter c2 indicative of a second amplitude of the step function, and a third parameter α
indicative of a point at which the step function transitions from the first amplitude to the second amplitude;
an estimating circuit structured and arranged to use a non-linear optimization method to determine jointly an estimated signal parameter and estimated step function parameters representative of the unknown signal parameter θ and
the unknown step function parameters c1, c2, and α
(0≦
α
<
N); and
a correction circuit structured and arranged to correct yn based on the estimated step function parameters.
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3. A computer program stored on a computer readable medium or a propagated signal, the computer program comprising:
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an observation code segment configured to cause a computer to observe a finite duration signal yn having N samples that comprises a representation of a mixture of a desired signal and an undesired signal, in which the desired signal is a function of at least one unknown signal parameter θ and
the undesired signal comprises an offset component based on interference of an external interference source;
a modeling code segment configured to cause the computer to model the offset component of the undesired signal as comprising a step function u defined by unknown step function parameters that include a first parameter c1 indicative of a first amplitude of the step function, a second parameter c2 indicative of a second amplitude of the step function, and a third parameter α
indicative of a point at which the step function transitions from the first amplitude to the second amplitude;
an estimating code segment configured to cause the computer to use a non-linear optimization method to determine jointly an estimated signal parameter and estimated step function parameters representative of the unknown signal parameter θ and
the unknown step function parameters c1, c2, and α
(0≦
α
<
N); and
a correcting code segment configured to cause the computer to correct yn based on the estimated step function parameters.
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4. A processor which:
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observes a finite duration signal yn having N samples that comprises a representation of a mixture of a desired signal and an undesired signal, the undesired signal comprising an offset component based on interference of an external interference source;
models the offset component of the undesired signal as a step function u defined by unknown step function parameters that include a first parameter c1 indicative of a first amplitude of the step function, a second parameter c2 indicative of a second amplitude of the step function, and a third parameter α
(0≦
α
<
N) indicative of a point at which the step function transitions from the first amplitude to the second amplitude;
determines estimated step function parameters comprising;
a first estimate ĉ
1 of c1 wherea second estimate ĉ
2 of c2 wherea third estimate {circumflex over (α
)} of α
wherecorrects the signal yn based on the estimated step function parameters.
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5. A method comprising:
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observing a finite duration signal yn that comprises a discrete representation, including N samples, of a mixture of a desired signal, an undesired signal comprising an offset component, and a second signal including a generally sinusoidal waveform and an attenuated version of the desired signal;
modeling yn as including a discrete representation of the desired signal and a discrete representation of an offset component related to a square of the undesired signal, in which the offset component is modeled as comprising a step function u defined by unknown step function parameters;
estimating the unknown step function parameters; and
adjusting yn based on the estimated step function parameters. - View Dependent Claims (6, 7, 8, 9, 10, 11, 12, 13, 14, 15)
a first estimate ĉ
1 of c1 wherea second estimate ĉ
2 of c2 wherea third estimate {circumflex over (α
)} of α
where
-
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12. The method of claim 11 in which determining {circumflex over (α
- )} comprises;
selecting more than one value of α
Test;
determining a value g for each selected value of α
Test whereselecting from among the determined values of g one or more maximum values of g; and
selecting {circumflex over (α
)} based on the one or more maximum values of g.
- )} comprises;
-
13. The method of claim 12 in which less than N values of α
- Test are selected.
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14. The method of claim 10 in which estimating the step function parameters further comprises jointly estimating θ
- , c1, c2, and α
based on a non-linear minimization of a function comprisingin which the minimization is performed by computing one or more of the derivatives of ƒ
.
- , c1, c2, and α
-
15. The method of claim 5 wherein the desired signal comprises data of interest.
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16. A system comprising:
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an observation circuit structured and arranged to observe a finite duration signal yn that comprises a discrete representation, including N samples, of a mixture of a desired signal, an undesired signal comprising an offset component, and a second signal including a generally sinusoidal waveform and an attenuated version of the desired signal;
a modeling circuit structured and arranged to model yn as including a discrete representation of the desired signal and a discrete representation of an offset component related to a square of the undesired signal, in which the offset component is modeled as comprising a step function u defined by unknown step function parameters;
an estimating circuit structured and arranged to determine estimated step function parameters representative of the unknown step function parameters; and
a correction circuit structured and arranged to correct yn based on the estimated step function parameters. - View Dependent Claims (17, 18, 19, 20, 21, 22, 23, 24, 25, 26)
a first estimate ĉ
1, of c1 wherea second estimate ĉ
2 of c2 wherea third estimate {circumflex over (α
)} of α
where
-
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23. The system of claim 22 in which the estimating circuit is further configured to determine {circumflex over (α
- )} based on the following;
selecting more than one value of α
Test;
determining a value g for each selected value of α
Test whereselecting from among the determined values of g one or more maximum values of g; and
selecting {circumflex over (α
)} based on the one or more maximum values of g.
- )} based on the following;
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24. The system of claim 23 in which less than N values of α
- Test are selected by the estimating circuit.
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25. The system of claim 21 in which the estimating circuit is further configured to estimate jointly the unknown step function parameters θ
- , c1, c2, and α
based on non-linear minimization of a function comprisingin which minimization is performed by computing one or more of the derivatives of ƒ
.
- , c1, c2, and α
-
26. The system of claim 16 wherein the desired signal comprises data of interest.
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27. A computer program stored on a computer readable medium or a propagated signal, the computer program comprising:
-
an observation code segment configured to cause a computer to observe a finite duration signal yn that comprises a discrete representation, including N samples, of a mixture of a desired signal, an undesired signal comprising an offset component, and a second signal including a generally sinusoidal waveform and an attenuated version of the desired signal;
a modeling code segment configured to cause the computer to model yn as including a discrete representation of the desired signal and a discrete representation of an offset component related to a square of the undesired signal, in which the offset component is modeled as comprising a step function u defined by unknown step function parameters;
an estimating code segment configured to cause the computer to determine estimated step function parameters representative of the unknown step function parameters; and
a correcting code segment configured to cause the computer to correct yn based on the estimated step function parameters. - View Dependent Claims (28, 29, 30, 31, 32, 33, 34, 35, 36, 37)
a first estimate ĉ
1 of c1 wherea second estimate ĉ
2 of c2 wherea third estimate {circumflex over (α
)} of α
where
-
-
34. The computer program of claim 33 in which the maximum likelihood code segment further comprises:
-
a selecting code segment configured to cause the computer to select more than one value of α
Test;
a calculating code segment configured to cause the computer to determine a value g for each selected value of α
Test wherea g_max code segment configured to cause the computer to select from among the determined values of g one or more maximum values of g; and
an {circumflex over (α
)}_max code segment configured to cause the computer to select {circumflex over (α
)} based on the one or more maximum values of g.
-
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35. The computer program of claim 34 in which the selecting code segment is further configured to cause the computer to select less than N values of α
- Test.
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36. The computer program of claim 32 in which the maximum likelihood code segment is further configured to cause the computer to estimate jointly the unknown step function parameters θ
- , c1, c2, and α
based on non-linear minimization of a function comprisingin which the minimization is performed by computing one or more of the derivatives of ƒ
.
- , c1, c2, and α
-
37. The computer program of claim 27 wherein the desired signal comprises data of interest.
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38. A processor which:
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observes a finite duration signal yn that comprises a discrete representation, including N samples, of a mixture of a desired signal, an undesired signal comprising an offset component, and a second signal including a generally sinusoidal waveform and an attenuated version of the desired signal;
models yn as including a discrete representation of the desired signal and a discrete representation of an offset component related to a square of the undesired signal, in which the offset component is modeled as comprising a step function u defined by unknown step function parameters;
determines estimated step function parameters; and
corrects the signal yn based on the estimated step function parameters. - View Dependent Claims (39, 40, 41, 42, 43)
a first estimate ĉ
1 of c1 wherea second estimate ĉ
2 of c2 wherea third estimate {circumflex over (α
)} of α
where
-
-
43. The processor of claim 38 wherein the desired signal comprises data of interest.
Specification