Method of and apparatus for indicating characteristics of undulating data

• US 4,495,585 A
• Filed: 07/08/1981
• Issued: 01/22/1985
• Est. Priority Date: 07/08/1981
• Status: Expired due to Fees

• Current Assignee: William H. Buckley
• Original Assignee: William H. Buckley
• Inventors: Buckley, William H.
• Primary Examiner(s): Wise, Edward J.
• Application Number:
  US06/281,302
• Time in Patent Office: 1,294 Days
• Field of Search: 364/487, 364/550, 364/514, 364/522, 340/753-755, 340/784, 340/706, 340/722, 382/18, 382/29, 367/28-30, 367/68
• US Class Current: 702/180
• CPC Class Codes: G01R 23/16 Spectrum analysis; Fourier analysis

Abstract

Characteristics of undulating data having variations with oppositely directed peaks are displayed on a display having x and y axes. The consecutive, oppositely directed peak values of each variation are determined. Each variation is assigned to a coordinate position on the display so that the coordinate position in the x and y directions is respectively determined by the initial and final peak values of each variation. The variations having like initial and final peak values are accumulated so an indication of the accumulated variations is displayed on the coordinate positions of the display.

Claims

1. A method of indicating characteristics of undulating data having variations with oppositely directed peak values, the characteristics being indicated on a display having first and second mutually orthogonal coordinate directions, comprising the steps of determining the oppositely directed consecutive peak values of each variation, assigning each variation to a coordinate position on the display, the coordinate position in the first and second directions being respectively determined by the initial and final peak values of the variation, accumulating the variations having like initial and final peak values so an indication of the accumulated variations is displayed on the coordinate positions of the display, the display having discrete values in the first and second directions associated with different initial and final peak values, whereby a series of bins is formed in the first and second directions, the coordinate positions in the first and second directions being substantially determined by assigning each variation to an individual bin, the variations being accumulated by summing the number of variations assigned to each bin, each bin having a dead band associated with it, and in response to first and second adjacent like directed variations being associated with the same bin except for one of the values of the second variation differing from a corresponding value of the first variation by an amount less than the dead band assigning the second variation to the same bin as the first variation.

3. The method of claim 1 or 2 wherein distances along the coordinate directions are proportional to peak values of the variations, the variations being assigned in proportion to the peak values.

4. The method of claim 1 or 2 wherein the undulating data have main variations with maximum oppositely directed consecutive peak values on opposite polarity sides of a reference value and subordinate variations including a false peak value and intermediate oppositely directed consecutive peak values between the maximum consecutive peak values, the false peak having a value equal to the value of an intermediate peak and occurring between the two maximum peaks, each main variation between the maximum consecutive peak values being detected and assigned to a coordinate position as a variation in accordance with the maximum consecutive peak values, each subordinate variation being detected and assigned as a variation to coordinate positions in accordance with one of the false peak values and an intermediate peak value or in accordance with a pair of adjacent intermediate peak values.

5. The method of claim 1 or 2 wherein distances along the coordinate directions are proportional to a total statistical function of the displayed data, each variation being assigned in proportion to the fraction that the variation contributes to the total statistical function.

6. The method of claim 5 wherein the statistical function is standard deviation.

15. The method of claim 1, 2, 7, 9, 11, 12, 13 or 14 wherein the oppositely detected peak values are detected by reading the peak values from a chart containing the data with a digitizing tablet that derives digital signals indicative of the values of the read peak values, supplying the derived digital signals to a digital processor that assigns the variations to the coordinate positions and derives the signals that are displayed.

16. The method of claim 1, 2, 7, 9, 11, 12, 13 or 14 wherein the oppositely detected peak values are detected by transducing a stored indication of the data into an analog signal, converting the stored signal into a first digital signal indicative of the data, supplying the first digital signal to a digital signal processor that derives second digital signals indicative of the values of the peak values and which responds to the peak value signals to assign the variations to the coordinate positions and derives signals that are displayed.

17. The method of claim 1, 2, 7, 9, 11, 12, 13 or 14 wherein the oppositely detected peak values are detected by real time converting the data into a first digital signal indicative of the data, supplying the first digital signal to a digital signal processor that derives second digital signals indicative of the values of the peak values and which responds to the peak value signals to assign the variations to the coordinate positions and derives signals that are displayed.

2. A method of indicating characteristics of undulating data having variations with oppositely directed peak values, the characteristics being indicated on a display having first and second mutually orthogonal coordinate directions, comprising the steps of determining the oppositely directed consecutive peak values of each variation, assigning each variation to a coordinate position on the display, the coordinate position in the first and second directions being respectively determined by the initial and final peak values of the variation, and accumulating the variations having like initial and final peak values so an indication of the accumulated variations is displayed on the coordinate positions of the display, the display having discrete values in the first and second directions associated with different initial and final peak values, whereby a series of bins is formed in the first and second directions, the coordinate positions in the first and second directions being substantially determined by assigning each variation to an individual bin, the variations being accumulated by summing the number of variations assigned to each bin, the display including null and reference level diagonals at 45°

to each of the coordinate directions and at right angles to each other, whereby each variation is displaced from the null diagonal by an amount associated with the amplitude of the variation and is displaced from the reference level diagonal by an amount associated with the mean value of the variation, accumulating the values in the bins displaced a like amount from the null diagonal for each bin distance from the null diagonal, accumulating the values in the bins displaced a like amount from the reference level diagonal for each bin distance from the reference level diagonal, and displaying indications of the accumulated diagonal values.

10. The method of claim 2, 7 or 9 further including deriving an indication of the accumulated values in the bins displaced by bins numbered k and (k+1) from the null diagonal, where k equals every odd integer from 1 to N/2, and N equals the number of bins in the display along the reference level diagonal.

7. A method of indicating characteristics of undulating data having variations with oppositely directed peak values, the characteristics being indicated on a display having first and second mutually orthogonal coordinate directions, comprising the steps of determining the oppositely directed consecutive peak values of each variation, assigning each variation to a coordinate position on the display, the coordinate position in the first and second directions being respectively determined by the initial and final peak values of the variation, and accumulating the variations having like initial and final peak values so an indication of the accumulated variations is displayed on the coordinate positions of the display, the display having discrete values in the first and second directions associated with different initial and final peak values, whereby a series of bins is formed in the first and second directions, the coordinate positions in the first and second directions being substantially determined by assigning each variation to an individual bin, the variations being accumulated by summing the number of variations assigned to each bin, the display including null and reference level diagonals at 45°

to each of the coordinate directions and at right angles to each other, whereby each variation is displaced from the null diagonal by an amount associated with the amplitude of the variation and is displaced from the reference level diagonal by an amount associated with the mean value of the variation, accumulating the values in the bins displaced a like amount from the reference level diagonal for each bin distance from the reference level diagonal, and displaying indications of the accumulated diagonal values.

8. The method of claim 7 wherein the undulating data have main variations with maximum oppositely directed consecutive peak values on opposite polarity sides of a reference value and subordinate variations including a false peak value and intermediate oppositely directed consecutive peak values between the maximum consecutive peak values, the false peak having a value equal to the value of an intermediate peak and occurring between the two maximum peaks, each main variation between the maximum consecutive peak values being detected and assigned to a coordinate position as a variation in accordance with the maximum consecutive peak values, each subordinate variation being detected and assigned as a variation to coordinate positions in accordance with one of the false peak values and an intermediate peak value or in accordance with a pair of adjacent intermediate peak values.

9. A method of indicating characteristics of undulating data having variations with oppositely directed peak values, the characteristics being indicated on a display having first and second mutually orthogonal coordinate directions, comprising the steps of determining the oppositely directed consecutive peak values of each variation, assigning each variation to a coordinate position on the display, the coordinate position in the first and second directions being respectively determined by the initial and final peak values of the variation, and accumulating the variations having like initial and final peak values so an indication of the accumulated variations is displayed on the coordinate positions of the display, the display having discrete values in the first and second directions associated with different initial and final peak values, whereby a series of bins is formed in the first and second directions, the coordinate positions in the first and second directions being substantially determined by assigning each variation to an individual bin, the variations being accumulated by summing the number of variations assigned to each bin, the display including null and reference level diagonals at 45°

to each of the coordinate directions and at right angles to each other, whereby each variation is displaced from the null diagonal by an amount associated with the amplitude of the variation and is displaced from the reference level diagonal by an amount associated with the mean value of the variation, accumulating the values in the bins displaced a like amount from the null diagonal for each bin distance from the null diagonal, and displaying indications of the accumulated diagonal values.

11. A method of indicating characteristics of undulating data having variations with oppositely directed peak values, the characteristics being indicated on a display having first and second mutually orthogonal coordinate directions, comprising the steps of determining the oppositely directed consecutive peak values of each variation, assigning each variation to a coordinate position on the display, the coordinate position in the first and second directions being respectively determined by the initial and final peak values of the variation, and accumulating the variations having like initial and final peak values so an indication of the accumulated variations is displayed on the coordinate positions of the display, the display including null and reference level diagonals at 45°

to each of the coordinate directions and at right angles to each other, whereby each variation is displaced from the null diagonal by an amount associated with the amplitude of the variation and is displaced from the reference level diagonal by an amount associated with the mean value of the variation, summing the accumulated variations at positions displaced a like amount from the null diagonal for each position displaced from the null diagonal, and summing the accumulated variations at positions displaced a like amount from the reference level diagonal for each position displaced from the reference level diagonal.

12. A method of indicating characteristics of undulating data having variations with oppositely directed peak values, the characteristics being indicated on a display having first and second mutually orthogonal coordinate directions, comprising the steps of determining the oppositely directed consecutive peak values of each variation, assigning each variation to a coordinate position on the display, the coordinate position in the first and second directions being respectively determined by the initial and final peak values of the variation, and accumulating the variations having like initial and final peak values so an indication of the accumulated variations is displayed on the coordinate positions of the display, the display including null and reference level diagonals at 45°

to each of the coordinate directions and at right angles to each other, whereby each variation is displaced from the null diagonal by an amount associated with the amplitude of the variation and is displaced from the reference level diagonal by an amount associated with the mean value of the variation, and summing the accumulated variations at positions displaced a like amount from the reference level diagonal for each position displaced from the reference level diagonal.

13. A method of indicating characteristics of undulating data having variations with oppositely directed peak values, the characteristics being indicated on a display having first and second mutually orthogonal coordinate directions, comprising the steps of determining the oppositely directed consecutive peak values of each variation, assigning each variation to a coordinate position on the display, the coordinate position in the first and second directions being respectively determined by the initial and final peak values of the variation, and accumulating the variations having like initial and final peak values so an indication of the accumulated variations is displayed on the coordinate positions of the display, the display including null and reference level diagonals at 45°

to each of the coordinate directions and at right angles to each other, whereby each variation is displaced from the null diagonal by an amount associated with the amplitude of the variation and is displaced from the reference level diagonal by an amount associated with the mean value of the variation, and summing the accumulated variations at positions displaced a like amount from the null diagonal for each position displaced from the null diagonal.

14. A method of indicating characteristics of undulating data having variations with oppositely directed peak values, the characteristics being indicated on a display having first and second mutually orthogonal coordinate directions, comprising the steps of determining the oppositely directed consecutive peak values of each variation, assigning each variation to a coordinate position on the display, the coordinate position in the first and second directions being respectively determined by the initial and final peak values of the variation, and accumulating the variations having like initial and final peak values so an indication of the accumulated variations is displayed on the coordinate positions of the display, the display including null and reference level diagonals at 45°

to each of the coordinate directions and at right angles to each other, whereby each variation is displaced from the null diagonal by an amount associated with the amplitude of the variation and is displaced from the reference level diagonal by an amount associated with the mean value of the variation, separately summing the accumulated variations at like coordinate positions in one coordinate direction on each side of the null diagonal, and indicating the summed accumulated variations.

18. A method of indicating characteristics of undulating data having variations with oppositely directed peak values, the characteristics being indicated on a display having first and second mutually orthogonal coordinate directions, comprising the steps of determining the oppositely directed consecutive peak values of each variation, assigning each variation to a coordinate position on the display, the coordinate position in the first and second directions being respectively determined by the initial and final peak values of the variation, and accumulating the variations having like initial and final peak values so an indication of the accumulated variations is displayed on the coordinate positions of the display, distances along the coordinate directions being proportional to a total statistical function of the displayed data, each variation being assigned in proportion to the fraction that the variation contributes to the total statistical function.

19. The method of claim 18 wherein the undulating data have main variations with maximum oppositely directed consecutive peak values on opposite polarity sides of a reference value and subordinate variations including a false peak value and intermediate oppositely directed consecutive peak values between the maximum consecutive peak values, the false peak having a value equal to the value of an intermediate peak and occurring between the two maximum peaks, each main variation between the maximum consecutive peak values being detected and assigned to a coordinate position as a variation in accordance with the maximum consecutive peak values, each subordinate variation being detected and assigned as a variation to coordinate positions in accordance with one of the false peak values and an intermediate peak value or in accordance with a pair of adjacent intermediate peak values.

20. The method of claim 18 wherein the display has discrete values in the first and second directions associated with different initial and final peak values, whereby a series of bins is formed in the first and second directions, the coordinate positions in the first and second directions being substantially determined by assigning each variation to an individual bin, the variations being accumulated by summing the number of variations assigned to each bin.

21. The method of claim 18 or 20 wherein the statistical function is standard deviation.

22. A method of indicating characteristics of undulating data having variations with oppositely directed peak values, the characteristics being indicated on a display having first and second mutually orthogonal coordinate directions, comprising the steps of determining the oppositely directed consecutive peak values of each variation, assigning each variation to a coordinate position on the display, the coordinate position in the first and second directions being respectively determined by the initial and final peak values of the variation, and accumulating the variations having like initial and final peak values so an indication of the accumulated variations is displayed on the coordinate positions of the display, the oppositely detected peak values being detected by reading the peak values from a chart containing the data with a digitizing tablet that derives digital signals indicative of the values of the read peak values, and supplying the derived digital signals to a digital processor that assigns the variations to the coordinate positions and derives the signals that are displayed.

23. The method of claim 22 wherein the display has discrete values in the first and second directions associated with different initial and final peak values, whereby a series of bins is formed in the first and second directions, the coordinate positions in the first and second directions being substantially determined by assigning each variation to an individual bin, the variations being accumulated by summing the number of variations assigned to each bin.

24. A method of indicating characteristics of undulating data having variations with oppositely directed peak values, the characteristics being indicated on a display having first and second mutually orthogonal coordinate directions, comprising the steps of determining the oppositely directed consecutive peak values of each variation, assigning each variation to a coordinate position on the display, the coordinate position in the first and second directions being respectively determined by the initial and final peak values of the variation, and accumulating the variations having like initial and final peak values so an indication of the accumulated variations is displayed on the coordinate positions of the display, the oppositely detected peak values being detected by transducing a stored indication of the data into an analog signal, converting the stored signal into a first digital signal indicative of the data, and supplying the first digital signal to a digital signal processor that derives second digital signals indicative of the values of the peak values and which responds to the peak value signals to assign the variations to the coordinate positions and derives signals that are displayed.

25. The method of claim 24 wherein the display has discrete values in the first and second directions associated with different initial and final peak values, whereby a series of bins is formed in the first and second directions, the coordinate positions in the first and second directions being substantially determined by assigning each variation to an individual bin, the variations being accumulated by summing the number of variations assigned to each bin.

26. A method of indicating characteristics of undulating data having variations with oppositely directed peak values, the characteristics being indicated on a display having first and second mutually orthogonal coordinate directions, comprising the steps of determining the oppositely directed consecutive peak values of each variation, assigning each variation to a coordinate position on the display, the coordinate position in the first and second directions being respectively determined by the initial and final peak values of the variation, and accumulating the variations having like initial and final peak values so an indication of the accumulated variations is displayed on the coordinate positions of the display, the oppositely detected peak values being detected by real time converting the data into a first digital signal indicative of the data, and supplying the first digital signal to a digital signal processor that derives second digital signals indicative of the values of the peak values and which responds to the peak value signals to assign the variations to the coordinate positions and derives signals that are displayed.

27. The method of claim 26 wherein the display has discrete values in the first and second directions associated with different inital and final peak values, whereby a series of bins is formed in the first and second directions, the coordinate positions in the first and second directions being substantially determined by assigning each variation to an individual bin, the variations being accumulated by summing the number of variations assigned to each bin.

28. Apparatus for indicating characteristics of undulating data having variations with detected oppositely directed consecutive peak values, comprising a display having first and second mutually orthogonal coordinate directions, means responsive to the detected peak values for assigning each variation a coordinate position on the display, the coordinate position in the first and second directions being respectively determined by the initial and final peak values of the variation, means for accumulating the variations having like initial and final peak values so an indication of the accumulated variations is displayed on the coordinate positions of the display, the display having discrete values in the first and second directions associated with different initial and final peak values, whereby a series of bins is formed in the first and second directions, the assigning means including means for substantially assigning each variation to an individual bin, the means for accumulating including means for accumulating the number of variations assigned to each bin, each bin having a dead band associated with it, and means responsive to first and second adjacent variations being associated with the same bin except for one of the values of the second variation differing from a corresponding value of the first variation by an amount less than the dead band for assigning the second variation to the same bin as the first variation.

30. The apparatus of claim 28, or 29 wherein distances along the coordinate directions are proportional to peak values of the variations, the assigning means including means for assigning the variations in proportion to the peak values.

31. The apparatus of claim 30 wherein the undulating data have main variations with maximum oppositely directed consecutive peak values on opposite polarity sides of a reference value and subordinate variations including a false peak value and intermediate oppositely directed consecutive peak values between the maximum consecutive peak values, the false peak having a value equal to the value of an intermediate peak and occurring between the two maximum peaks, each main variation between the maximum consecutive peak values being detected and assigned to a coordinate position as a variation in accordance with the maximum consecutive peak values, each subordinate variation being detected and assigned as a variation to coordinate positions in accordance with one of the false peak values and an intermediate peak value or in accordance with a pair of adjacent intermediate peak values.

32. The apparatus of claim 28 or 29 wherein each bin has a dead band associated with it, and means responsive to first and second adjacent variations being associated with the same bin except for one of the values of the second variation differing from a corresponding value of the first variation by an amount less than the dead band for assigning the second variation to the same bin as the first variation, means for detecting a total statistical function of the displayed data, means responsive to the detected total statistical function for establishing proportionality values for displayed variations along the coordinate directions, the means for assigning including means for assigning each variation in proportion to the fraction that the variation contributes to the total statistical function.

33. The apparatus of claim 32 wherein the undulating data have main variations with maximum oppositely directed consecutive peak values on opposite polarity sides of a reference value and subordinate variations including a false peak value and intermediate oppositely directed consecutive peak values between the maximum consecutive peak values, the false peak having a value equal to the value of an intermediate peak and occurring between the two maximum peaks, each main variation between the maximum consecutive peak values being detected and assigned to a coordinate position as a variation in accordance with the maximum consecutive peak values, each subordinate variation being detected and assigned as a variation to coordinate positions in accordance with one of the false peak values and an intermediate peak value or in accordance with a pair of adjacent intermediate peak values.

34. The apparatus of claim 32 wherein the statistical function is standard deviation.

35. The apparatus of claim 28 or 29 wherein each bin has a dead band associated with it, and means responsive to first and second adjacent variations being associated with the same bin except for one of the values of the second variation differing from a corresponding value of the first variation by an amount less than the dead band for assigning the second variation to the same bin as the first variation, the display having discrete values in the first and second directions associated with different initial and final peak values, whereby a series of bins is formed in the first and second directions, the assigning means including means for substantially assigning each variation to an individual bin, the means for accumulating including means for accumulating the number of variations assigned to each bin, the undulating data having main variations with maximum oppositely directed consecutive peak values on opposite polarity sides of a reference value and subordinate variations including a false peak value and intermediate oppositely directed consecutive peak values between the maimum consecutive peak values, the false peak having a value equal to the value of an intermediate peak and occuring between the two maximum peaks, each main variation between the maximum consecutive peak values being detected and assigned to a coordinate position as a variation in accordance with the maximum consecutive peak values, each subordinate variation being detected and assigned as a variation to coordinate positions in accordance with one of the false peak values and an intermediate peak value or in accordance with a pair of adjacent intermediate peak values.

43. The apparatus of claim 28, 29, 36, 37, 39, 40, 41 or 42 further including means responsive to the undulating data for deriving a signal indicative of the detected peak value.

44. The appparatus of claim 43 wherein the means for deriving the peak value indicating signal includes a digital to analog converter responsive to the undulating data for deriving a digital signal indicative of the undulations, and digital processing means responsive to the digital signal indicative of the undulations.

29. Apparatus for indicating characteristics of undulating data having variations with detected oppositely directed consecutive peak values, comprising a dislay having first and second mutually orthogonal coordinate directions, means responsive to the detected peak values for assigning each variation a coordinate position on the display, the coordinate position in the first and second directions being respectively determined by the inital and final peak values of the variation, means for accumulating the variations having like initial and final peak values so an indication of the accumulated variations is displayed on the coordinate positions of the display, the display having discrete values in the first and second directions associated with different initial and final peak values, whereby a series of bins is formed in the first and second directions, the assigning means including means for substantially assigning each variation to an individual bin, the means for accumulating including means for accumulating the number of variations assigned to each bin, the display including null and reference level diagonals at 45°

to each of the coordinate directions and at right angles to each other whereby each variation is displaced from the null diagonal by an amount associated with the amplitude of the variation and is displaced with the mean value of the variation, means for accumulating the values in the bins displaced a like amount from the null diagonal for each bin distance from the null diagonal, means for accumulating the values in the bins displaced a like amount from the reference level diagonal for each bin distance from the reference level diagonal, and means for displaying indications of the accumulated diagonal values.

38. The apparatus of claim 29, 36 or 37 further including means for deriving an indication of the accumulated values in the bins displaced by k and (k+1) from the null diagonal, where k equals every odd integer from 1 to N/2, and N equals the number of bins in the display along the referenced level diagonal.

36. Apparatus for indicating characteristics of undulating data having variations with detected oppositely directed consecutive peak values, comprising a display having first and second mutually orthogonal coordinate directions, means responsive to the detected peak values for assigning each variation a coordinate position on the display, the coordinate position in the first and second directions being respectively determined by the initial and final peak values of the variation, means for accumulating the variations having like initial and final peak values so an indication of the accumulated variations is displayed on the coordinate positions of the display, the display having discrete values in the first and second directions associated with different initial and final peak values, whereby a series of bins is formed in the first and second directions, the assigning means including means for substantially assigning each variation to an individual bin, the means for accumulating including means for accumulating the number of variations assigned to each bin, the display including null and reference level diagonals at 45°

to each of the coordinate directions and at right angles to each other whereby each variation is displaced from the null diagonal by an amount associated with the amplitude of the variation and is displaced from the reference level diagonal by an amount associated with the mean value of the variation, means for accumulating the values in the bins displaced a like amount from the reference level diagonal for each bin distance from the reference level diagonal, and means for displaying indications of the accumulated diagonal values.

37. Apparatus for indicating characteristics of undulating data having variations with detected oppositely directed consecutive peak values, comprising a display having first and second mutually orthogonal coordinate directions, means responsive to the detected peak values for assigning each variation a coordinate position on the display, the coordinate position in the first and second directions being respectively determined by the initial and final peak values of the variation, and means for accumulating the variations having like initial and final peak values so an indication of the accumulated variations is displayed on the coordinate positions of the display, the display having discrete values in the first and second directions associated with different initial and final peak values, whereby a series of bins is formed in the first and second directions, the assigning means including means for substantially assigning each variation to an individual bin, the means for accumulating including means for accumulating the number of variations assigned to each bin, the display including null and reference level diagonals at 45°

to each of the coordinate directions and at right angles to each other whereby each variation is displaced from the null diagonal by an amount associated with the amplitude of the variation and is displaced from the reference level diagonal by an amount associated with the mean value of the variation, means for accumulating the values in the bins displaced a like amount from the null diagonal for each bin distance from the null diagonal, and means for displaying indications of the accumulated diagonal values.

39. Apparatus for indicating characteristics of undulating data having variations with detected oppositely directed consecutive peak values, comprising a display having first and second mutually orthogonal coordinate directions, means responsive to the detected peak values for assigning each variation a coordinate position on the display, the coordinate position in the first and second directions being respectively determined by the initial and final peak values of the variation, means for accumulating the variations having like initial and final peak values so an indication of the accumulated variations is displayed on the coordinate positions of the display, the display including null and reference level diagonals at 45°

to each of the coordinate directions and at right angles to each other whereby each variation is displaced from the null diagonal by an amount associated with the amplitude of the variation and is displaced from the reference level diagonal by an amount associated with the mean value of the variation, means for summing the accumulated variations at positions displaced a like amount from the null diagonal and for each position displaced from the null diagonal and for summing the accumulated variations at positions displaced a like amount from the reference level diagonal for each position displaced from the reference level diagonal.

40. Apparatus for indicating characteristics of undulating data having variations with detected oppositely directed consecutive peak values, comprising a display having first and second mutually orthogonal coordinate directions, means responsive to the detected peak values for assigning each variation a coordinate position on the display, the coordinate position in the first and second directions being respectively determined by the initial and final peak values of the variation, means for accumulating the variations having like initial and final peak values so an indication of the accumulated variations is displayed on the coordinate positions of the display, the display including null and reference level diagonals at 45°

to each of the coordinate directions and at right angles to each other whereby each variation is displaced from the null diagonal by an amount associated with the amplitude of the variation and is displaced from the reference level diagonal by an amount associated with the means value of the variation, means for summing the accumulated variations at positions displaced a like amount from the reference level diagonal for each position displaced from the reference level diagonal, and means for indicating the summed accumulated variations.

41. Apparatus for indicating characteristics of undulating data having variations with detected oppositely directed consecutive peak values, comprising a display having first and second mutually orthogonal coordinate directions, means responsive to the detected peak values for assigning each variation a coordinate position on the display, the coordinate position in the first and second directions being respectively determined by the initial and final peak values of the variation, means for accumulating the variations having like initial and final peak values so an indication of the accumulated variations is displayed on the coordinate positions of the display, the display including null and reference level diagonals at 45°

to each of the coordinate directions and at right angles to each other whereby each variation is displaced from the null diagonal by an amount associated with the amplitude of the variation and is displaced from the reference level diagonal by an amount associated with the mean value of the variation, means for summing the accumulated variations at positions displaced a like amount from the null diagonal for each position displaced from the null diagonal, and means for indicating the summed accumulated variations.

42. Apparatus for indicating characteristics of undulating data having variations with detected oppositely directed consecutive peak values, comprising a display having first and second mutually orthogonal coordinate directions, means responsive to the detected peak values for assigning each variation a coordinate position on the display, the coordinate position in the first and second directions being respectively determined by the initial and final peak values of the variation, means for accumulating the variations having like initial and final peak values so an indication of the accumulated variations is displayed on the coordinate positions of the display, the display including null and reference level at diagonal at 45°

to each of the coordinate directions and at right angles to each other whereby each variation is displaced from the null diagonal by an amount associated with the amplitude of the variation and is displaced from the reference level diagonal by an amount associated with the mean value of the variation, means for separately summing the accumulated variations at like coordinate positions in one coordinate direction of each side of the null diagonal, and means for indicating the summed accumulated variations.

45. Apparatus for indicating characteristics of undulating data having variations with detected oppositely directed consecutive peak values comprising a display having first and second mutually orthogonal coordinate directions, means responsive to the detected peak values for assigning each variation a coordinate position on the display, the coordinate position in the first and second directions being respectively determined by the initial and final peak values of the variation, means for accumulating the variations having like initial and final peak values so an indication of the accumulated variations is displayed on the coordinate positions of the display, means for detecting a total statistical function of the displayed data, means responsive to the detected total statistical function for establishing proportionality values for displayed variations along the coordinate directions, the means for assigning including means for assigning each variation in proportion to the fraction that the variation contributes to the total statistical function.

46. The apparatus of claim 45 wherein the display has discrete values in the first and second directions associated with different initial and final peak values, whereby a series of bins is formed in the first and second directions, the assigning means including means for substantially assigning each variation to an individual bin, the means for accumulating including means for accumulating the number of variations assigned to each bin.

47. The apparatus of claim 46 wherein the undulating data have main variations with maximum oppositely directed consecutive peak values on opposite polarity sides of a reference value and subordinate variations including a false peak value and intermediate oppositely directed consecutive peak values between the maximum consecutive peak values, the false peak having a value equal to the value of an intermediate peak and occurring between the two maximum peaks, each main variation between the maximum consecutive peak values being detected and assigned to a coordinate position as a variation in accordance with the maximum consecutive peak values, each subordinate variation being detected and assigned as a variation to coordinate positions in accordance with one of the false peak values and an intermediate peak value or in accordance with a pair of adjacent intermediate peak values.

48. The apparatus of claim 46 wherein the statistical function is standard deviation.

49. The apparatus of claim 45 wherein the undulating data have main variations with maximum oppositely directed consecutive peak values on opposite polarity side of a reference value and subordinate variations including a false peak value and intermediate oppositely directed consecutive peak values between the maximum consecutive peak values, the false peak having a value equal to the value of an intermediate peak and occurring between the two maximum peaks, each main variation between the maximum consecutive peak values being detected and assigned to a coordinate position as a variation in accordance with the maximum consecutive peak values, each subordinate variation being detected and assigned as a variation to coordinate positions in accordance with one of the false peak values and an intermediate peak value or in accordance with a pair of adjacent intermediate peak values.

50. The apparatus of claim 45 wherein the statistical function is standard deviation.

51. Apparatus for indicating characteristics of undulating data having variations with detected oppositely directed consecutive peak values, comprising a display having first and second mutually orthogonal coordinate directions, means responsive to the detected peak values for assigning each variation a coordinate position on the display, the coordinate position in the first and second directions being respectively determined by the initial and final peak values of the variation, means for accumulating the variations having like initial and final peak values so an indication of the accumulated variations is displayed on the coordinate positions of the display, the undulating data having main variations with maximum oppositely directed consecutive peak values on opposite polarity sides of a reference value and subordinate variations including a false peak value and intermediate oppositely directed consecutive peak values between the maximum consective peak values, the false peak having a value equal to the value of an intermediate peak and occurring between the two maximum peaks, each main variation between the maximum consecutive peak values being detected and assigned to a coordinate position as a variation in accordance with the maximum consecutive peak values, each subordinate variation being detected and assigned as a variation to coordinate positions in accordance with one of the false peak values and an intermediate peak value or in accordance with a pair of adjacent intermediate peak values.