US2005043931A1PendingUtilityA1
Interference reduction by step function removal
Priority: Dec 28, 2001Filed: Oct 4, 2004Published: Feb 24, 2005
Est. expiryDec 28, 2021(expired)· nominal 20-yr term from priority
H04L 25/061
43
PatentIndex Score
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Cited by
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Claims
Abstract
Correcting a signal offset may include observing a finite duration signal y n that comprises a representation of a mixture of a desired signal and an undesired signal. 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, y n may be corrected based on the estimated step function parameters.
Claims
exact text as granted — not AI-modified1 . A method comprising:
observing a finite duration signal y n 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; modeling the offset component of the undesired signal as comprising a step function u defined by unknown step function parameters; estimating the unknown step function parameters; and adjusting y n based on the estimated step function parameters.
2 . The method of claim 1 in which y n comprises a continuous signal.
3 . The method of claim 1 in which y n comprises a discrete signal.
4 . The method of claim 3 in which:
y n includes N samples and comprises a discrete representation of a mixture of the desired signal, the undesired signal, and a second signal including a generally sinusoidal waveform and an attenuated version of the desired signal; and y n is modeled 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.
5 . The method of claim 1 in which the step function parameters include a first parameter c 1 indicative of a first amplitude of the step function, a second parameter c 2 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, and in which the desired signal is a function of at least one unknown signal parameter θ.
6 . The method of claim 5 in which y n includes N samples and estimating the step function parameters includes jointly estimating θ, c 1 , c 2 , and α (0≦α<N) based on a non-linear optimization method.
7 . The method of claim 5 in which y n includes N samples and estimating the step function parameters includes estimating c 1 , c 2 , and α (0≦α<N) based on a maximum likelihood method.
8 . The method of claim 7 in which the estimates of the step function parameters comprise:
a first estimate ĉ 1 of c 1 where c ^ 1 ≈ 1 α ^ ∑ n = 0 α ^ - 1 y n ; a second estimate ĉ 2 of c 2 where c ^ 2 ≈ 1 N - α ^ ∑ n = α ^ N - 1 y n ; and a third estimate {circumflex over (α)} of α where α ^ ≈ arg max α Test 1 α Test ∑ n = 0 α Test - 1 y n 2 + 1 N - α Test ∑ n = α Test N - 1 y n 2 , 0 ≤ α Test < N - 1.
9 . The method of claim 8 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 where g ≈ 1 α Test ∑ n = 0 α Test - 1 y n 2 + 1 N - α Test ∑ n = α Test N - 1 y n 2 ; selecting 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.
10 . The method of claim 9 in which less than N values of α Test are selected.
11 . The method of claim 7 in which estimating the step function parameters further comprises jointly estimating θ, c 1 , c 2 , and α based on a non-linear minimization of a function comprising
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in which the minimization is performed by computing one or more of the derivatives of f.
12 . A system comprising:
an observation circuit structured and arranged to observe a finite duration signal y n that comprises a discrete 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; 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; 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 y n based on the estimated step function parameters.
13 . The system of claim 12 in which y n comprises a continuous signal.
14 . The system of claim 12 in which y n comprises a discrete signal.
15 . The system of claim 14 in which:
y n includes N samples and comprises a discrete representation of a mixture of the desired signal, the undesired signal, and a second signal including a generally sinusoidal waveform and an attenuated version of the desired signal; and the modeling circuit is further configured to model y n as comprising a discrete representation of the desired signal and also a discrete representation of an offset component related to a square of the undesired signal.
16 . The system of claim 12 in which the unknown step function parameters include a first parameter c 1 indicative of a first amplitude of the step function, a second parameter c 2 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, and in which the desired signal is a function of at least one unknown signal parameter θ.
17 . The system of claim 16 in which y n includes N samples and the estimating circuit is further configured to estimate jointly the unknown step function parameters θ, c 1 , c 2 , and α (0≦α<N) based on a non-linear optimization method.
18 . The system of claim 16 in which y n includes N samples and the estimating circuit is further configured to estimate the unknown step function parameters c 1 , c 2 , and α (0≦α<N) based on a maximum likelihood method.
19 . The system of claim 18 in which the estimating circuit is further configured to estimate the unknown step function parameters as comprising:
a first estimate ĉ 1 of c 1 where c ^ 1 ≈ 1 α ^ ∑ n = 0 α ^ - 1 y n ; a second estimate ĉ 2 of c 2 where c ^ 2 ≈ 1 N - α ^ ∑ n = α ^ N - 1 y n ; and a third estimate {circumflex over (α)} of α where α ^ ≈ arg max α Test 1 α Test ∑ n = 0 α Test - 1 y n 2 + 1 N - α Test ∑ n = α Test N - 1 y n 2 , 0 ≤ α Test < N .
20 . The system of claim 19 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 where g ≈ 1 α Test ∑ n = 0 α Test - 1 y n 2 + 1 N - α Test ∑ n = α Test N - 1 y n 2 ; selecting 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.
21 . The system of claim 20 in which less than N values of α Test are selected by the estimating circuit.
22 . The system of claim 18 in which the estimating circuit is further configured to estimate jointly the unknown step function parameters θ, c 1 , c 2 , and α based on non-linear minimization of a function comprising
f
(
θ
,
c1
,
c2
,
α
)
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0
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2
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m
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θ
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2
in which minimization is performed by computing one or more of the derivatives of f.
23 . 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 y n 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; 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; 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 y n based on the estimated step function parameters.
24 . The computer program of claim 23 in which y n comprises a continuous signal.
25 . The computer program of claim 23 in which y n comprises a discrete signal.
26 . The computer program of claim 25 in which:
y n includes N samples and comprises a discrete representation of a mixture of the desired signal, the undesired signal, 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 y n as comprised of s n , a discrete representation of the desired signal and also a discrete representation of an offset component related to a square of the undesired signal, in which the modeling code segment also is configured to cause the computer to model the offset component as comprising a step function u defined by unknown step function parameters.
27 . The computer program of claim 23 in which the unknown step function parameters include a first parameter c 1 indicative of a first amplitude of the step function, a second parameter c 2 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, and in which the desired signal is a function of at least one unknown signal parameter θ.
28 . The computer program of claim 27 in which y n includes N samples and the estimating code segment further comprises a non-linear optimization code segment configured to cause the computer program to estimate jointly the unknown step function parameters θ, c 1 , c 2 , and a (0≦α<N) based on a non-linear optimization method.
29 . The computer program of claim 27 in which y n includes N samples and the estimating code segment further comprises a maximum likelihood code segment configured to cause the computer to estimate the unknown step function parameters c 1 , c 2 , and a (0≦α<N) based on a maximum likelihood method.
30 . The computer program of claim 29 in which the maximum likelihood code segment is further configured to cause the computer to estimate the unknown step function parameters as comprising:
a first estimate ĉ 1 of c 1 where c ^ 1 ≈ 1 α ^ ∑ n = 0 α ^ - 1 y n ; a second estimate ĉ 2 of c 2 where c ^ 2 ≈ 1 N - α ^ ∑ n = α ^ N - 1 y n ; and a third estimate {circumflex over (α)} of α where α ^ ≈ arg max α Test 1 α Test ∑ n = 0 α Test - 1 y n 2 + 1 N - α Test ∑ n = α Test N - 1 y n 2 , 0 ≤ α Test < N .
31 . The computer program of claim 30 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 where g ≈ 1 α Test ∑ n = 0 α Test - 1 y n 2 + 1 N - α Test ∑ n = α Test N - 1 y n 2 ; a 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 â_max code segment configured to cause the computer to select {circumflex over (α)} based on the one or more maximum values of g.
32 . The computer program of claim 31 in which the selecting code segment is further configured to cause the computer to select less than N values of α Test .
33 . The computer program of claim 29 in which the maximum likelihood code segment is further configured to cause the computer to estimate jointly the unknown step function parameters θ, c 1 , c 2 , and α based on non-linear minimization of a function comprising
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(
θ
,
c1
,
c2
,
α
)
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in which the minimization is performed by computing one or more of the derivatives of f.
34 . A processor which:
observes a finite duration signal y n 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; determines estimated step function parameters; and corrects the signal y n based on the estimated step function parameters.
35 . The processor of claim 34 in which y n comprises a continuous signal.
36 . The processor of claim 34 in which y n comprises a discrete signal.
37 . The processor of claim 36 in which:
y n includes N samples and comprises a discrete representation of a mixture of the desired signal, the undesired signal, and a second signal including a generally sinusoidal waveform and an attenuated version of the desired signal; and y n is modeled as including a discrete representation of the desired signal and also a discrete representation of an offset component related to a square of the undesired signal, and models the offset component as a step function u defined by unknown step function parameters.
38 . The processor of claim 34 in which y n includes N samples and the unknown step function parameters include a first parameter c 1 indicative of a first amplitude of the step function, a second parameter c 2 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.
39 . The processor of claim 38 in which the processor estimates the unknown step function parameters as comprising:
a first estimate ĉ 1 of c 1 where c ^ 1 ≈ 1 α ^ ∑ n = 0 α ^ - 1 y n ; a second estimate ĉ 2 of c 2 where c ^ 2 ≈ 1 N - α ^ ∑ n = α ^ N - 1 y n ; and a third estimate {circumflex over (α)} of α where α ^ ≈ arg max α Test 1 α Test ∑ n = 0 α Test - 1 y n + 1 N - α Test ∑ n = α Test N - 1 y n 2 .
40 . The method of claim 1 wherein the desired signal comprises data of interest.
41 . The system of claim 12 wherein the desired signal comprises data of interest.
42 . The computer program of claim 23 wherein the desired signal comprises data of interest.
43 . The processor of claim 34 wherein the desired signal comprises data of interest.Join the waitlist — get patent alerts
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