WO1999050620A1 - Procede d'interpolation de donnees sur un signal de serie temporelle et support d'enregistrement sur lequel est enregistre le programme relatif a ce procede - Google Patents

Procede d'interpolation de donnees sur un signal de serie temporelle et support d'enregistrement sur lequel est enregistre le programme relatif a ce procede Download PDF

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Publication number
WO1999050620A1
WO1999050620A1 PCT/JP1999/001635 JP9901635W WO9950620A1 WO 1999050620 A1 WO1999050620 A1 WO 1999050620A1 JP 9901635 W JP9901635 W JP 9901635W WO 9950620 A1 WO9950620 A1 WO 9950620A1
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WIPO (PCT)
Prior art keywords
patch
data
patches
center
time
Prior art date
Application number
PCT/JP1999/001635
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English (en)
Japanese (ja)
Inventor
Masayoshi Shimono
Shigeru Nakashima
Takeshi Yamakawa
Eiji Uchino
Yuu Nakamura
Original Assignee
Masayoshi Shimono
Shigeru Nakashima
Takeshi Yamakawa
Eiji Uchino
Yuu Nakamura
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Masayoshi Shimono, Shigeru Nakashima, Takeshi Yamakawa, Eiji Uchino, Yuu Nakamura filed Critical Masayoshi Shimono
Priority to AU29608/99A priority Critical patent/AU2960899A/en
Publication of WO1999050620A1 publication Critical patent/WO1999050620A1/fr

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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01D—MEASURING NOT SPECIALLY ADAPTED FOR A SPECIFIC VARIABLE; ARRANGEMENTS FOR MEASURING TWO OR MORE VARIABLES NOT COVERED IN A SINGLE OTHER SUBCLASS; TARIFF METERING APPARATUS; MEASURING OR TESTING NOT OTHERWISE PROVIDED FOR
    • G01D3/00—Indicating or recording apparatus with provision for the special purposes referred to in the subgroups
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F7/00—Methods or arrangements for processing data by operating upon the order or content of the data handled

Definitions

  • the present invention relates to a method for interpolating data of a time-series signal, and more particularly, to measuring a time-series signal represented by discrete measurement data contaminated by noise or the like, which is superior in reproducibility of the original signal even with coarse sample data.
  • the present invention relates to a data interpolation method for performing interpolation between values, smoothing a time series signal or reproducing a missing data portion, and a recording medium on which a program for the method is recorded.
  • Japanese Patent Application Laid-Open No. HEI 6-343866 discloses that even when a time-series signal is contaminated with noise, the basic function f (X) can be obtained.
  • An improved interpolation method has been proposed which grasps the outline, performs accurate data interpolation, and is extremely suitable for data smoothing.
  • this method includes a step of dividing the time-series signal into a plurality of patches having an arbitrary time width, and a step of obtaining a straight line connecting the centers (g ; ) of the patches as a main straight line. , the center of the front and rear of the patch adjacent the center (gi) of each patch - the upward-sloping diagonal of the patch when the (gi have g i + 1) compared to the gi- i ⁇ gi rather than gi + 1, g Bok !
  • the method includes a step of superimposing the main straight line and the related sub-straight lines before and after the main straight line with weights determined by a predetermined membership function, thereby achieving desired interpolation, smoothing or missing data. Playback is possible.
  • the above method presupposes that the reliability of the sampled data is high in the first place, and when the reliability of the data itself is low, such as coarse sampling data, it is close to the sampled data. It is difficult to faithfully reproduce the original signal from this sampled data simply by inferring that there is a true value.
  • so-called ripples may occur in the process of fuzzy inference.
  • the present invention further develops the data interpolation method disclosed in the above-mentioned Japanese Patent Application Laid-Open No. Hei 6-33486, and proposes a data interpolation method excellent in reproducibility of the original signal even with coarse sampling data, and a program therefor.
  • the purpose is to provide a recorded recording medium. Disclosure of the invention
  • the present inventor found that in the case of low-reliability data, it was assumed that excellent reproducibility could be obtained by inferring that there was a true value in the periphery of the obtained data and forming a patch. Is completed. That is, the time series signal data interpolation method of the present invention achieves the above object. For this purpose, a step of dividing a time-series signal into a plurality of patches having an arbitrary time width using data sampled at a predetermined sampling rate and a predetermined amplitude, and a straight line connecting the centers ( gi ) of the patches.
  • a data interpolation method wherein the patch section is A process of creating a sampling frequency width or a real multiple of the sampling frequency width centered on the sampling data with respect to the sampling data. Based on the sampling data, the method includes a step of setting the centers of the two in the amplitude axis direction to the lower and upper ends of the patch, respectively, and a step of moving the center of the patch in the amplitude axis direction so as to overlap the sampling data.
  • an outline of a time-series signal is obtained by continuously setting a plurality of patches of an arbitrary time width from coarse sampling data.
  • FIG. 1 is an explanatory diagram of a sampling method of an original signal.
  • FIGS. 2, 3, 4, and 5 are explanatory diagrams showing a patch forming method based on sampling data.
  • FIG. 6 is an explanatory diagram showing coordinates of representative patches.
  • FIG. 7 is an explanatory diagram in which a main straight line and a sub-straight line are given to the patch arrangement, and an explanatory diagram showing a membership function set for these.
  • FIG. 8 is an explanatory diagram showing a fuzzy inference rule in the present invention.
  • FIG. 9 is an explanatory diagram showing an example of a patch near an extreme value according to the present invention.
  • FIG. 10 is an explanatory diagram showing a variable sub-line for the interpolation processing near the extremum shown in FIG.
  • FIG. 11 is an explanatory diagram showing the positional relationship between patches near the extremum in the present invention.
  • FIG. 12 is a circuit block diagram for realizing each step of the method of the embodiment recorded on the recording medium.
  • FIG. 13 is a graph showing the relationship between the signal interpolated by the method of the present invention and the original signal.
  • FIG. 14 is an explanatory diagram of a method of sampling the original signal with a non-linear quantization level.
  • Figure 15 is a flowchart of the conventional data interpolation method using fuzzy inference.
  • Fig. 1 is an explanatory diagram of the sampling method of the original signal (speech waveform). Based on this original signal, an appropriate sampling frequency is considered in the time axis direction.
  • the original signal is divided at this sampling frequency.
  • the dashed line in the vertical direction divides the original signal at an appropriate sampling frequency
  • the intersection of the original signal and the appropriate segment provided above is captured. It is marked with X in the figure.
  • the intersection is moved to the nearest upper and lower sampling levels from the intersection, and this is used as sampling data.
  • the sampled data is indicated by a black circle in the figure.
  • a patch is created with a width corresponding to the sampling frequency around the sampling data.
  • the width of the sampling frequency is set as described above, but may be a real number multiple of the sampling frequency.
  • the width is two or three times wider than the sampling frequency, high-frequency components will be cut off, and the human ear will hear the noise-free sound.
  • the reproducibility will be better if the patch width is narrower than the sampling frequency.
  • the data with the larger amplitude value is taken as the middle point in the amplitude axis direction of both. Is the top of the patch.
  • the midpoint in the amplitude axis direction of the data with the small amplitude value is taken as the lower base of the patch. I do. If the upper or lower base is not required here, disassemble as shown in the figure. The upper or lower base value for a certain sampling data with half the value of the function. This makes it possible to generate a patch centered on the sampling data and covering the error range from the true value.
  • the function of the time series signal to be obtained is roughly approximated according to the arrangement of each patch, and then the approximate shape is interpolated by a plurality of adjacent positional relations of these patches.
  • the above outline is represented as a main straight line connecting the centers of the patches, and at least a pair of patches before and after constitute a plurality of sub straight lines with respect to the main straight line to be interpolated.
  • the center is indicated by the center of gravity G of each patch Ri, and FIG. 6 shows the center in the present embodiment, that is, the center of gravity G ; for a single patch R;
  • the main straight line F i (t) is corrected based on the relationship with a plurality of adjacent patches.
  • the interpolation area to be targeted for this purpose ie, the interpolation area from time t to time t i +1 in FIG. 7 up to four patches R i, R i, R From each of the four patches i + 1 and Ri + 2, a subline f; (t) is obtained.
  • the coordinates of each patch are represented by symbols shown in FIG. 6, the above-mentioned sub-lines f, (t) are determined in the following three types according to the characteristics between adjacent patches.
  • fi (t) gi (3)
  • the minor line fi (t) is a horizontal line parallel to the horizontal axis and passing through gi .
  • FIG. 7 described above shows these membership functions.
  • the ship function W i (t) and the respective membership functions W i (t) for the four adjacent sub-lines fi (t) are shown.
  • a weight S determined by the membership function is given to the main straight line and the sub straight line, respectively, and a function S (t) to be interpolated by the weighted average value to be described later is obtained.
  • the feature of this interpolation method is that if the true time function T (t) increases with a steep slope, the vertical length of the patch created by the observed data will increase, and if it is smooth, it will decrease. Show the trend. That is, when the time function increases with a steep slope, the length of the patch in the vertical direction increases, and as a result, the slope of the sub-line becomes steep, and as a result, the slope of the interpolated function also becomes steep. Used for interpolation.
  • the arrangement of patches represents an overall rough outline of the time function T (t), so that the main straight line connecting the center of gravity G i has an outline.
  • a straight line is approximated by a polygonal line. Since the main straight line F i (t) best approximates the patch R i +1 from the patch R; in the interpolation area of ⁇ T i, T i +1 ⁇ , The membership value is fixed as shown in the membership function W i (t). Since the sum of the membership function values for the sub-line at a certain time t is 2, the membership function value for weighting the main line F i (t) twice is also 2.
  • the sub-line represents the inclination around the interpolation area, and it can be estimated that the closer to the patch R ; , the closer the true time function approaches the inclination of the sub-line created by the patch R ; .
  • the value at the time t in the interpolation area is a main straight line F connecting the patch R i and the center of gravity G or G i +1 of the patch R i +1 ; Tutsi R i _!, R i, R i + R i + 2 of the sub linear fi 1 constituted by the respective positional relationship (t), f (t) f i + 1 (t), f i + 2 (
  • patch R to 2 and patch R i are required to determine the sub-line f (t), and patch R to determine the sub-line f i +2 (t). Since i + 1 and patch Ri + 3 are required, the output value described above is determined by six patches.
  • Fig. 8 expresses the above rules using fuzzy rules, and it is understood from this that the values are obtained by combining the five rules at time t.
  • the setting of the patch divides the time-series signal by an arbitrary time width.
  • a certain patch may include a bias near the extreme value of the function.
  • FIG. 9 shows a patch R, which approximates the vicinity of the extreme value.
  • the extremum of the true function is closer to R i + 1 from the center of patch R; and in FIG. 9 (b), the extremum is closer to patch R; c) Then, no.
  • the extremum exists everywhere in the patch R i, good interpolation cannot be performed unless the position of the extremum also varies with the position of the extremum.
  • fi (t) (di-c,) u (t-t / Cb i-ai) + g-r> 0
  • fi (t) -(ds-c ⁇ -u (t-t JZ i — aj + g-r ⁇ 0 (9)
  • u approaches 1 as the extremum of the true function approaches the patch R i +1 so the sub-line fi ( t) rises to the right
  • a desired signal can be obtained by dividing a time-series signal into a plurality of patches and combining the main straight line and the sub-straight line of each patch by fuzzy inference using a membership function. Interpolation, smoothing, or reproduction of missing data can be performed, and when these are concretely constructed, known MAX circuits, MIN circuits, sample-and-hold circuits, and logical operation circuits are combined. It is possible to do it.
  • FIG. 12 is a circuit block diagram for realizing each step of the method of the embodiment recorded on the recording medium.
  • 1 201 is an original signal input section
  • 1 202, 1 203, and 1 204 are delay devices, which delay an input signal at time k, and time k + 1, k + 2, k + Generate the signals X k +1, X k +2, X k +3 at 3.
  • 1205 and 1206 are adders
  • 1207 and 1208 are dividers, each of which divides the input by 2.
  • the divider 1 210 divides by the unit time (corresponding to the sampling frequency).
  • 1209 and 1214 are subtracters.
  • 1 2 1 1, 1 2 1 2, 1 2 1 3 are delay units, which respectively determine the inclination of the sub-line generated from the patch made from the input signal, fk + 2, fk + 3, and fk + 4 To generate.
  • the subtractor 1 2 1 4 generates the inclination F k +2 of the main straight line corresponding to the delay signal X k +2.
  • 1 2 15 is an adder / multiplier, which performs calculation (weighted addition) of the numerator of equation (4).
  • the gain is a coefficient of F k, here 2.
  • the coefficients Wk + 1, Wk + 2, Wk + 3, Wk + 4 and the gain are added by the adder 1216, and the denominator of the equation (4) is obtained.
  • the sampling unit 1 218 outputs final interpolation data by alternately sampling X k +3 and S.
  • the patch section is defined based on the process of creating a width corresponding to the sampling frequency with respect to a certain sampled data centered on the sampled data, and the sampled data, the sampled data after the sampled data, and the sampled data before the sampled data.
  • the step of setting the center of the patch in the amplitude axis direction to the lower and upper ends of the patch, and the step of moving the center of the patch in the amplitude axis direction so as to overlap the sampling data include the step of centering the sampling point. Is obtained, and the error between the inferred value and the true time-series signal can be reduced.
  • Fig. 13 shows the relationship between the signal interpolated by the above method and the original signal.
  • the root mean square of the error is improved by about 10% as compared with that of Japanese Patent Application Laid-Open No. Hei 6-33486. It was confirmed that extremely effective interpolation was obtained.
  • the quantization levels are set at regular intervals as shown in FIG. 1.
  • the quantization The levels may be non-linear (eg, non-linear sampling using logarithmic functions). This is because a small amount of noise does not affect the sound reproducibility of a strong voice signal, but the noise is considered to have a large effect on a weak voice signal.
  • the interval between the quantization levels is reduced near the amplitude of 0, and the interval between the quantization levels is increased in the region where the amplitude is large. This has the effect of improving the reproducibility of weak speech.
  • a filter into a telephone or a personal computer of an Internet telephone is described.
  • it can be applied simply by adding a circuit to a part of the input / output terminals of a transceiver or a relay terminal, and it can be embedded in a part of an existing program and can be provided as an engine. have.
  • the following effects can be obtained by the present invention.

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  • Physics & Mathematics (AREA)
  • Engineering & Computer Science (AREA)
  • General Physics & Mathematics (AREA)
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  • General Engineering & Computer Science (AREA)
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Abstract

Cette invention concerne un procédé permettant d'interpoler des données sur un signal de série temporelle, lequel procédé consiste à diviser un signal de série temporelle, lors d'une première étape, en des fragments qui possèdent des largeurs temporelles arbitraires. On détermine ensuite une largeur dont la valeur est le produit entre un nombre réel et la valeur de la fréquence d'échantillonnage, et au centre de laquelle se trouve une donnée d'échantillonnage. On établit ensuite que les bases inférieure et supérieure du fragment de la donnée d'échantillonnage sont égaux aux centres des données qui précèdent et qui suivent ladite donnée d'échantillonnage, après quoi on déplace le fragment de sorte que son centre corresponde, dans la direction de l'amplitude, à la donnée d'échantillonnage. Cette invention concerne également un dispositif d'interpolation de données, ainsi qu'un support d'enregistrement sur lequel le programme est enregistré.
PCT/JP1999/001635 1998-03-31 1999-03-29 Procede d'interpolation de donnees sur un signal de serie temporelle et support d'enregistrement sur lequel est enregistre le programme relatif a ce procede WO1999050620A1 (fr)

Priority Applications (1)

Application Number Priority Date Filing Date Title
AU29608/99A AU2960899A (en) 1998-03-31 1999-03-29 Method of interpolating data on time-series signal and recording medium on whichprogram therefor is recorded

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
JP10/87456 1998-03-31
JP8745698 1998-03-31

Publications (1)

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WO1999050620A1 true WO1999050620A1 (fr) 1999-10-07

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AU (1) AU2960899A (fr)
TW (1) TW513663B (fr)
WO (1) WO1999050620A1 (fr)

Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPH05115448A (ja) * 1991-10-25 1993-05-14 Omron Corp 波形処理装置
JPH0634386A (ja) * 1992-07-15 1994-02-08 Eiji Uchino 時系列信号のデータ補間方法

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPH05115448A (ja) * 1991-10-25 1993-05-14 Omron Corp 波形処理装置
JPH0634386A (ja) * 1992-07-15 1994-02-08 Eiji Uchino 時系列信号のデータ補間方法

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AU2960899A (en) 1999-10-18

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