20

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

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]

Download PDF Report

Upload
others
View
1
Download
0

Embed Size (px)

Citation preview

Page 1: 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 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

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

Hint: Q (.) is a decreasing function …

N SIAMREVIEW N The AlgorithmRevisited N · N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N

N SIAMREVIEW N The AlgorithmRevisited N · N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N

Documents

ABSTRACT H arXiv:2002.01053v3 [cs.CV] 7 Jun 2020 · Chirag Agarwal, Shahin Khobahi, Arindam Bose, Mojtaba Soltanalian, Dan Schonfeld Department of Electrical & Computer Engineering,

ABSTRACT H arXiv:2002.01053v3 [cs.CV] 7 Jun 2020 · Chirag Agarwal, Shahin Khobahi, Arindam Bose, Mojtaba Soltanalian, Dan Schonfeld Department of Electrical & Computer Engineering,

Documents

Trends in Amplification Volume 12 Number 4 …web.cse.ohio-state.edu/~wang.77/papers/Wang.tia08.pdfbinary weight matrix to the mixture in the T-F domain (Weintraub, 1985; see also

Trends in Amplification Volume 12 Number 4 …web.cse.ohio-state.edu/~wang.77/papers/Wang.tia08.pdfbinary weight matrix to the mixture in the T-F domain (Weintraub, 1985; see also

Documents

W ATER QU L IY C SF ON PLYMOU TH, Ccteco.uconn.edu/maps/town/wtrqualcl/WtrQualCl_Plymouth.pdf · !n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!o!n!n!n!n!n!n!n!n!n!n!4!n!n!n!n!n!n!n!n!n!n!n H!n!n!n!n!n!n!n!o!n!n!n

W ATER QU L IY C SF ON PLYMOU TH, Ccteco.uconn.edu/maps/town/wtrqualcl/WtrQualCl_Plymouth.pdf · !n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!o!n!n!n!n!n!n!n!n!n!n!4!n!n!n!n!n!n!n!n!n!n!n H!n!n!n!n!n!n!n!o!n!n!n

Documents

Vbinary: variable length integer coding revisitedpsta.psiras.ru/read/psta2018_4_239-252.pdfbinary 5 5 5 5 32 Unary 1 8.5 8 17 unlimited Elias 1 5.94 7 9 unlimited Elias 1 6.53 8 9

Vbinary: variable length integer coding revisitedpsta.psiras.ru/read/psta2018_4_239-252.pdfbinary 5 5 5 5 32 Unary 1 8.5 8 17 unlimited Elias 1 5.94 7 9 unlimited Elias 1 6.53 8 9

Documents

Covariance Matrix Estimation - Mojtaba Soltanalian

Covariance Matrix Estimation - Mojtaba Soltanalian

Documents

digilib.uns.ac.id/WABAH... · perpustakaanyunyayid n digilibyunyayid n n n n n n n n n n n n n n n n n n n n N N N N N N N N N N N N N N N N N N N N N N N N commit to user WABAH PENYAKIT

digilib.uns.ac.id/WABAH... · perpustakaanyunyayid n digilibyunyayid n n n n n n n n n n n n n n n n n n n n N N N N N N N N N N N N N N N N N N N N N N N N commit to user WABAH PENYAKIT

Documents

ACTA UNIVERSITATIS UPSALIENSIS Uppsala Dissertations from ...741349/FULLTEXT01.pdf · Soltanalian, M. 2014. Signal Design for Active Sensing and Communications. Uppsala Dissertations

ACTA UNIVERSITATIS UPSALIENSIS Uppsala Dissertations from ...741349/FULLTEXT01.pdf · Soltanalian, M. 2014. Signal Design for Active Sensing and Communications. Uppsala Dissertations

Documents

Dissipation-Induced HeteroclinicOrbitsinTippeTops · N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N

Dissipation-Induced HeteroclinicOrbitsinTippeTops · N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N

Documents

Trees Family Tree - ERNETlcm.csa.iisc.ernet.in/esc101/MJT/ProgAlgs-2.pdfBinary Tree Definition: A binary tree is either empty or consists of a node called the root together with 2

Trees Family Tree - ERNETlcm.csa.iisc.ernet.in/esc101/MJT/ProgAlgs-2.pdfBinary Tree Definition: A binary tree is either empty or consists of a node called the root together with 2

Documents

Fall 2019 Mojtaba Soltanalian

Fall 2019 Mojtaba Soltanalian

Documents

Mean Field Competitive Binary MDPs and Structured Solutionshelper.ipam.ucla.edu/publications/mfg2017/mfg2017_14526.pdfBinary choice models are widely used in various decision problems

Mean Field Competitive Binary MDPs and Structured Solutionshelper.ipam.ucla.edu/publications/mfg2017/mfg2017_14526.pdfBinary choice models are widely used in various decision problems

Documents

Ch 15. Binary Search Trees - Seoul National Universityocw.snu.ac.kr/sites/default/files/NOTE/491.pdfBinary Search Trees ©copyright 2006 SNU IDB Lab. 2 SNU Data Structures IDBLab

Ch 15. Binary Search Trees - Seoul National Universityocw.snu.ac.kr/sites/default/files/NOTE/491.pdfBinary Search Trees ©copyright 2006 SNU IDB Lab. 2 SNU Data Structures IDBLab

Documents

Efficient Multiple and Predicate Dispatchingdefude/P2P/PAPIERS/chambers99.pdfbinary decision tree blending class identity tests, class range tests, ... compiled by the Vortex optimizing

Efficient Multiple and Predicate Dispatchingdefude/P2P/PAPIERS/chambers99.pdfbinary decision tree blending class identity tests, class range tests, ... compiled by the Vortex optimizing

Documents

30 and Towns...n n n n n n n n n n n n n n n n n n n n n n nn n n n n n n n nn n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n

30 and Towns...n n n n n n n n n n n n n n n n n n n n n n nn n n n n n n n nn n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n

Documents

Binary Search Tree - UTM OpenCoursewareocw.utm.my/file.php/31/Module/ocwSearchTreeDec2011.pdfbinary search tree operation is the number of nodes along the longest path from root to

Binary Search Tree - UTM OpenCoursewareocw.utm.my/file.php/31/Module/ocwSearchTreeDec2011.pdfbinary search tree operation is the number of nodes along the longest path from root to

Documents

CSC 344 – Algorithms and Complexitysiegfried/cs344/344l5.pdfBinary Search (A Decrease and Conquer Algorithm) • Very efficient algorithm for searching in sorted array: – K vs

CSC 344 – Algorithms and Complexitysiegfried/cs344/344l5.pdfBinary Search (A Decrease and Conquer Algorithm) • Very efficient algorithm for searching in sorted array: – K vs

Documents

Two Components Systemnanowires.berkeley.edu/teaching/253a/2014/253A-201407.pdfBinary Isomorphous System Phase present Point A - Point B - + L Mutually soluble in solid State Mutually

Two Components Systemnanowires.berkeley.edu/teaching/253a/2014/253A-201407.pdfBinary Isomorphous System Phase present Point A - Point B - + L Mutually soluble in solid State Mutually

Documents

An Experimental Analysis of a Compact Graph …people.csail.mit.edu/jshun/6886-s18/lectures/lecture12-1.pdfbinary code for its offset Snip, Nibble, and Byte codes (Turns out Byte codes

An Experimental Analysis of a Compact Graph …people.csail.mit.edu/jshun/6886-s18/lectures/lecture12-1.pdfbinary code for its offset Snip, Nibble, and Byte codes (Turns out Byte codes

Documents

CONTOUR MAP - CT ECO Homecteco.uconn.edu/maps/town/Contour_Map/Contour_Map_Hartford.pdf · !4!4!4!4!4!4!4!4!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n

CONTOUR MAP - CT ECO Homecteco.uconn.edu/maps/town/Contour_Map/Contour_Map_Hartford.pdf · !4!4!4!4!4!4!4!4!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n

Documents

n n n n n n n n n n n n n n n n

n n n n n n n n n n n n n n n n

Documents

Binary Puzzles as an Erasure Decoding Problem - TU/eruudp/paper/72.pdfBinary Puzzles as an Erasure Decoding Problem ... (J. Roland, F. Horlin. Eds.) pp. 129-134, ... is well established

Binary Puzzles as an Erasure Decoding Problem - TU/eruudp/paper/72.pdfBinary Puzzles as an Erasure Decoding Problem ... (J. Roland, F. Horlin. Eds.) pp. 129-134, ... is well established

Documents

QáO - Tomioka...N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N

QáO - Tomioka...N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N

Documents

Detection and Estimation Theory - Mojtaba Soltanalian 19.pdfDetection and Estimation Theory Lectures 19 Mojtaba Soltanalian- UIC msol@uic.edu

Detection and Estimation Theory - Mojtaba Soltanalian 19.pdfDetection and Estimation Theory Lectures 19 Mojtaba Soltanalian- UIC [email protected]

Documents

W ATER QU L IY C SF ON CHESHIRE, CT Hcteco.uconn.edu/maps/town/wtrqualcl/WtrQualCl_Cheshire.pdf · !n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!4!n!n!n H!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!o!n!n!n!n!n!n!n

W ATER QU L IY C SF ON CHESHIRE, CT Hcteco.uconn.edu/maps/town/wtrqualcl/WtrQualCl_Cheshire.pdf · !n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!4!n!n!n H!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!o!n!n!n!n!n!n!n

Documents

unizar.espcmap.unizar.es/.../publicaciones/joseluis/universality.pdfN N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N

unizar.espcmap.unizar.es/.../publicaciones/joseluis/universality.pdfN N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N N

Documents

UConn CT ECOcteco.uconn.edu/maps/town/apa/apa_NewBritain.pdf · 2019. 8. 26. · !n!n!n!n!n!n!n!n!n!n!n!n!n!4!n!n!n!n!n! n!n!n!n!H!n!n!n!n!n!n!n!H!n!H!n!n !n!n!n!n!n!H!n!4!n!n!n!n!n!n!n!n!4!n!n!^!n!n!n!n!H!n!n!n!n!n!n!n!n!n

UConn CT ECOcteco.uconn.edu/maps/town/apa/apa_NewBritain.pdf · 2019. 8. 26. · !n!n!n!n!n!n!n!n!n!n!n!n!n!4!n!n!n!n!n! n!n!n!n!H!n!n!n!n!n!n!n!H!n!H!n!n !n!n!n!n!n!H!n!4!n!n!n!n!n!n!n!n!4!n!n!^!n!n!n!n!H!n!n!n!n!n!n!n!n!n

Documents

WATER QUALITY CLASSIFICATIONS EAS TON, Ccteco.uconn.edu/maps/town/wtrqualcl/WtrQualCl_Easton.pdf · !n!n!n H!n!n!n!n!n!n!n Ã!!n!n!o!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n Ã!!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!4!n!n!n!n!n

WATER QUALITY CLASSIFICATIONS EAS TON, Ccteco.uconn.edu/maps/town/wtrqualcl/WtrQualCl_Easton.pdf · !n!n!n H!n!n!n!n!n!n!n Ã!!n!n!o!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n Ã!!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!n!4!n!n!n!n!n

Documents

A LOCK FOR EVERY LOOK. - Kirsch Millwork€¦ · Camelot n n n n n n n n n Century n n n n n n n Collins n Greenwich n n n n n Greyson* n n n n n n Upland* n Wakefield n n n n n n

A LOCK FOR EVERY LOOK. - Kirsch Millwork€¦ · Camelot n n n n n n n n n Century n n n n n n n Collins n Greenwich n n n n n Greyson* n n n n n n Upland* n Wakefield n n n n n n

Documents

RNA secondary structure prediction and analysis02710/Lectures/RNALecture2015.pdfBinary Tree Representation of RNA Secondary Structure •Representation of RNA structure using Binary

RNA secondary structure prediction and analysis02710/Lectures/RNALecture2015.pdfBinary Tree Representation of RNA Secondary Structure •Representation of RNA structure using Binary

Documents