Laser & Optoelectronics Progress, Volume. 60, Issue 17, 1714008(2023)
Laser Doppler Signal Processing Based on Hybrid Convolution Window
Figures & Tables(25)
Fig. 1. Sidelobe characteristics of various window functions. (a) Blackman Harris window; (b) four-term Nuttall window; (c) four-term RV window; (d) five-term MSD windows
Fig. 3. Spectral lines. (a) Frequency point is close to the spectral line k3; (b) frequency point is close to the spectral line k4; (c) frequency point corresponds to the spectral line; (d) frequency point is in the middle of the two spectral lines
Fig. 4. Ideal signals of LDV. (a) Components of the signal; (b) signal time domain waveform
Fig. 7. Signal spectrograms with different signal-to-noise ratios in the low frequency domain. (a) RSN=+5 dB; (b) RSN= -5 dB; (c) RSN=-10 dB; (d) RSN=-15 dB
Fig. 8. Comparison of absolute errors of signal frequency detection with different signal-to-noise ratios in low frequency domain
Fig. 9. Signal spectrograms with different signal-to-noise ratios in the high frequency domain. (a) RSN=+5 dB; (b) RSN= -5 dB;(c) RSN= -10 dB; (d) RSN= -15 dB
Fig. 10. Comparison of absolute errors of signal frequency detection with different signal-to-noise ratios in low frequency domain
Table 1. Accuracy comparison of frequency detection in low frequency range
View tableTable 1. Accuracy comparison of frequency detection in low frequency range
No. Frequency /kHz Arithmetic mean error of frequency detection /Hz Method 1 Method 2 Method 3 Method 4 1 60 0.14612 0.03394 0.00311 0.00043 2 120 0.21278 0.05835 0.00570 0.00044 3 180 0.28677 0.06641 0.00946 0.00089 4 240 0.51563 0.11426 0.00709 0.00043 5 300 0.28149 0.06543 0.00928 0.00071 6 360 0.51563 0.11182 0.00803 0.00083 7 420 0.27638 0.06445 0.01013 0.00148 8 480 0.55653 0.10938 0.00791 0.00074 9 540 0.50886 0.06299 0.01247 0.00198 10 600 0.70963 0.10742 0.01038 0.00099 11 660 0.89343 0.06377 0.01201 0.00132 12 720 0.80304 0.06096 0.00916 0.00116 13 780 0.85076 0.06128 0.00707 0.00109 14 840 0.59613 0.05695 0.00713 0.00197 15 900 0.59272 0.06997 0.01402 0.00198
Table 2. Accuracy comparison of frequency detection in high frequency range
View tableTable 2. Accuracy comparison of frequency detection in high frequency range
No. Frequency /MHz Arithmetic mean error of frequency detection /Hz Method 1 Method 2 Method 3 Method 4 1 60 352.58333 85.10400 5.24102 0.56917 2 120 501.79167 101.60000 11.12227 0.63840 3 180 750.15000 111.82080 11.27520 0.64300 4 240 537.40350 118.33333 12.72240 1.21042 5 300 884.41500 236.29760 28.78092 1.35044 6 360 597.87011 178.52800 18.16214 1.72480 7 420 898.27500 194.54400 29.65572 1.23250 8 480 630.36000 108.39600 15.76973 1.46664 9 540 973.89021 268.07760 28.61121 1.02708 10 600 602.56000 208.08000 16.52556 2.00390 11 660 917.64000 266.31360 31.96869 1.38240 12 720 811.15043 157.22100 19.10038 3.52998 13 780 1289.40000 219.13920 21.50608 2.37312 14 840 805.75000 177.69600 27.56436 2.48270 15 900 902.55010 247.39200 27.11180 3.56040
Table 3. Comparison of absolute errors of signal frequency detection with different signal-to-noise ratios in low frequency domain
View tableTable 3. Comparison of absolute errors of signal frequency detection with different signal-to-noise ratios in low frequency domain
No. Frequency /kHz Arithmetical mean of error /Hz RSN=+5 dB RSN=-5 dB RSN=-10 dB RSN=-15 dB 1 60 0.00010 0.19175 1.91040 311.33200 2 120 0.00013 0.35768 1.55472 307.64800 3 180 0.00017 0.41007 2.97344 1847.73040 4 240 0.00027 0.74996 2.01240 1923.08880 5 300 0.00017 0.56809 1.59552 1815.69040 6 360 0.00028 0.41415 4.99992 1938.87440 7 420 0.00020 0.73958 11.77808 861.35548 8 480 0.00025 0.90391 9.94064 870.19822 9 540 0.00035 1.19215 19.06470 745.90264 10 600 0.00029 0.93306 10.10534 731.23548 11 660 0.00043 1.18215 30.13222 583.45921 12 720 0.00035 0.93405 26.01698 472.77065 13 780 0.00038 1.12902 21.44346 588.97846 14 840 0.00042 1.11308 26.87693 950.60786 15 900 0.00045 1.05872 30.75494 882.29743
Table 4. Comparison of absolute errors of signal frequency detection with different signal-to-noise ratios in high frequency domain
View tableTable 4. Comparison of absolute errors of signal frequency detection with different signal-to-noise ratios in high frequency domain
No. Frequency /MHz Arithmetical mean of error /Hz RSN =+5 dB RSN=-5 dB RSN=-10 dB RSN=-15 dB 1 60 0.41691 300.48639 1509.27371 454325.23911 2 120 0.49814 338.76866 1228.59782 1768065.17692 3 180 0.92389 526.98932 1369.85067 2385840.38721 4 240 0.97161 405.18828 9136.98548 558740.56227 5 300 0.63717 422.34939 9411.28992 521070.28999 6 360 1.06819 516.84130 9580.61613 446435.45613 7 420 0.79913 786.61318 6553.47962 1287100.12932 8 480 1.04420 531.24111 3526.26674 1313235.31676 9 540 0.97155 574.56118 3147.99428 935988.91351 10 600 0.58315 607.62123 6279.61570 558740.60196 11 660 0.89542 622.92420 9411.28991 521070.30481 12 720 1.10816 796.86612 9580.67975 446435.60156 13 780 0.84019 814.86427 8419.41077 2101635.54417 14 840 1.06821 612.24224 2350.84414 1313235.31558 15 900 0.99453 612.24617 2098.62523 2385350.23874
Table 5. Precision comparisons in low frequency range
View tableTable 5. Precision comparisons in low frequency range
No. Frequency /kHz Arithmetical mean of error /Hz FFT Method 1 Method 2 Method 3 Method4 1 64.5264 4194.14941 4.70772 1.93381 0.32256 0.14568 2 123.1934 4152.20793 7.81245 3.47223 0.56742 0.27769 3 181.8604 4110.68583 8.14860 3.98346 0.84420 0.30182 4 240.5273 4069.57892 11.63889 6.20820 1.20541 0.50791 5 299.1943 4028.88316 15.33006 7.31160 1.59180 0.71136 6 357.8613 3988.59433 13.71006 8.38440 1.42384 0.84032 7 416.5283 3948.70831 17.15013 8.40424 1.77663 0.76533 8 475.1953 3909.22123 18.90783 10.10342 1.96140 1.00400 9 528.9795 3870.12924 20.66472 12.84120 2.15043 0.99814 10 587.6465 3831.42774 24.07887 12.97624 2.49912 0.95342 11 646.3135 3793.11352 22.45887 13.73043 2.33120 1.42140 12 704.9805 3755.18236 25.74423 13.40101 2.67124 1.36353 13 763.6475 3717.63057 29.05551 14.20563 2.84346 1.29140 14 822.3145 3680.45421 32.28012 17.21520 3.17943 1.43463 15 880.9814 3643.64973 33.88392 19.57682 3.51544 1.75682
Table 6. Precision comparisons in high frequency range
View tableTable 6. Precision comparisons in high frequency range
No. Frequency /MHz Arithmetical mean of error /Hz FFT Method 1 Method2 Method3 Method4 1 54.7852 3808593.75686 3997.02938 2036.72159 343.86209 176.33953 2 113.4277 3759765.63471 6352.98234 3237.21821 546.54333 280.27863 3 172.0703 3710937.53730 11860.12172 5385.60410 1020.31929 523.24066 4 230.7129 3662109.38275 17203.43953 6876.16441 1480.00178 641.10807 5 289.3555 3613281.25344 14531.78766 7404.80062 1250.16114 717.94732 6 347.9980 3564453.13781 19756.84712 10067.27940 1699.66994 871.62561 7 416.4063 3515625.69218 24762.72983 12618.06748 2130.32308 1092.47338 8 475.0488 3466796.88477 22310.24485 11368.38211 2949.41357 984.27551 9 528.8086 3417968.75109 27215.20969 13867.75023 2750.42503 1200.67102 10 587.4512 3369140.63511 29592.98431 15079.36627 2279.33724 1305.57284 11 646.0938 3320312.51726 34283.78167 17469.60345 2341.30848 1512.51978 12 704.7363 3271484.38414 31970.75250 16290.97903 2545.86703 1410.47438 13 763.3789 3222656.25844 36596.80313 18648.22394 3148.40145 1614.56484 14 822.0215 3173828.13282 38856.96480 19799.90684 3342.84141 1714.27765 15 880.6641 3125000.11710 41117.10844 20951.58540 3537.28065 1813.99008
Table 7. Relative error averages in the low and high frequency ranges
View tableTable 7. Relative error averages in the low and high frequency ranges
Item Method 1 Method 2 Method 3 Method 4 Low frequency 0.0044 0.00229 0.00043 0.00020 High frequency 0.0055 0.00273 0.00048 0.00024
Table 8. Main parameters of APD 430A/M
View tableTable 8. Main parameters of APD 430A/M
Wavelength range /nm Output
bandwidth /MHz
Active area
diameter /mm
Input optical power range / 400‒1000 400 0.5 8‒80
Table 9. Processing results of measured signals
View tableTable 9. Processing results of measured signals
No. Reference
speed /（m·s-1）
Arithmetical mean of error /（m·s-1） Method 1 Method 2 Method 3 Method 4 1 0.5415 1.58518×10-4 8.67780×10-5 1.88374×10-5 1.15203×10-5 2 0.5898 1.79469×10-4 9.70299×10-5 1.93083×10-5 1.18081×10-5 3 0.6377 2.15047×10-4 9.78912×10-5 1.91513×10-5 1.17123×10-5 4 0.7056 2.60572×10-4 9.86931×10-5 1.93083×10-5 1.18080×10-5 5 0.7683 3.14231×10-4 1.03356×10-4 2.15460×10-5 1.19047×10-5 6 0.8675 3.67119×10-4 1.12973×10-4 2.58036×10-5 1.26724×10-5 7 0.9369 3.10047×10-4 1.25720×10-4 2.78561×10-5 1.36800×10-5 8 0.9897 3.36604×10-4 1.31654×10-4 2.89313×10-5 1.77600×10-5 9 1.0425 2.69283×10-4 1.17746×10-4 3.56754×10-5 1.96536×10-5 10 1.0832 2.67506×10-4 1.04587×10-4 3.69357×10-5 2.15417×10-5 11 1.1238 2.56270×10-4 1.07916×10-4 4.29600×10-5 2.21475×10-5 12 1.1605 2.71244×10-4 1.36797×10-4 4.76400×10-5 2.38255×10-5 13 1.1972 2.48648×10-4 1.43981×10-4 4.76400×10-5 2.38213×10-5 14 1.2492 2.39082×10-4 1.57070×10-4 4.77600×10-5 2.38846×10-5 15 1.2971 2.51415×10-4 1.70160×10-4 4.81200×10-5 2.40676×10-5
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Hao Chen, Da Zhang. Laser Doppler Signal Processing Based on Hybrid Convolution Window[J]. Laser & Optoelectronics Progress, 2023, 60(17): 1714008
Paper Information
Category: Lasers and Laser Optics
Received: Jul. 13, 2022
Accepted: Sep. 28, 2022
Published Online: Sep. 13, 2023
The Author Email: Hao Chen (chenhaoqyl1325@163.com)
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