detection and estimation theory - mojtaba soltanalian 17.pdfbinary detection: determine whether a...

Detection and Estimation Theory Lectures 17 Mojtaba Soltanalian- UIC [email protected] http://msol.people.uic.edu Based on ECE 531 Slides- 2011 (Prof. Natasha Devroye) & http://ens.ewi.tudelft.nl/Education/courses/et4386/Slides/09.detection.pdf

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Detection and Estimation Theory

Lectures 17

Mojtaba Soltanalian- [email protected]

http://msol.people.uic.edu

Based on ECE 531 Slides- 2011 (Prof. Natasha Devroye) & http://ens.ewi.tudelft.nl/Education/courses/et4386/Slides/09.detection.pdf

mailto:[email protected]

http://msol.people.uic.edu/

Page 2: Detection and Estimation Theory - Mojtaba Soltanalian 17.pdfBinary detection: Determine whether a certain signal that is embedded in noise is present or not. Ho x[n] w [n] HI x[n]

Detection Theory

Page 3: Detection and Estimation Theory - Mojtaba Soltanalian 17.pdfBinary detection: Determine whether a certain signal that is embedded in noise is present or not. Ho x[n] w [n] HI x[n]

Detection Theory

Examples: Radar

Page 4: Detection and Estimation Theory - Mojtaba Soltanalian 17.pdfBinary detection: Determine whether a certain signal that is embedded in noise is present or not. Ho x[n] w [n] HI x[n]

Detection Theory

Examples: Digital Communication

Page 5: Detection and Estimation Theory - Mojtaba Soltanalian 17.pdfBinary detection: Determine whether a certain signal that is embedded in noise is present or not. Ho x[n] w [n] HI x[n]

Detection Theory

Examples: Speech Processing

Page 6: Detection and Estimation Theory - Mojtaba Soltanalian 17.pdfBinary detection: Determine whether a certain signal that is embedded in noise is present or not. Ho x[n] w [n] HI x[n]

Detection Theory

Examples: Tests in Medicine

Page 7: Detection and Estimation Theory - Mojtaba Soltanalian 17.pdfBinary detection: Determine whether a certain signal that is embedded in noise is present or not. Ho x[n] w [n] HI x[n]

Statistical Detection Theory

Neyman-Pearson Theorem

Page 8: Detection and Estimation Theory - Mojtaba Soltanalian 17.pdfBinary detection: Determine whether a certain signal that is embedded in noise is present or not. Ho x[n] w [n] HI x[n]

Statistical Detection Theory

Neyman-Pearson Theorem

Page 9: Detection and Estimation Theory - Mojtaba Soltanalian 17.pdfBinary detection: Determine whether a certain signal that is embedded in noise is present or not. Ho x[n] w [n] HI x[n]

Statistical Detection Theory

Neyman-Pearson Theorem

Page 10: Detection and Estimation Theory - Mojtaba Soltanalian 17.pdfBinary detection: Determine whether a certain signal that is embedded in noise is present or not. Ho x[n] w [n] HI x[n]

Statistical Detection Theory

Receiver Operating Characteristic (ROC)

Page 11: Detection and Estimation Theory - Mojtaba Soltanalian 17.pdfBinary detection: Determine whether a certain signal that is embedded in noise is present or not. Ho x[n] w [n] HI x[n]

Statistical Detection Theory

Receiver Operating Characteristic (ROC)

Page 12: Detection and Estimation Theory - Mojtaba Soltanalian 17.pdfBinary detection: Determine whether a certain signal that is embedded in noise is present or not. Ho x[n] w [n] HI x[n]

Detection Theory

- For -

Deterministic Signals

Page 13: Detection and Estimation Theory - Mojtaba Soltanalian 17.pdfBinary detection: Determine whether a certain signal that is embedded in noise is present or not. Ho x[n] w [n] HI x[n]

Known Signal in Gaussian Noise

>>> Matched Filter

Page 14: Detection and Estimation Theory - Mojtaba Soltanalian 17.pdfBinary detection: Determine whether a certain signal that is embedded in noise is present or not. Ho x[n] w [n] HI x[n]

>>> Matched Filter

a.k.a. Correlator, or Replica-Correlator

Page 15: Detection and Estimation Theory - Mojtaba Soltanalian 17.pdfBinary detection: Determine whether a certain signal that is embedded in noise is present or not. Ho x[n] w [n] HI x[n]

>>> Matched Filter

a.k.a. Correlator, or Replica-Correlator

The matched filter maximizes output SNR of the detector

(over all linear filters):

Page 16: Detection and Estimation Theory - Mojtaba Soltanalian 17.pdfBinary detection: Determine whether a certain signal that is embedded in noise is present or not. Ho x[n] w [n] HI x[n]

Performance of Matched Filter

Page 17: Detection and Estimation Theory - Mojtaba Soltanalian 17.pdfBinary detection: Determine whether a certain signal that is embedded in noise is present or not. Ho x[n] w [n] HI x[n]

Generalized Matched Filter

Page 18: Detection and Estimation Theory - Mojtaba Soltanalian 17.pdfBinary detection: Determine whether a certain signal that is embedded in noise is present or not. Ho x[n] w [n] HI x[n]

Generalized Matched Filter

-- Prewhitening

Page 19: Detection and Estimation Theory - Mojtaba Soltanalian 17.pdfBinary detection: Determine whether a certain signal that is embedded in noise is present or not. Ho x[n] w [n] HI x[n]

Performance of Generalized Matched Filters

Page 20: Detection and Estimation Theory - Mojtaba Soltanalian 17.pdfBinary detection: Determine whether a certain signal that is embedded in noise is present or not. Ho x[n] w [n] HI x[n]

Signal Design of Generalized Matched Filters

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