![Page 1: 1 Rising Noise Level Simulation Henry Skiba. 2 Sinusoid Signal to noise level –SNRdB = 10log 10 SNR Tested range was -60dB to 90db with stepping of 1](https://reader035.vdocument.in/reader035/viewer/2022072010/56649dc95503460f94abfe56/html5/thumbnails/1.jpg)
1
Rising Noise Level Simulation
Henry Skiba
![Page 2: 1 Rising Noise Level Simulation Henry Skiba. 2 Sinusoid Signal to noise level –SNRdB = 10log 10 SNR Tested range was -60dB to 90db with stepping of 1](https://reader035.vdocument.in/reader035/viewer/2022072010/56649dc95503460f94abfe56/html5/thumbnails/2.jpg)
2
• Sinusoid
• Signal to noise level– SNRdB = 10log10SNR
• Tested range was -60dB to 90db with stepping of 1 dB
Generating Signal with Noise
f0 f
f0 ft t
+
t
Signal +Noise
Sinusoid Noise FFT
f0 f
![Page 3: 1 Rising Noise Level Simulation Henry Skiba. 2 Sinusoid Signal to noise level –SNRdB = 10log 10 SNR Tested range was -60dB to 90db with stepping of 1](https://reader035.vdocument.in/reader035/viewer/2022072010/56649dc95503460f94abfe56/html5/thumbnails/3.jpg)
3
Signal Distortion
• Wobble algorithm was used– Standard deviation of velocity was varied
• Three different values ranging from .01 to .10
![Page 4: 1 Rising Noise Level Simulation Henry Skiba. 2 Sinusoid Signal to noise level –SNRdB = 10log 10 SNR Tested range was -60dB to 90db with stepping of 1](https://reader035.vdocument.in/reader035/viewer/2022072010/56649dc95503460f94abfe56/html5/thumbnails/4.jpg)
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Signal Recovery
0 0.5 1 1.5 2 2.5 3-0.02
-0.01
0
0.01
0.02
0.03
0.04
0.05
• DeWobble algorithm used– Recovery bandwidth
estimated with varying standard deviation of velocity
– Example at right is standard deviation of velocity of .1 with -30 SNRdB
• Average relative error was .0279
• Max relative error was .0585
![Page 5: 1 Rising Noise Level Simulation Henry Skiba. 2 Sinusoid Signal to noise level –SNRdB = 10log 10 SNR Tested range was -60dB to 90db with stepping of 1](https://reader035.vdocument.in/reader035/viewer/2022072010/56649dc95503460f94abfe56/html5/thumbnails/5.jpg)
5
Results
• What was used to evaluate effectiveness of deWobble algorithm?– Max and average relative error of recovered
wobble versus actual wobble
![Page 6: 1 Rising Noise Level Simulation Henry Skiba. 2 Sinusoid Signal to noise level –SNRdB = 10log 10 SNR Tested range was -60dB to 90db with stepping of 1](https://reader035.vdocument.in/reader035/viewer/2022072010/56649dc95503460f94abfe56/html5/thumbnails/6.jpg)
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Results
-60 -40 -20 0 20 40 60 80 10010
-6
10-5
10-4
10-3
10-2
10-1
100
101
Standard Dev. is .010 - avg rel err
-60 -40 -20 0 20 40 60 80 10010
-6
10-5
10-4
10-3
10-2
10-1
100
101
Standard Dev. is .050 - avg rel err
-60 -40 -20 0 20 40 60 80 10010
-6
10-5
10-4
10-3
10-2
10-1
100
101
Standard Dev. is .100 - avg rel err
![Page 7: 1 Rising Noise Level Simulation Henry Skiba. 2 Sinusoid Signal to noise level –SNRdB = 10log 10 SNR Tested range was -60dB to 90db with stepping of 1](https://reader035.vdocument.in/reader035/viewer/2022072010/56649dc95503460f94abfe56/html5/thumbnails/7.jpg)
7
Conclusions
• Recovery algorithm begins to work at a SNRdB of 0 with linear improvement up to 60 dB
• No further improvement after 60 dB due to interpolation error
• Least aggressive wobble has worst performance