| 摘要 |
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 at least two partial frequencies of the compound wave; identifying mathematically the harmonic relationships among the detected partial frequencies and 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 includes: selecting, from the set of detected partial frequencies, a subset of partial frequencies. 3. The method of Claim 2, 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 a way 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. 4. The method of claims 1-3, wherein identifying the harmonic relationships includes comparing frequency ratios and ratios of differences to integer ratios by adjusting the detected frequencies to account for the degree to which harmonic frequencies vary from fn = f1 x n, where fn 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 detected frequencies by the function f*n = fn : [G(n) : n], where fn is the detected frequency, G(n) is the function of an integer variable n in the model fn = f1 x G(n), and f*n is the detected frequency adjusted so that ratios and ratios of differences can be compared directly to integer ratios. 5. The method of Claim 4 wherein G(n) is a function of an integer variable by which harmonics are sharper than those that would be produced by the function fn = f1 x n. 6. The method of Claim 5 wherein G(n) = n x (S)<LOG>2<N> and f*n = fn : (S)<LOG>2<N>. 7. The method of Claims 2 and 3 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 fit the sunset previously tested is replaced by the new partial frequency: designating the subset thus formed to be the new subset of partial frequencies. 8. The method of Claims 2, 3 and 7 wherein the subsets of partial frequencies, and the sets of modeled harmonic frequencies contain at least three members. 9. The method of Claim 1, wherein identifying harmonic relationships includes comparing relationships between measured partial frequencies to modeled harmonic frequencies. 10. The method of Claims 2, 3 and 9, whereby harmonic frequencies are modeled by functions in the form of fn= f1x G(n) where fn is the frequency of the nth harmonic, f1is the fundamental frequency from which the harmonicn f stems, and G(n) is a function of an integer variable, n, which takes on only positive integer values, typically 1 through 17. 11. The method of Claim 10, wherein G(n) = n x (S)<LOG>2<N>, where S is the harmonic sharping constant, greater than or equal to 1 and typically less than 1.003. 12. The method of Claim 10, wherein G(n) = n. 13. The method of Claims 1-4, 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 scab 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. 14. The method according to Claim 13, 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. 15. The method according to Claim 14, 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 J, H and G are used to authenticate them. 16. The method according to Claim 14, 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 there. 17. The method according to Claim 14, 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. 18. The method according to Claims 1, 2 and 3, 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. 19. The method according to Claim 18, including determining three harmonic ranking numbers for the selected partial frequencies from the ratios of the three selected partial frequencies. 20. The method according to Claim 18, including determining ratios of integers which arc 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. 21. The method according to Claims 2 and 3, 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. 22. The method of Claim 21, 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. 23. The method of Claims 1, 2 and 3, 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. 24. The method of Claim 23, wherein ratios are compared by comparing their quotients. 25. The method of Claim 23 wherein comparisons are made by markin
|
