Signal filtering using orthogonal polynomials and removal of edge effects

• US 7,221,975 B2
• Filed: 12/04/2003
• Issued: 05/22/2007
• Est. Priority Date: 12/04/2003
• Status: Expired due to Fees

• Current Assignee: Maquet Critical Care AB (Getinge AB)
• Original Assignee: Maquet Critical Care AB (Getinge AB)
• Inventors: Lindstrom, Lars
• Primary Examiner(s): Pezzuto; Robert E.
• Assistant Examiner(s): Gedeon; Brian T.
• Application Number:
  US10/728,081
• Publication Number:
  US 20050125473A1
• Time in Patent Office: 1,265 Days
• Field of Search: 128/901, 600/509, 455/78, 324/76, 708/300, 708/313
• US Class Current: 600/509
• CPC Class Codes: A61B 5/316 Modalities, i.e. specific diagnostic methods
• CPC Class Codes: A61B 5/389 Electromyography [EMG]
• CPC Class Codes: A61B 5/7207 of noise induced by motion artifacts
• CPC Class Codes: G06F 2218/02 Preprocessing
• CPC Class Codes: H03H 17/0248 Filters characterised by a particular frequency response or filtering method
• CPC Class Codes: Y10S 128/901 Suppression of noise in electric signal

Abstract

A method and device for filtering an input signal containing wanted signal components and unwanted signal components, wherein the signal is modeled as a set of polynomials. Polynomials from the set are identified to model the unwanted signal components. These unwanted signal components are removed from the input signal by removing the polynomials identified as modeling the unwanted signal components from the set of polynomials to thereby leave in the input signal only the wanted signal components. According to an alternative, polynomials from the set are identified to model the wanted signal components, and the polynomials identified as modeling the wanted signal components are outputted as an estimate of the wanted signal components substantially free from the unwanted signal components. According to another aspect, a weighting factor indicative of signal strength is determined for each polynomial and these weighting factors are summed to provide an estimate of the strength of the input signal.

Claims

1. A method of filtering an EMG input signal contaminated by a disturbance signal, the filtering method comprising:

modeling the disturbance signal as polynomials of lower orders; and

;

removing the disturbance signal by removing the polynomials of lower orders from the contaminated EMG input signal to thereby obtain an EMG input signal substantially free from the disturbance signal.

2. A method of filtering as defined in claim 1, wherein the disturbance signal comprises at least one signal selected from the group consisting of:

ECG signals, movement induced disturbances, and background noise.

3. A method of filtering as defined in claim 1, wherein polynomials of lower orders comprise Legendre polynomials of orders from zero (0) to seven (7).

4. A method of filtering as defined in claim 1, wherein the polynomials of lower orders comprise at least one of Tchebychev T-polynomials and Tchebychev U-polynomials.

5. A method of filtering as defined in claim 1, further comprising modeling the contaminated EMG input signal as a set of polynomials and wherein removing the disturbance signal comprises removing the polynomials of lower orders from the set of polynomials modeling the contaminated EMG input signal to thereby obtain an EMG input signal substantially free from the disturbance signal.

6. A method of filtering an input signal containing wanted signal components and unwanted signal components, comprising:

modeling the input signal as a set of polynomials;

modeling the unwanted signal components with a number of polynomials from the set; and

removing the unwanted signal components from the input signal by removing the number of polynomials modeling the unwanted signal components from the set of polynomials to thereby leave in the input signal only the wanted signal components;

wherein modeling the input signal as a set of polynomials comprises;

considering an epoch S(t) of the input signal in a limited time interval, said epoch S(t) having a time scale; and

normalizing the time scale of the epoch S(t).

7. A method as defined in claim 6, wherein normalizing the time scale of the epoch S(t) comprises:

shifting and scaling the limited time interval under consideration into a new variable x in an interval −

1<

x<

1 whereby the signal epoch becomes S(x).

8. A method as defined in claim 7, wherein modeling the input signal as a set of polynomials comprises modeling the input signal as a set of orthogonal polynomials Q_n(x).

9. A method as defined in claim 8, wherein the set of orthogonal polynomials Q_n(x) comprises:

a first initial polynomial Q₀(x) having a constant value; and

a second initial polynomial Q₁(x) having a constant slope.

10. A method as defined in claim 8, wherein modeling the input signal as a set of polynomials comprise:

expressing the input signal as a sum of the polynomials Q_n(x);

$S<br><br>\left(x\right)=\underset{n=0}{\overset{P}{\sum <br><br>}}<br><br><br><br>C_n<br><br><br><br>Q_n<br><br>\left(x\right)$

where P represents a limited number of terms, and

$C_n=\frac{1}{K_n}<br><br>{\int <br><br>}_{-1}^{+1}<br><br>S<br><br>\left(x\right)<br><br><br><br>Q_n<br><br>\left(x\right)<br><br><br><br>f<br><br>\left(x\right)<br><br><br><br>d<br><br>x$

where f(x) is a function of x and K_n is a constant depending on the order n.

11. A method as defined in claim 10, wherein modeling the unwanted signal components comprises:

associating particular orders of the polynomials with the unwanted signal components; and

modeling the unwanted signal components as a sum of the polynomials of said particular orders, comprising weighting the polynomials of said particular orders by means of the coefficients C_n.

12. A method as defined in claim 11, wherein removing the number of polynomials modeling the unwanted signal components from the set of polynomials comprises:

removing the sum of weighted polynomials from the sum of polynomials Q_n(x).

13. A method as defined in claim 6, wherein modeling the input signal as a set of polynomials comprises modeling the input signal as a set of orthogonal polynomials.

14. A method as defined in claim 13, comprising selecting the orthogonal polynomials from the group consisting of:

Legendre polynomials;

Tchebyshev T-polynomials; and

Tchebyshev U-polynomials.

15. A method as of filtering an input signal containing wanted signal components and unwanted signal components, comprising:

modeling the input signal as a set of polynomials;

modeling the unwanted signal components with a number of polynomials from the set; and

removing the unwanted signal components from the input signal by removing the number of polynomials modeling the unwanted signal components from the set of polynomials to thereby leave in the input signal only the wanted signal components;

wherein;

modeling the input signal as a set of polynomials comprises modeling the input signal as a sum of a limited number of polynomials; and

said method further comprises eliminating edge effects constituted by imperfections having a strength depending on the limited number of polynomials.

16. A method as defined in claim 15, wherein:

eliminating the edge effects comprises defining overlapping windows;

modeling the unwanted signal components comprises modeling, in each window, the unwanted signal components with a number of polynomials from the set;

removing the disturbance signal from the input signal comprises removing, in each window, the number of polynomials modeling the unwanted signal components from the set of polynomials to thereby produce in said window a filtered signal part; and

eliminating edge effects further comprises;

in each window, weighting the filtered signal part to suppress the filtered signal part at opposite ends of the window and emphasize the filtered signal part in the central portion of said window; and

summing the weighted filtered signal parts of the overlapping windows to form an output filtered signal generally free from edge effects.

17. A method as defined in claim 16, wherein defining overlapping windows comprises:

defining 50% overlapping windows.

18. A method as defined in claim 16, wherein weighting the filtered signal part in each window comprises:

providing for each window an edge effect suppressing function; and

in each window, multiplying the filtered signal part by the edge effect suppressing function of said window.

19. A method as defined in claim 18, wherein providing for each window an edge effect suppressing function comprises:

constructing an edge effect suppressing function in such a manner that;

a sum of the edge effect suppressing functions of the various overlapping windows is equal to unity; and

a value of the edge suppressing function at opposite ends of each window is equal to zero.

20. A method as defined in claim 19, comprising selecting the edge effect suppressing functions of the overlapping windows from the group consisting of:

a triangular function and a squared cosine function.

21. A method of filtering an input signal containing wanted signal components and unwanted signal components, comprising:

modeling the input signal as a set of polynomials;

modeling the unwanted signal components with a number of polynomials from the set; and

removing the unwanted signal components from the input signal by removing the number of polynomials modeling the unwanted signal components from the set of polynomials to thereby leave in the input signal only the wanted signal components;

wherein modeling the input signal as a set of polynomials comprises;

using higher order polynomials that mimic an oscillatory pattern of the input signal.

22. A device for filtering an EMG input signal contaminated by a disturbance signal, the device comprising:

means for modeling the disturbance signal as polynomials of lower orders; and

means for removing the disturbance signal from the contaminated input signal, wherein the disturbance signal removing means comprises means for removing the polynomials of lower orders from the input signal to thereby obtain an EMG input signal substantially free from the disturbance signal.

23. A device as defined in claim 22, wherein the disturbance signal comprises at least one signal selected from the group consisting of:

ECG signals, movement induced disturbances and background noise.

24. A device as defined in claim 22, wherein the polynomials of lower orders comprise Legendre polynomials of orders from zero (0) to seven (7).

25. A device as defined in claim 22, wherein the polynomials of lower orders comprise at least one of Tchebychev T-polynomials and Tchebychev U-polynomials.

26. A device as defined in claim 22, further comprising means for modeling the contaminated EMG input signal as a set of polynomials and wherein the means for removing the disturbance signal comprises means for removing the polynomials of lower orders from the set of signal substantially free from the disturbance signal.

27. A device for filtering an input signal containing wanted signal components and unwanted signal components, comprising:

means for modeling the input signal as a set of polynomials;

means for modeling the unwanted signal components with a number of polynomials of said set; and

means for removing the unwanted signal components from the contaminated input signal, wherein the unwanted signal components removing means comprises means for removing the number of polynomials modeling the unwanted signal components from the set of polynomials to thereby leave in the input signal only the wanted signal components;

wherein the input signal modeling means comprises;

means for considering an epoch S(t) of the input signal in a limited time interval, said epoch S(t) having a time scale; and

means for nonnalizing the time scale of the epoch S(t), wherein said time scale normalizing means comprises means for shifting and scaling the limited time interval under consideration into a new variable x in an interval −

1<

x<

1 whereby the signal epoch becomes S(x).

28. A device as defined in claim 27, wherein the input signal modeling means comprises:

means for modeling the input signal as a set of orthogonal polynomials Q_n(x).

29. A device as defined in claim 28, wherein the set of orthogonal polynomials Q_n(x) comprises:

a first initial polynomial Q₀(x) having a constant value; and

a second initial polynomial Q₁(x) having a constant slope.

30. A device as defined in claim 29, wherein the input signal modeling means comprises:

means for expressing the input signal as a sum of the polynomials Q_n(x);

$S<br><br>\left(x\right)=\underset{n=0}{\overset{P}{\sum <br><br>}}<br><br><br><br>C_n<br><br><br><br>Q_n<br><br>\left(x\right)$

where P represents a limited number of terms, and

$C_n=\frac{1}{K_n}<br><br>{\int <br><br>}_{-1}^{+1}<br><br>S<br><br>\left(x\right)<br><br><br><br>Q_n<br><br>\left(x\right)<br><br><br><br>f<br><br>\left(x\right)<br><br><br><br>d<br><br>x$

where f(x) is a function of x and K_n is a constant depending on the order n.

31. A device as defined in claim 30, wherein:

the input signal modeling means comprises means for modeling the input signal as a sum of a limited number of polynomials; and

said device further comprises means for eliminating edge effects constituted by imperfections having a strength depending on the limited number of polynomials.

32. A device as defined in claim 31, wherein:

the edge effects eliminating means comprises means for defining overlapping windows;

the means for modeling the unwanted signal components comprises means for modeling, in each window, the unwanted signal components with a number of polynomials of said set;

the unwanted signal components removing means comprises means for removing, in each window, the number of polynomials modeling the unwanted signal components from the set of polynomials to thereby produce in said window a filtered signal part; and

the edge effects eliminating means further comprises;

for each window, means for weighting the filtered signal part to suppress the filtered signal part at opposite ends of the window and emphasize the filtered signal part in the central portion of said window; and

means for summing the weighted filtered signal parts of the overlapping windows to form an output filtered signal generally free from edge effects.

33. A device as defined in claim 32, wherein the overlapping windows comprise 50% overlapping windows.

34. A device as defined in claim 32, wherein the filtered signal part weighting means comprises:

means for providing for each window an edge effect suppressing function; and

means for multiplying, in each window, the filtered signal part by the edge effect suppressing function of said window.

35. A method of filtering an EMG input signal contaminated by a disturbance signal, the filtering method comprising:

modeling the EMG input signal polynomials of higher orders; and

outputting the polynomials of higher orders as an estimate of the EMG input signal substantially free from the disturbance signal.

36. A method as defined in claim 35, wherein the disturbance signal comprises at least one of a cardiac signal, motion disturbance, and background noise.

37. A method as defined in claim 35, wherein modeling the EMG input signal as polynomials of higher orders comprises modeling said EMG input signal as orthogonal of higher orders.

38. A method as defined in claim 37, comprising selecting the orthogonal polynomials from the group consisting of:

Legendre polynomials;

Tchebyshev T-polynomials; and

Tchebyshev U-polynomials. as orthogonal polynomials of higher orders.

39. A method as defined in claim 35, further comprising weighting the polynomials modeling the EMG input signal by means of weighting coefficients.

40. A method of filtering as defined in claim 35, wherein the disturbance signal comprises at least one signal selected from the group consisting of:

ECG signals, movement induced disturbances and background noise.

41. A method of filtering an input signal containing wanted signal components and unwanted signal components, comprising:

modeling the input signal as a set of polynomials;

modeling the wanted signal components with a number of the polynomials of said set; and

outputting the polynomials modeling the wanted signal components as an estimate of the input signal substantially free from the unwanted signal components;

wherein modeling the input signal comprises;

considering an epoch S(t) of the signal in a limited time interval, said epoch S(t) having a time scale; and

normalizing the time scale of the epoch S(t).

42. A method as defined in claim 41, wherein normalizing the time scale of the epoch S(t) comprises:

shifting and scaling the limited time interval under consideration into a new variable x in an interval −

1<

x<

1 whereby the signal epoch becomes S(x).

43. A method as defined in claim 42, wherein modeling the input signal as a set of polynomials comprises modeling the input signal as a set of orthogonal polynomials Q_n(x).

44. A method as defined in claim 43, wherein the set of orthogonal polynomials Q_n(x) comprises:

a first initial polynomial Q₀(x) having a constant value; and

a second initial polynomial Q₁(x) having a constant slope.

45. A method as defined in claim 43, wherein modeling the input signal as a set of polynomials comprises:

expressing the input signal as a sum of the polynomials Q_n(x);

$S<br><br>\left(x\right)=\underset{n=0}{\overset{P}{\sum <br><br>}}<br><br><br><br>C_n<br><br><br><br>Q_n<br><br>\left(x\right)$

where P represents a limited number of terms, and

$C_n=\frac{1}{K_n}<br><br>{\int <br><br>}_{-1}^{+1}<br><br>S<br><br>\left(x\right)<br><br><br><br>Q_n<br><br>\left(x\right)<br><br><br><br>f<br><br>\left(x\right)<br><br><br><br>d<br><br>x$

where f(x) is a function of x and K_n is a constant depending on the order n.

46. A method as defined in claim 45, wherein modeling the wanted signal components with a number of the polynomials of said set comprises:

associating particular orders of the polynomials with the wanted signal components; and

modeling the wanted signal components as a sum of the polynomials of said particular orders, comprising weighting the polynomials of said particular orders by means of the coefficients C_n.

47. A method of filtering an input signal containing wanted signal components and unwanted signal components, comprising:

modeling the input signal as a set of polynomials;

modeling the wanted signal components with a number of the polynomials of said set; and

outputting the polynomials modeling the wanted signal components as an estimate of the input signal substantially free from the unwanted signal components;

wherein modeling the input signal as a set of polynomials comprises;

using higher order polynomials that mimic an oscillatory pattern of the input signal.

48. A method of filtering an input signal containing wanted signal components and unwanted signal components, comprising:

modeling the input signal as a set of polynomials;

modeling the wanted signal components with a number of the polynomials of said set; and

outputting the number of polynomials modeling the wanted signal components as an estimate of the input signal substantially free from the unwanted signal components;

wherein;

modeling the input signal as a set of polynomials comprises modeling the input signal as a sum of a limited number of polynomials; and

said method further comprises eliminating edge effects constituted by imperfections having a strength depending on the limited number of polynomials.

49. A method as defined in claim 48, wherein:

eliminating the edge effects comprises defining overlapping windows;

modeling the wanted signal components comprises modeling, in each window, the wanted signal components with a number of polynomials of said set;

outputting the number of polynomials modeling the wanted signal components comprises outputting, for each window, the number of polynomials modeling the wanted signal components to thereby produce in said window a filtered signal part; and

eliminating the edge effects further comprises;

in each window, weighting the filtered signal part to suppress the filtered signal part at opposite ends of the window and emphasize the filtered signal part in the central part of said window; and

summing the weighted filtered signal parts of the overlapping windows to form an output filtered signal generally free from edge effects.

50. A method as defined in claim 49, wherein defining overlapping windows comprises:

defining 50% overlapping windows.

51. A method as defined in claim 49, wherein weighting the filtered signal part in each window comprises:

providing for each window an edge effect suppressing function; and

in each window, multiplying the filtered signal part by the edge effect suppressing function of said window.

52. A method as defined in claim 51, wherein providing for each window an edge effect suppressing function comprises:

constructing an edge effect suppressing function in such a manner that;

a sum of the edge effect suppressing functions of the various overlapping windows is equal to unity; and

a value of the edge suppressing function at opposite ends of each window is equal to zero.

53. A method as defined in claim 51, comprising selecting the edge effect suppressing functions of the overlapping windows from the group consisting of:

a triangular function and a squared cosine function.

54. A device for filtering an EMG input signal contaminated by a disturbance signal, the device comprising:

means for modeling the EMG input signal polynomials of higher orders; and

means for outputting the polynomials of higher orders as an estimate of the EMG input signal substantially free from the disturbance signal.

55. A device for filtering an input signal containing wanted signal components and unwanted signal components, comprising:

means for modeling the input signal as a set of polynomials;

means for modeling the wanted signal components with a number of the polynomials of said set; and

means for outputting the polynomials modeling the wanted signal components as an estimate of the input signal substantially free from the unwanted signal components;

wherein the input signal modeling means comprises;

means for considering an epoch S(t) of the signal in a limited time interval, said epoch S(t) having a time scale; and

means for normalizing the time scale of the epoch S(t), wherein said time scale normalizing means comprises means for shifting and scaling the limited time interval under consideration into a new variable x in an interval −

1<

x<

1 whereby the signal epoch becomes S(x).

56. A device as defined in claim 55, wherein the input signal modeling means comprises:

means for modeling said input signal as a set of orthogonal polynomials Q_n(x).

57. A device as defined in claim 56, wherein the set of orthogonal polynomials Q_n(x) comprises:

a first initial polynomial Q₀(x) having a constant value; and

a second initial polynomial Q₁(x) having a constant slope.

58. A device as defined in claim 57, wherein the input signal modeling means comprises:

means for expressing the input signal as a sum of the polynomials Q_n(x);

$S<br><br>\left(x\right)=\underset{n=0}{\overset{P}{\sum <br><br>}}<br><br><br><br>C_n<br><br><br><br>Q_n<br><br>\left(x\right)$

where P represents a limited number of terms, and

$C_n=\frac{1}{K_n}<br><br>{\int <br><br>}_{-1}^{+1}<br><br>S<br><br>\left(x\right)<br><br><br><br>Q_n<br><br>\left(x\right)<br><br><br><br>f<br><br>\left(x\right)<br><br><br><br>d<br><br>x$

where f(x) is a function of x and K_n is a constant depending on the order n.

59. A device as defined in claim 58, wherein:

the input signal modeling means comprises means for modeling the input signal as a sum of a limited number of polynomials; and

said device further comprises means for eliminating edge effects constituted by imperfections having a strength depending on the limited number of polynomials.

60. A device as defined in claim 59, wherein:

the edge effects eliminating means comprises means for defining overlapping windows;

the means for modeling the wanted signal components comprises means for modeling, in each window, the wanted signal components with a number of the polynomials of said set;

the polynomials outputting means comprises means for outputting, for each window, the polynomials modeling the wanted signal components to thereby produce in said window a filtered signal part; and

the edge effects eliminating means further comprises;

for each window, means for weighting the filtered signal part to suppress the filtered signal part at opposite ends of the window and emphasize the filtered signal part in a central portion of said window; and

means for summing the weighted filtered signal parts of the overlapping windows to form an output filtered signal generally free from edge effects.

61. A device as defined in claim 60, wherein the overlapping windows comprise 50% overlapping windows.

62. A device as defined in claim 60, wherein the filtered signal part weighting means comprises:

means for providing for each window an edge effect suppressing function; and

means for multiplying, in each window, the filtered signal part by the edge effect suppressing function of said window.

63. A method of filtering an input signal containing wanted signal components and unwanted signal components, comprising:

modeling the input signal as a set of polynomials;

determining, for each polynomial, a weighting coefficient indicative of signal strength; and

summing the weighting coefficients to provide an estimate of the strength of the wanted signal components;

wherein summing the weighting coefficients comprises;

summing the weighting coefficients on a square law basis with polynomial order weighting to give an estimate of a power of the wanted signal components.

64. A method as defined in claim 63, wherein determining, for each polynomial, a weighting coefficient indicative of signal strength comprises:

modeling the strength of the wanted signal components through the weighting coefficients.

65. A method of filtering an input signal containing wanted signal components and unwanted signal components, comprising:

modeling the input signal as a set of polynomials;

determining, for each polynomial a weighting coefficient indicative of signal strength; and

summing the weighting coefficients to provide an estimate of the strength of the wanted signal components;

wherein summing the weighting coefficients comprises;

calculating a sum of the weighting coefficients on a square law basis with a weighting proportional to the number of oscillations for the order of the polynomial, normalized with respect to the sum of the weighting coefficients on a square law basis with polynomial order weighting, in order to obtain a dominating periodicity of the wanted signal components.

66. A method of filtering an input signal containing wanted signal components and unwanted signal components, comprising:

modeling the input signal as a set of polynomials;

determining, for each polynomial, a weighting coefficient indicative of signal strength; and

summing the weighting coefficients to provide an estimate of the strength of the wanted signal components;

wherein modeling the input signal as a set of polynomials comprises;

considering an epoch S(t) of the input signal in a limited time interval, said epoch S(t) having a time scale; and

normalizing the time scale of the epoch S(t).

67. A method as defined in claim 66, wherein normalizing the time scale of the epoch S(t) comprises:

shifting and scaling the limited time interval under consideration into a new variable x in an interval −

1<

x<

1 whereby the signal epoch becomes S(x).

68. A method as defined in claim 67, wherein modeling the input signal as a set of polynomials comprises modeling the signal as a set of orthogonal polynomials Q_n(x).

69. A method as defined in claim 68, comprising selecting the orthogonal polynomials from the group consisting of:

Legendre polynomials;

Tchebyshev T-polynomials; and

Tchebyshev U-polynomials.

70. A method as defined in claim 68, wherein modeling the input signal as a set of polynomials comprises:

expressing the input signal as a sum of the polynomials Q_n(x);

$S<br><br>\left(x\right)<br><br>\underset{n=0}{\overset{P}{\sum <br><br>}}<br><br>C_n<br><br><br><br>Q_n<br><br>\left(x\right)$

where P represents a limited number of terms, and

$C_n=\frac{1}{K_n}<br><br>{\int <br><br>}_{-1}^{+1}<br><br>S<br><br>\left(x\right)<br><br><br><br>Q_n<br><br>\left(x\right)<br><br><br><br>f<br><br>\left(x\right)<br><br><br><br>d<br><br>x$

where f(x) is a function of x and K_n is a constant depending on the order n,

wherein the terms C_n constitute said weighting factors.

71. A device for filtering an input signal containing wanted signal components and unwanted signal components, comprising:

means for modeling the input signal as a set of polynomials;

means for determining, for each polynomial, a weighting factor indicative of signal strength; and

means for summing the weighting coefficients to provide an estimate of the strength of the wanted signal components;

wherein the weighting coefficients summing means comprises;

means for summing the weighting coefficients on a square law basis with polynomial order weighting to give an estimate of a power of the EMG input signal substantially free from the disturbance signal.

72. A device as defined in claim 71, wherein the determining means comprises:

means for modeling the strength of the wanted signal components through the weighting coefficients.

73. A device for filtering an input signal containing wanted signal components and unwanted signal components, comprising:

means for modeling the input signal as a set of polynomials;

means for determining, for each polynomial, a weighting factor indicative of signal strength; and

means for summing the weighting coefficients to provide an estimate of the strength of the wanted signal components;

wherein the means for summing the weighting coefficients comprises;

means for calculating a sum of the weighting coefficients on a square law basis with a weighting proportional to the number of oscillations for the order of the polynomial, normalized with respect to the sum of the weighting coefficients on a square law basis with polynomial order weighting, in order to obtain a dominating periodicity of the input signal.

74. A device for filtering an input signal containing wanted signal components and unwanted signal components, comprising:

means for modeling the input signal as a set of polynomials;

means for determining, for each polynomial, a weighting factor indicative of signal strength; and

means for summing the weighting coefficients to provide an estimate of the strength of the wanted signal components;

wherein the input signal modeling means comprises;

means for considering an epoch S(t) of the input signal in a limited time interval, said epoch S(t) having a time scale; and

means for normalizing the time scale of the epoch S(t).

75. A device as defined in claim 74, wherein the time scale normalizing means comprises:

means for shifting and scaling the limited time interval under consideration into a new variable x in an interval −

1<

x<

1 whereby the signal epoch becomes S(x).

76. A device as defined in claim 75, wherein the input signal modeling means comprises means for modeling the signal as a set of orthogonal polynomials Q_n(x).

77. A device as defined in claim 76, wherein the input signal modeling means comprises:

means for expressing the input signal as a sum of the polynomials Q_n(x);

$S<br><br>\left(x\right)<br><br>\underset{n=0}{\overset{P}{\sum <br><br>}}<br><br>C_n<br><br><br><br>Q_n<br><br>\left(x\right)$

where P represents a limited number of terms, and

$C_n=\frac{1}{K_n}<br><br>{\int <br><br>}_{-1}^{+1}<br><br>S<br><br>\left(x\right)<br><br><br><br>Q_n<br><br>\left(x\right)<br><br><br><br>f<br><br>\left(x\right)<br><br><br><br>d<br><br>x$

where f(x) is a function of x and K_n is a constant depending on the order n,

wherein the terms C_n constitute said weighting factors.