Fast find fundamental method

• US 6,766,288 B1
• Filed: 10/29/1999
• Issued: 07/20/2004
• Est. Priority Date: 10/29/1998
• Status: Expired due to Term

• Current Assignee: Digital Harmonic LLC
• Original Assignee: Paul Reed Smith Guitars, Limited Partnership
• Inventors: Smith, Jack W.
• Primary Examiner(s): Dorvil, Richemond
• Assistant Examiner(s): Armstrong, Angela
• Application Number:
  US09/430,295
• Time in Patent Office: 1,726 Days
• Field of Search: 704/500, 704/501, 704/582, 704/205, 704/206, 704/207, 704/209, 841/01
• US Class Current: 704/207
• CPC Class Codes: G10H 1/383 Chord detection and/or recognition, e.g. for correction, or automatic bass generation
• CPC Class Codes: G10H 2250/161 Logarithmic functions, scaling or conversion, e.g. to reflect human auditory perception of loudness or frequency
• CPC Class Codes: G10H 3/125 Extracting or recognising the pitch or fundamental frequency of the picked up signal

Abstract

The present invention contains three methods for quickly deducing the fundamental frequency of a complex wave form or signal. One method uses the relationships among the frequencies of higher harmonics including ratios of frequencies, differences between frequencies, ratios of frequency differences, and relationships stemming from the fact that harmonic frequencies are modeled by functions of an integer variable whose values represent harmonic ranking numbers. Another method depicts the predicted/modeled relationships of the harmonics of selected frequency registers on logarithmic scales, records the frequencies of detected partials on like scales, and moves the scales searching for a match of harmonics. Possible harmonic ranking numbers and the implied fundamental frequency can be extracted directly from a match. By still another method, harmonic frequencies for a plurality of fundamentals are compared to partials linked to an unknown fundamental, and the unknown fundamental is deduced.

Claims

1. A method to identify which partials are harmonics in a compound wave, the method being characterized by being performed without relying on the fundamental frequency, and the method further comprising:

detecting partial frequencies of the compound wave;

selecting, from the set of detected partial frequencies, a subset of partial frequencies;

identifying mathematically the harmonic relationships among the detected subset of partial frequencies by comparing relationships among the frequencies of the members of the subset with like harmonic relationships among expected frequency values of harmonics derived from a modeling function that depends upon harmonic ranking numbers of harmonic frequencies; and

deducing the frequency of at least one other harmonic from the identified harmonic relationship.

2. The method of claim 1, wherein the determining further includes:

determining possible sets of ranking numbers to be paired with members of the subset of partial frequencies by comparing the harmonic relationships among the frequencies of the members of the subset to corresponding modeled harmonic relationships that exist among the frequencies of harmonics as calculated by the modeling function; and

selecting a set of consistent ranking numbers from the possible sets of ranking numbers which can be paired with the members of the subset in such away that the harmonic relationships among the members of the subset and the frequencies derived from the modeling function using the ranking numbers with which the members are paired are determinative of the relationships among the frequencies of legitimate harmonics sharing a common fundamental frequency.

3. The method of claim 1 or 2 wherein identifying the harmonic relationships includes comparing frequency ratios and ratios of differences to integer ratios by adjusting the value of the detected frequencies to account for the degree to which harmonic frequencies vary from f_n=f₁×

n, where f_n is the frequency of a harmonic and f₁ is the fundamental frequency from which it stems and n is an integer, the method further comprising;

adjusting the value of the detected frequencies by the function

4. The method of claim 3 wherein G(n) is a function of an integer variable by which harmonics are sharper than those that would be produced by the function f_n=f₁×

n.

5. The method of claim 4 wherein G(n)=n×

(S)^log₂ⁿ and f*_n=f_n÷

(S)^log₂ⁿ.

6. The method of claim 2, wherein the adjusted detected partial frequencies are marked and tagged on a scale, harmonic multiplier values, G(n), are marked and tagged on a like scale, and the scales are moved with respect to each other to find matches.

7. The method according to claim 6, including determining the ranking number of the candidate frequencies from the match of the scales.

8. The method according to claim 7, wherein the scales are logarithmic scales of the same base.

9. The method of claim 1 or 2 including forming new subsets of partial frequencies when previously tested subsets of partial frequencies were not identified to be a group of harmonic frequencies, by the method of:

selecting a new partial frequency from the compound wave;

establishing a new subset such that one of the partial frequencies in the subset previously tested is replaced by the new partial frequency;

designating the subset thus formed to be the new subset of partial frequencies.

10. The method of claim 1 or 2 wherein the subsets of partial frequencies, and the sets of modeled harmonic frequencies contain at least three members.

11. The method of claim 1, whereby harmonic frequencies are modeled by functions in the form of f_n=f₁×

G(n) where f_n is the frequency of the nth harmonic, f₁ is the fundamental frequency from which the harmonic stems, and G(n) is a function of an integer variable, n, which takes on only positive integer values, typically 1 through 17.

12. The method of claim 11, wherein G(n)=n×

(S)^log₂ⁿ, where S is the harmonic sharping constant, greater than or equal to 1 and typically less than 1.003.

13. The method of claim 11, wherein G(n)=n.

14. The method of claim 1, wherein the identifying of harmonic relationships includes using combinations of one or more of the comparisons A through N below to isolate and authenticate possible sets of ranking numbers to be paired with detected partial frequencies:

A. comparing ratios of detected partial frequencies with ratios of modeled harmonic frequencies;

B. comparing ratios of adjusted detected partial frequencies with ratios of small integers;

C. comparing differences between detected partial frequencies with differences between modeled harmonic frequencies;

D. comparing differences between adjusted detected partial frequencies with differences between small integers;

E. comparing ratios of differences between adjusted detected partial frequencies with ratios of differences between small integers;

F. comparing ratios of differences between pairs of detected partial frequencies linked by a common detected partial frequency with ratios of differences between pairs of modeled harmonic frequencies linked by a common modeled harmonic frequency;

G. comparing ratios of differences of pairs of adjusted detected partial frequencies with ratios of differences of small integers linked by a common integer, said integers being considered as possible ranking numbers to pair with the detected partial frequencies;

H. comparing ratios of differences between pairs of detected partial frequencies linked by a common detected partial frequency with ratios of the differences between the ranking numbers which may be paired with the detected partial frequencies;

I. comparing detected partial frequencies divided by ranking numbers with which they might be paired with fundamental frequencies that can be produced by sources of the compound wave;

J. comparing ratios of differences between adjusted detected partial frequencies with ratios of differences between ranking numbers with which they might be paired;

K. comparing logarithms of detected partial frequencies with logarithms of modeled harmonic frequencies or with logarithms of harmonic multipliers, G(n);

L. comparing a scale where detected partial frequencies are marked and tagged with a like scale where modeled harmonic frequencies or harmonic multipliers, G(n), and their ranking numbers are marked and tagged;

M. comparing a logarithmic scale where logarithms of detected partial frequencies are marked and tagged with a like scale where logarithms of modeled harmonic frequencies or logarithms of harmonic multipliers, G(n), and their ranking numbers are marked and tagged; and

N. comparing detected partial frequencies to calculated and/or previously detected harmonic frequencies having a broad range of ranking numbers and stemming from a plurality of fundamental frequencies, all organized by fundamental frequency and harmonic ranking number.

15. The method according to claim 14, wherein one set of comparisons is used to isolate sets of detected partial frequencies and ranking numbers with which they might be paired, and another set is used to authenticate the ranking number pairings and isolate detected partial frequencies which are legitimate harmonics.

16. The method according to claim 15, wherein combinations of comparisons A, B, D E and G are used to isolate sets of ranking numbers paired with detected partial frequencies, and comparisons I, H and G are used to authenticate them.

17. The method according to claim 15, wherein comparison M is used to isolate sets of ranking numbers paired with detected partial frequencies, and comparisons A, B, F and I are used to authenticate them.

18. The method according to claim 15, wherein N is used to isolate sets of ranking numbers paired with detected partial frequencies, and combinations of comparisons A through I are used to authenticate them.

19. The method according to claim 1, including selecting three detected partial frequencies and identifying the harmonic relationship includes using one or more of ratios of the selected partial frequencies, differences of the selected partial frequencies, and ratio of differences of the selected partial frequencies.

20. The method according to claim 19, including determining three harmonic ranking numbers for the selected partial frequencies from the ratios of the three selected partial frequencies.

21. The method according to claim 19, including determining ratios of integers which are substantially equal to the ratios of the selected partial frequencies and determining harmonic ranking numbers for each selected partial frequency from a match of a number from the integer ratios of one of the selected partial frequency with the other two selected partial frequencies.

22. The method according to claim 1 or 2, wherein the fundamental frequency is deduced using one or more of the frequencies of the subset being divided by its ranking number and differences of the frequencies of the subset being divided by differences of their ranking numbers.

23. The method of claim 6, wherein the fundamental frequency is determined by a weighted average of frequencies of the subset divided by their ranking numbers and of differences between those frequencies divided by the differences between their ranking numbers.

24. The method of claim 1, wherein identifying harmonic relationships includes isolating possible subsets of legitimate harmonic frequencies from the set of detected partial frequencies and corresponding ranking numbers with which they can be paired by comparing one or more of a) order, b) ratios, c) differences and, d) ratios of differences of detected partial frequencies to corresponding one or more of a) order, b) ratios, c) differences and, d) ratios of differences of modeled harmonic frequencies.

25. The method of claim 24, wherein ratios are compared by comparing their quotients.

26. The method of claim 24, wherein comparisons are made by marking and tagging detected partial frequencies on a scale, marking modeled harmonic frequencies on a like scale, and moving the scales with respect to each other to find matches.

27. The method of claim 24, wherein detected partial frequencies are matched with values in an array of historical or calculated harmonic frequencies organized by frequency in fundamental frequency order and by ranking number.

28. The method of claim 1 or 2 wherein identifying harmonic relationships includes authenticating subsets of detected frequencies and corresponding ranking numbers with which they are paired by comparing one or more of a) ratios and, b) ratios of differences of adjusted detected partial frequencies with corresponding one or more of a) integer ratios and, b) ratios of differences of integers.

29. The method of claim 28, including adjusting detected partial frequencies using the method of claim 3.

30. The method of claim 28, wherein the comparisons include comparisons of quotients of ratios.

31. The method of claim 28, wherein the comparisons include comparing frequency and frequency difference quotients to quotients of small integer ratios.

32. The method of claim 1, wherein subsets of detected frequencies are eliminated if no sets of ranking numbers with which they can be paired can be authenticated.

33. The method of claim 1 or 2 wherein identifying harmonic relationships includes authenticating or eliminating the detected frequencies together with the ranking numbers with which they are paired by comparing the fundamental frequencies which they imply with fundamental frequencies that could be produced by sources of the compound wave.

34. The method of claim 1 or 2 wherein identifying harmonic relationships includes matching the detected partial frequencies with values in an array of historical or calculated harmonic frequencies organized by frequency in fundamental frequency order and by ranking number.

35. The method of claim 1, wherein the members of subset of detected partial frequencies are designated as legitimate harmonic frequencies if they have been authenticated, and if the sets of ranking numbers with which they have been paired are authenticated.

36. The method of claim 35, wherein the fundamental frequency is deduced from the authenticated candidate harmonic frequencies and their corresponding ranking numbers, and including picking the lowest fundamental frequency if two or more sets of ranking numbers have been authenticated.

37. The method of claim 1 or 2, including discarding sets of possible ranking numbers which imply fundamental frequencies that could not have been produced by sources of the compound wave.

38. The method of claim 1 or 2, further including deducing the fundamental frequency from the identified harmonic relationship of the detected frequencies and ranking numbers with which they are paired.

39. The method of claim 1 wherein the decuced harmonic includes the fundamental frequency of the identified harmonic relationship.

41. The method as in any of claim 1, 2 or 40 including storing the method as instructions in and performing the method on a digital signal processor.

42. The method of claim 1, 2, or 40, wherein the method is preformed before the fundamental frequency can be measured.

43. The method of claim 1, 2, or 40, wherein the compound wave includes plural sets of harmonics, each set stemming from a different common fundamental frequency;

and the method is repeated to determine all sets of harmonics in the compound wave.

40. A method for isolating a set of measured partial frequencies in a compound wave whose members are legitimate harmonics having a harmonic relationship and stemming from the same fundamental frequency, the method comprising:

a. selecting a set of partial frequencies of the compound wave;

b. identifying one or more sets of harmonic frequencies which are based on models such that the ratios of modeled frequencies within a given set are substantially equal to ratios of corresponding selected partial frequencies;

c. designating the partial frequencies as candidate harmonics and designating the corresponding ranking numbers of the matching identified harmonic frequencies as a consistent set of ranking numbers with which said candidate harmonics can be paired;

d. authenticating each consistent set of ranking numbers which when matched against the candidate frequencies designated by c. yield ratios which are substantially equal to the ratios of the candidate frequencies;

e. determining the fundamental frequencies implied by each of the sets of ranking numbers with which the candidate harmonic frequencies can be paired and authenticated as per Step d. above;

f. further authenticating the matched pairs of candidate harmonic frequencies and ranking numbers which imply fundamental frequencies that can be produced by sources of the compound wave; and

g. designating the authenticated candidate harmonics as a set of partial frequencies which are legitimate harmonic frequencies;

or

h. repeating the process a. through g. above for a new set of partial frequencies of the compound wave when the original set cannot be designated legitimate harmonic frequencies.

44. A method to identify which partials are harmonics in a compound wave, the method being characterized by being performed without relying on the fundamental frequency, and the method further comprising:

detecting partial frequencies of the compound wave;

adjusting the detected frequencies to account for the degree to which harmonic frequencies vary from f_n=f₁×

n, where f_n is the frequency of a harmonic and f₁ is the fundamental frequency from which it stems and n is an integer; and

identifying mathematically the harmonic relationships among the adjusted detected partial frequencies.

45. A method for isolating a set of measured partial frequencies in a compound wave whose members are legitimate harmonics having a harmonic relationship and stemming from the same fundamental frequency, the method comprising:

a. selecting a set of partial frequenceis of the compound wave;

b. identifying one or more sets of harmonic frequencies which are based on models such that the ratios of frequencies within a given set are substantially equal to ratios of selected partial frequencies;

c. designating the partial frequencies as candidate harmonics and designating corresponding ranking numbers of the matching identified harmonic frequencies as a consistent set of ranking numbers with which said candidate harmonics can be paired;

d. authenticating each consistent set of ranking numbers which when matched against the candidate frequencies determined by c. yield ratios which are substantially equal to the ratios of the candidate frequencies;

e. further authenticating the matched pairs of candidate harmonic frequencies and ranking numbers; and

f. designating the authenticated candidate harmonics as a set of partial frequencies which are legitimate harmonic frequencies;

or

g. repeating the process a. through f. above for new set of partial frequencies of the compound wave when the original set cannot be designated legitimate harmonic frequencies.

46. A method of measuring the fundamental frequency of at least one harmonic spectrum that resides within a compound wave, comprising;

detecting partial frequencies in the compound wave;

determining whether at least three of the detected partials are part of the same harmonic spectrum, such determination made by mathematically verifying the existence of a mathematical relationship among the detected partials that is consistent with a harmonic spectrum;

the determining further including determining harmonic ranking numbers which can be paired with the three partial frequencies by mathematically verifying that the harmonic relationships among the three partial frequencies is consistent with the corresponding modeled harmonic relationships that are calculated using the modeling function, the same ranking number candidates and the same fundamental frequency; and

calculating the fundamental of the harmonic spectrum using the verified mathematical relationship.

47. The method of claim 46 where the mathematical relationship in the determining step is one of:

A. comparing ratios of detected partial frequencies with ratios of modeled harmonic frequencies;

B. comparing ratios of adjusted detected partial frequencies with ratios of small integers;

C. comparing differences between detected partial frequencies with differences between modeled harmonic frequencies;

D. comparing differences between adjusted detected partial frequencies with differences between small integers;

E. comparing ratios of differences between adjusted detected partial frequencies with ratios of differences between small integers;

F. comparing ratios of differences between pairs of detected partial frequencies linked by a common detected partial frequency with ratios of differences between pairs of modeled harmonic frequencies linked by a common modeled harmonic frequency;

G. comparing ratios of differences of pairs of adjusted detected partial frequencies with ratios of differences of small integers linked by a common integer, said integers being considered as possible ranking numbers to pair with the detected partial frequencies;

H. comparing ratios of differences between pairs of detected partial frequencies linked by a common detected partial frequency with ratios of the differences between the ranking numbers which may be paired with the detected partial frequencies;

I. comparing detected partial frequencies divided by ranking numbers with which they might be paired with fundamental frequencies that can be produced by sources of the compound wave;

J. comparing ratios of differences between adjusted detected partial frequencies with ratios of differences between ranking numbers with which they might be paired;

K. comparing logarithms of detected partial frequencies with logarithms of modeled harmonic frequencies or with logarithms of harmonic multipliers, G(n);

L. comparing a scale where detected partial frequencies are marked and tagged with a like scale where modeled harmonic frequencies or harmonic multipliers, G(n), and their ranking numbers are marked and tagged.

M. comparing a logarithmic scale where logarithms of detected partial frequencies are marked and tagged with a like scale where logarithms of modeled harmonic frequencies or logarithms of harmonic multipliers, G(n), and their ranking numbers are marked and tagged; and

N. comparing detected partial frequencies to calculated and/or previously detected harmonic frequencies having a broad range of ranking numbers stemming from a plurality of fundamental frequencies, all organized by fundamental frequency and harmonic ranking number.

48. A method to identify which partials are harmonics in a compound wave, the method comprising:

detecting partial frequencies of the compound wave;

adjusting the detected frequencies to account for the degree to which harmonic frequencies vary from f_n=f₁×

n, where f_n is the frequency of harmonic and f₁ is the fundamental frequency from which it stems and n is an integer; and

identifying mathematically the harmonic relationships among the adjusted detected partial frequencies.

49. The method of claim 48, wherein the adjustment is f_n =f₁×

n×

(S ^log₂n, where S is a harmonic sharping constant, greater than or equal to 1 and typically less than 1.003.