WO1999061925A1 - Method for improving the accuracy in the determination of a waveform center - Google Patents
Method for improving the accuracy in the determination of a waveform center Download PDFInfo
- Publication number
- WO1999061925A1 WO1999061925A1 PCT/US1999/011836 US9911836W WO9961925A1 WO 1999061925 A1 WO1999061925 A1 WO 1999061925A1 US 9911836 W US9911836 W US 9911836W WO 9961925 A1 WO9961925 A1 WO 9961925A1
- Authority
- WO
- WIPO (PCT)
- Prior art keywords
- sample point
- amplitude
- waveform
- sample
- centroid
- Prior art date
Links
- 238000000034 method Methods 0.000 title claims description 18
- 238000004364 calculation method Methods 0.000 abstract description 61
- 238000010586 diagram Methods 0.000 description 13
- 238000010606 normalization Methods 0.000 description 4
- 230000000694 effects Effects 0.000 description 3
- 230000008030 elimination Effects 0.000 description 3
- 238000003379 elimination reaction Methods 0.000 description 3
- 238000005070 sampling Methods 0.000 description 3
- 238000012360 testing method Methods 0.000 description 3
- 238000012935 Averaging Methods 0.000 description 2
- 230000010363 phase shift Effects 0.000 description 2
- 238000007792 addition Methods 0.000 description 1
- 238000012937 correction Methods 0.000 description 1
- 230000006870 function Effects 0.000 description 1
- 238000005259 measurement Methods 0.000 description 1
- 238000012545 processing Methods 0.000 description 1
Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R19/00—Arrangements for measuring currents or voltages or for indicating presence or sign thereof
- G01R19/25—Arrangements for measuring currents or voltages or for indicating presence or sign thereof using digital measurement techniques
- G01R19/2506—Arrangements for conditioning or analysing measured signals, e.g. for indicating peak values ; Details concerning sampling, digitizing or waveform capturing
- G01R19/2509—Details concerning sampling, digitizing or waveform capturing
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R19/00—Arrangements for measuring currents or voltages or for indicating presence or sign thereof
- G01R19/04—Measuring peak values or amplitude or envelope of ac or of pulses
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R23/00—Arrangements for measuring frequencies; Arrangements for analysing frequency spectra
- G01R23/02—Arrangements for measuring frequency, e.g. pulse repetition rate; Arrangements for measuring period of current or voltage
Definitions
- the present invention relates to signal processing, and more particularly to the determination of a center value of a waveform.
- centroid or center of mass
- Equation 1 can be used for example to determine the center wavelength ( ⁇ c ) of a waveform where a number N of discrete power level (P N ) measurements are taken for each wavelength ( ⁇ ).
- Figs. 1-3 illustrate examples of sampled waveforms using a fixed number of points, i.e., seven (7) points.
- the sample points are distributed symmetrically over the waveform.
- the sample points are shifted relative to the symmetrical sampling locations in Fig.
- Fig. 3 illustrates the extreme case, where again seven discrete sample points are shown. The first point will effectively skew the calculation from the correct value.
- Fig. 4 illustrates the error associated with asymmetric distribution of discrete sample points. In particular, Fig. 4 shows the percent error in the calculation from the FWHM versus the phase difference between the sampled points and the waveform. For a 0-degree phase difference, the peak of the waveform coincides exactly with the center-sampled point. For a 180- degree phase shift, the waveform peak is exactly between two sampled points.
- the sample error can be reduced by increasing the number of sample points.
- the number of sample points and therefore the accuracy of centroid determination, is limited by the sampling rate and the available memory. There therefore exists a need for an improved method of determining a center wavelength of an arbitrary waveform, particularly where the waveform is discretely sampled at a limited number of sample points.
- Objects of the present invention include improved accuracy of the centroid calculation of a waveform.
- a waveform is discretely sampled at a limited number of sample points, each sample point being a set (V N , A N ) including a sample value (V N ) and an amplitude (A N ), and N being the number of non-eliminated sample points.
- the last sample point (V N , A N ) is eliminated if the magnitude of the amplitude at the first sample point (A,) is greater than the last sample point (A N ), and the difference in magnitude between the first and last sample points (A,-A N ) is greater than the difference in magnitude between the second to last sample point and the first sample point (A N. ,-A,).
- the first sample point (V 1; A,) is eliminated prior to the centroid calculation if the magnitude of the amplitude at the last sample point (A N ) is greater than the first sample point (A,), and the difference in magnitude between the last and first sample points (A N -A,) is greater than the difference in magnitude between the second sample point and the last sample point (A 2 -A N ).
- a first centroid calculation is found using a set of samples in which one side of the waveform has the lowest amplitude value sample. Sample values on the side of the waveform initially having the lowest amplitude value are then eliminated until the opposing side of the waveform has the lowest amplitude value sample. A second centroid calculation is then performed and the two centroid calculations are averaged together to arrive at an average centroid calculation.
- the amplitude components of the waveform sample values are normalized to the lowest amplitude value sample point and a first centroid calculation is performed on the normalized waveform.
- the waveform is normalized to the lowest amplitude value sample point on the other side of the waveform and a second centroid calculation is performed.
- the two centroid calculations are then averaged to provide an averaged normalized centroid calculation.
- Fig. 1 is a diagram of a discretely sampled waveform wherein the sample values are symmetrically distributed over the waveform;
- Fig. 2 is a diagram of the discretely sampled waveform of Fig. 1 wherein the sample values are asymmetrically distributed over the waveform;
- Fig. 3 is a diagram of the discretely sampled waveform Fig. 1 wherein the sample values are asymmetrically distributed over the waveform and wherein the peak of the waveform is exactly between two sample points;
- Fig. 4 is a diagram showing the percent error in the calculation from the FWHM versus the phase difference between the sample points and the waveform of
- Fig. 5 is a diagram of a discretely sampled waveform wherein the sample values are asymmetrically distributed over the waveform, and showing the determination of whether one of the sample points should be eliminated prior to calculating the centroid of the waveform;
- Fig. 6 is a flowchart of a subroutine for determining whether one of the sample points should be eliminated prior to calculating the centroid of the waveform of Fig.
- Fig. 7 is a diagram showing the percent error in the calculation from the FWHM versus the phase difference between the sample points and the waveform using the flowchart of Fig. 6 for determining the centroid of the waveform;
- Fig. 8 is a diagram of a discretely sampled waveform wherein the sample values are asymmetrically distributed over the waveform;
- Fig. 9 is a diagram of the discretely sampled waveform of Fig. 8 with the sample having the lowest magnitude amplitude eliminated;
- Fig. 10 is a diagram showing the percent error in the calculation from the FWHM versus the phase difference between the sample points and the waveform wherein the centroid calculations of the diagrams of Fig. 8 and Fig. 9 are averaged to determine a centroid of the waveform in accordance with a second embodiment of the invention
- Fig. 11 is a diagram of a discretely sampled waveform wherein the sample values are asymmetrically distributed over the waveform and wherein the waveform is offset in amplitude;
- Fig. 12 is a diagram showing the percent error in the calculation from the FWHM versus the phase difference between the sample points and the waveform of Fig. 11, wherein the waveform is normalized prior to determination of its centroid;
- Fig. 13 is a diagram of a discretely sampled waveform wherein the sample values are asymmetrically distributed over the waveform and wherein a portion of the waveform is not sampled.
- the present invention is particularly well suited for determining the center value (centroid) of a waveform.
- the present invention is particularly suitable for use with a waveform having a generally symmetrical distribution, e.g., a Gaussian or Lorentz relationship.
- the present invention is also suitable for use with waveforms having a generally asymmetrical distribution, such as a Rayleigh function.
- the present invention will be described with respect to a waveform where the value of interest is wavelength and the amplitude of interest is the power. However, it will be understood by those skilled in the art that the present inventions may be used with any waveform representing a value and amplitude of interest.
- one of the sample points in this case the first point
- a 180 degree phase shift the waveform peak is exactly between two sampled points
- one of the sample points effectively skews the calculation from the correct value.
- the error in the calculation of center wavelength is significantly reduced.
- Fig. 5 illustrates a waveform having an asymmetric distribution of seven sample points.
- the determination of whether or not a sample point should be eliminated can be performed using the subroutine of Fig. 6.
- the subroutine is entered in a step 100, and in a step 101, the waveform of interest is sampled and the sample values (V N , A N ) are stored in memory.
- the sample values V N , A N
- seven (7) samples are taken of the waveform.
- any number of samples may be used.
- a test 105 is performed wherein the amplitude of the first sample (A,) is compared to the amplitude of the last sample (A 7 ). If A, is less than A 7 , steps 110 and 111 are consecutively performed wherein the difference in amplitude between A, and A 7 is determined
- DA ⁇ DA 2 + A 7 ⁇ DA 2 ⁇ DA 2 ⁇ DA 2 ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇
- step 120 the centroid calculation is performed on all of the sample points in step 120.
- the subroutine then returns to step 101 wherein discrete samples of a new waveform are taken and stored in memory.
- steps 130 and 131 are performed wherein the difference in amplitude between A, and A 7 is determined (DA 3 ) and the difference in amplitude between the amplitude of the sixth sample (A 6 ) and A, is determined (DA 4 ).
- DA 3 the difference in amplitude between the amplitude of the sixth sample
- a 6 the difference in amplitude between the amplitude of the sixth sample
- DA 4 the difference in amplitude between the amplitude of the sixth sample
- DA 4 DA 4
- a test 135 is performed wherein the magnitude of DA 3 is compared to the magnitude of DA 4 . If DA 3 is greater than DA 4 , a step 137 is performed wherein the last sample point is eliminated.
- the centroid calculation of Equation 1 is then performed on the remaining points in step 120. If DA 3 is less than DA 4 , the centroid calculation is performed on all of the sample points in step 120.
- the subroutine then returns to step 101 wherein discrete samples of a new waveform
- Fig. 7 shows the reduction in centroid calculation error when the centroid is determined in accordance with the first embodiment of the invention.
- the maximum percent error in the calculation from the FWHM versus the phase difference between the sampled points and the waveform using the first embodiment of the invention is cut in half with respect to the percent error if the centroid determination in accordance with the first embodiment of the invention is not used (as illustrated by curve 155).
- centroid calculation further reduction in the errors associated with a centroid calculation can be achieved by averaging two centroid calculations for a given asymmetrically sampled waveform.
- the first centroid calculation is found using a set of samples in which one side of the waveform has the lowest amplitude value sample. In this case, because of the asymmetry of the discrete samples, the centroid calculated is slightly below the true center.
- Fig. 9 for the same set of samples, sample values on the side of the waveform initially having the lowest amplitude value are eliminated until the opposing side of the waveform has the lowest amplitude value sample.
- a second centroid calculation is then performed using Equation 1. The two centroid calculations are then averaged together to arrive at an average centroid calculation.
- the samples may not span the entire waveform, or the amplitude values may not return to zero.
- an additional error may be introduced in the centroid calculation associated with the offset of the waveform from zero.
- the centroid calculation will be biased towards the centroid of the offset area. For a large offset area, this biasing effect can negate the effects of the waveform shape itself.
- a third embodiment of the invention is particularly useful for reducing errors in the calculation of the centroid of the waveform of interest, especially when the waveform contains a fixed offset.
- the amplitude components of the waveform sample values are normalized to the lowest amplitude value sample point.
- FIG. 11 shows that an offset sampled waveform is equivalent to the actual waveform of interest on top of a fixed offset, or an offset "box” 170. Elimination of this "box" by normalization of the waveform amplitude to the lowest amplitude value sampled point will minimize the offset associated errors in the calculation.
- a centroid calculation is performed on the normalized waveform. Next, sample values on the side of the waveform initially having the lowest amplitude value are eliminated until the opposing side of the waveform has the new lowest amplitude value sample. The waveform is then normalized to the new lowest amplitude value sample point and a second offset box 175 is eliminated prior to a second centroid calculation being performed. The two centroid calculations are then averaged to provide an averaged normalized centroid calculation.
- Figure 12 shows an example of the reduction in centroid calculation error achieved with an averaged normalized centroid calculation.
- the third embodiment of the invention is described herein as eliminating an "offset box", it will be understood by those skilled in the art that the amplitude values of each of the discrete sample points are simply normalized to the value of the smallest magnitude amplitude value. In effect, this smallest value amplitude value is simply subtracted from all of the other amplitude values.
- either the first embodiment of the invention, wherein sample points are eliminated under certain circumstance, or the second embodiment of the invention, wherein two centroid calculations are averaged may be used to determine the center value or centroid of the waveform of interest after the initial normalization of the waveform.
- the present invention has been described thus far wherein the number and distribution of sample points on either side of a waveform are generally evenly distributed, with an error in the centroid determination of the waveform being introduced by a generally asymmetric distribution of sample points over the waveform of interest.
- the waveform is extremely asymmetric, the distribution of sample points on the waveform may be extremely skewed. In this case, it may be desirable to delete certain sample values.
- sample values on both sides of the waveform are compared, and sample values are eliminated on the side of the waveform having the lowest amplitude values until there is only one sample value on one side of the waveform having a smaller amplitude than the smallest amplitude value on the other side of the waveform.
- sample values 9, 10 and 11 are eliminated.
- the centroid of the waveform may be determined in accordance with the first, second or third embodiments of the invention as described above. Additionally, as described above with respect to the third embodiment of the invention, all of the sample values may be normalized, either before or after elimination of sample points.
Abstract
Description
Claims
Priority Applications (4)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
JP2000551268A JP2002517029A (en) | 1998-05-29 | 1999-05-27 | How to improve the accuracy of waveform center determination |
AU42151/99A AU4215199A (en) | 1998-05-29 | 1999-05-27 | Method for improving the accuracy in the determination of a waveform center |
GB0031567A GB2356060B (en) | 1998-05-29 | 1999-05-27 | Method for improving the accuracy in the determination of a waveform center |
CA002334281A CA2334281A1 (en) | 1998-05-29 | 1999-05-27 | Method for improving the accuracy in the determination of a waveform center |
Applications Claiming Priority (2)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
US09/087,447 | 1998-05-29 | ||
US09/087,447 US6529923B2 (en) | 1998-05-29 | 1998-05-29 | Method for improving the accuracy in the determination of a waveform center of a waveform signal |
Publications (1)
Publication Number | Publication Date |
---|---|
WO1999061925A1 true WO1999061925A1 (en) | 1999-12-02 |
Family
ID=22205248
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
PCT/US1999/011836 WO1999061925A1 (en) | 1998-05-29 | 1999-05-27 | Method for improving the accuracy in the determination of a waveform center |
Country Status (6)
Country | Link |
---|---|
US (1) | US6529923B2 (en) |
JP (1) | JP2002517029A (en) |
AU (1) | AU4215199A (en) |
CA (1) | CA2334281A1 (en) |
GB (1) | GB2356060B (en) |
WO (1) | WO1999061925A1 (en) |
Cited By (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
JP2004096704A (en) * | 2002-08-30 | 2004-03-25 | Ulead Systems Inc | Method of dynamically filtering document |
US6763063B1 (en) | 2000-10-23 | 2004-07-13 | Telefonaktiebolaget Lm Ericsson (Publ) | Peak value estimation of sampled signal |
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Publication number | Priority date | Publication date | Assignee | Title |
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US6804693B2 (en) * | 2001-08-14 | 2004-10-12 | Cidra Corporation | Method for reducing skew in a real-time centroid calculation |
US7006206B2 (en) * | 2003-05-01 | 2006-02-28 | Cidra Corporation | Method and apparatus for detecting peaks in an optical signal using a cross-correlation filter |
USRE46672E1 (en) | 2006-07-13 | 2018-01-16 | Velodyne Lidar, Inc. | High definition LiDAR system |
CN102708394B (en) * | 2012-04-17 | 2016-02-17 | 重庆大学 | Based on passive temperature label and the reader thereof of SAW |
US10627490B2 (en) | 2016-01-31 | 2020-04-21 | Velodyne Lidar, Inc. | Multiple pulse, LIDAR based 3-D imaging |
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US10393877B2 (en) | 2016-06-01 | 2019-08-27 | Velodyne Lidar, Inc. | Multiple pixel scanning LIDAR |
CN110914705A (en) | 2017-03-31 | 2020-03-24 | 威力登激光雷达有限公司 | Integrated LIDAR lighting power control |
CN115575928A (en) | 2017-05-08 | 2023-01-06 | 威力登激光雷达美国有限公司 | LIDAR data acquisition and control |
US20190137549A1 (en) * | 2017-11-03 | 2019-05-09 | Velodyne Lidar, Inc. | Systems and methods for multi-tier centroid calculation |
US11294041B2 (en) | 2017-12-08 | 2022-04-05 | Velodyne Lidar Usa, Inc. | Systems and methods for improving detection of a return signal in a light ranging and detection system |
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US11082010B2 (en) | 2018-11-06 | 2021-08-03 | Velodyne Lidar Usa, Inc. | Systems and methods for TIA base current detection and compensation |
US11885958B2 (en) | 2019-01-07 | 2024-01-30 | Velodyne Lidar Usa, Inc. | Systems and methods for a dual axis resonant scanning mirror |
US10613203B1 (en) | 2019-07-01 | 2020-04-07 | Velodyne Lidar, Inc. | Interference mitigation for light detection and ranging |
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EP0463600A2 (en) * | 1990-06-22 | 1992-01-02 | Matsushita Electric Industrial Co., Ltd. | Method of spectral measurement |
US5260647A (en) * | 1991-09-18 | 1993-11-09 | Hewlett-Packard Company | Measuring an AC signal value with sampling when the sampling interval does not exactly divide the AC signal's period |
US5274569A (en) * | 1991-10-15 | 1993-12-28 | International Business Machines Corporation | Dual sense non-differencing digital peak detector |
US5610827A (en) * | 1994-09-02 | 1997-03-11 | Ssi Technologies, Inc. | Method of and apparatus for peak amplitude detection |
US5818585A (en) * | 1997-02-28 | 1998-10-06 | The United States Of America As Represented By The Secretary Of The Navy | Fiber Bragg grating interrogation system with adaptive calibration |
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US5504318A (en) * | 1991-09-13 | 1996-04-02 | Symbol Technologies, Inc. | Analog waveform decoder using peak locations |
US5365428A (en) * | 1992-01-21 | 1994-11-15 | Quinton Instrument Company | Device and method for reducing number of data sample points sent to a video display system |
JP2826452B2 (en) * | 1993-10-25 | 1998-11-18 | 日立電子株式会社 | Waveform storage device |
US5987392A (en) * | 1997-08-14 | 1999-11-16 | Tucker; Lawrence J. | Wave form peak detector |
-
1998
- 1998-05-29 US US09/087,447 patent/US6529923B2/en not_active Expired - Lifetime
-
1999
- 1999-05-27 WO PCT/US1999/011836 patent/WO1999061925A1/en active Application Filing
- 1999-05-27 CA CA002334281A patent/CA2334281A1/en not_active Abandoned
- 1999-05-27 AU AU42151/99A patent/AU4215199A/en not_active Abandoned
- 1999-05-27 JP JP2000551268A patent/JP2002517029A/en active Pending
- 1999-05-27 GB GB0031567A patent/GB2356060B/en not_active Expired - Lifetime
Patent Citations (5)
Publication number | Priority date | Publication date | Assignee | Title |
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EP0463600A2 (en) * | 1990-06-22 | 1992-01-02 | Matsushita Electric Industrial Co., Ltd. | Method of spectral measurement |
US5260647A (en) * | 1991-09-18 | 1993-11-09 | Hewlett-Packard Company | Measuring an AC signal value with sampling when the sampling interval does not exactly divide the AC signal's period |
US5274569A (en) * | 1991-10-15 | 1993-12-28 | International Business Machines Corporation | Dual sense non-differencing digital peak detector |
US5610827A (en) * | 1994-09-02 | 1997-03-11 | Ssi Technologies, Inc. | Method of and apparatus for peak amplitude detection |
US5818585A (en) * | 1997-02-28 | 1998-10-06 | The United States Of America As Represented By The Secretary Of The Navy | Fiber Bragg grating interrogation system with adaptive calibration |
Cited By (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US6763063B1 (en) | 2000-10-23 | 2004-07-13 | Telefonaktiebolaget Lm Ericsson (Publ) | Peak value estimation of sampled signal |
JP2004096704A (en) * | 2002-08-30 | 2004-03-25 | Ulead Systems Inc | Method of dynamically filtering document |
Also Published As
Publication number | Publication date |
---|---|
GB2356060B (en) | 2002-10-09 |
GB2356060A (en) | 2001-05-09 |
US6529923B2 (en) | 2003-03-04 |
GB0031567D0 (en) | 2001-02-07 |
US20010011289A1 (en) | 2001-08-02 |
AU4215199A (en) | 1999-12-13 |
JP2002517029A (en) | 2002-06-11 |
CA2334281A1 (en) | 1999-12-02 |
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