Further Discussions and Beyond EE630 Further Discussions and Beyond - PowerPoint PPT Presentation

End of Semester Logistics End of Semester Logistics g  Project due Further Discussions and Beyond EE630 Further Discussions and Beyond EE630  Final exam: two hours, close book/notes – Mainly cover Part-2 and Part-3 – May involve basic multirate concepts from Part-1 Electrical & Computer Engineering p g g (decimation, expansion, basic filter bank) (d i ti i b i filt b k) University of Maryland, College Park  Office hours Acknowledgment: The ENEE630 slides here were made by Prof. Min Wu. Contact: minwu@umd.edu @ UMD ENEE630 Advanced Signal Processing UMD ENEE630 Advanced Signal Processing (v.1212) Discussions [2] m th th –order Moments of A Random Variable Higher Higher- -Order Signal Analysis: Brief Introduction Order Signal Analysis: Brief Introduction order Moments of A Random Variable  Moments:  m k = E[ X k ];  Information contained in the power spectrum  Central moments: subtract the mean  k = E[ (X   X ) k ] Central moments: subtract the mean  k  X ) ] – Reflect the 2 nd -order statistics of a signal (i.e. autocorrelation) g ( ) E[ (X => Power spectrum is sufficient for complete statistical description o Mean:  X = m 1 = E[X] of a Gaussian process, but not so for many other processes – Statistical centroid (“center of gravity”) ( g y )  Motivation for higher-order statistics o Variance:  X 2 =  2 = E[ (X -  X ) 2 ] – Higher-order statistics contain additional info. to measure the – Describe the spread/dispersion of the p.d.f. deviation of a non-Gaussian process from normality deviation of a non Gaussian process from normality o 3 rd Moment: normalize into K 3 =  3 /  X 3 – Help suppress Gaussian noise of unknown spectral characteristics. – Represent Skewness of p.d.f.  zero for symmetric p.d.f.  The higher-order spectra m ay becom e high SNR dom ains in w hich 4  3 one can perform detection, param eter estim ation, or signal o 4 th Moment: normalize into K 4 =  4 /  X reconstruction – “Kurtosis” for flat/peakiness deviation from Gaussian p.d.f. – Help identify a nonlinear system or to detect and characterize (which is zero) (which is zero) nonlinearities in a time series See Manolakis Sec.3.1.2 for further discussions UMD ENEE630 Advanced Signal Processing (v.1212) Frequency estimation [3] UMD ENEE630 Advanced Signal Processing (v.1212) Frequency estimation [4]

Relations Among 3+ Samples of a Random Process Relations Among 3+ Samples of a Random Process  Generalize from autocorrelation function between a pair of samples for a zero-mean stationary random process  Triplets of samples: 3 rd order cumulant d f  Quadruplets of samples: 4 th order cumulant First five cumulants for zero-mean r.v. ( Figures/Equations are from Manolakis Book Section 3.1; Note – moments of 3 rd and above for Gaussian moments of 3 rd and abo e for Ga ssian Note can be expressed in terms of  and  .) UMD ENEE630 Advanced Signal Processing (v.1212) Discussions [5] UMD ENEE630 Advanced Signal Processing (v.1212) Frequency estimation [7] [ Eq. from Manolakis Book Section 12.1 ] High High- -order Spectra order Spectra  Multi-variable DTFT on cumulant functions – Bispectrum & Trispectrum: may exhibit patterns in magnitude & phase  Extend properties under LTI to high-order stats See Manolakis et al. McGraw Hill book “Statistical & Adaptive S.P.” Sec.12.1 High-order statistics for further discussions UMD ENEE630 Advanced Signal Processing (v.1212) Discussions [8] UMD ENEE630 Advanced Signal Processing (v.1212) Discussions [9] [ Eq. from Manolakis Book Section 12.1 ]

Resource on Signal Processing Resource on Signal Processing Related Courses Beyond EE630 Related Courses Beyond EE630  IEEE Signal Processing Magazine  Adaptive and space-time signal processing: ENEE634* – E-copy on IEEE Xplore; Hard-copy by student membership E copy on IEEE Xplore; Hard copy by student membership  Image/video & audio/speech processing: ENEE631*, 632  IEEE “Inside Signal Processing eNewsletter” http:/ / signalprocessingsociety.org/ newsletter/ p / / g p g y g/ /  Detection/estimation & information theory: ENEE621 , 627  Detection/estimation & information theory: ENEE621* 627*  See also SP for digital com m unication in ENEE623  Signal Processing related journals/transactions  Pattern recognition and machine learning: ENEE633 P tt iti d hi l i ENEE633  Related conferences: ICASSP, ICIP, etc.  Special topic courses and seminars in signal processing: Special topic courses and seminars in signal processing:  Additional 2-cents beyond courses Occasionally offered. – Attend talks/seminars to broaden your vision E.g. on info forensics & multimedia security, compressive sensing, etc. – Oral communications (oral exams, presentations, etc) O l i ti ( l t ti t )  See also related applied math and statistics courses UMD ENEE630 Advanced Signal Processing (v.1212) Discussions [10] UMD ENEE630 Advanced Signal Processing (v.1212) Discussions [11] Digital Image and Video Processing (ENEE631) Digital Image and Video Processing (ENEE631)  Human visual perception; color vision  Image enhancement  Image restoration g  Image transform, quantization and coding  Motion analysis and video coding Figure is from slides at Gonzalez/ Woods  Feature extraction and analysis Feature extraction and analysis DIP book website (Chapter 8). Use “previous pixel  Security and forensic issues predictor”. Difference image has mid-range gray representing zero and amplifying …… factor of 8. UMD ENEE630 Advanced Signal Processing (v.1212) Discussions [12] UMD ENEE630 Advanced Signal Processing (v.1212) Discussions [13]

Forensic Question on “Time” and “Place” Ubiquitous Forensic Fingerprints from Power Grid 600 0.9 -80 500 -20 600 0.8 500 -90 -80 efficient 0.7 -100 onds) 400 -40 nds) 400 500 500 -90 90 Time (in seco Time (in seco Correlation co -110 0.6 300 -60 300 -100 -120 0.5 m e (in seconds) 400 200 200 -130 -80 0.4 -110 -140 300 100 0.3 100 -100 -120 -150 Tim -30 30 -20 20 -10 10 0 0 10 10 20 20 30 30 9.6 10 10.4 10.8 49.5 50 50.5 51 51.5 -130 Time frame lag 200 Frequency (in Hz) Frequency (in Hz) Video ENF signal Normalized correlation Power ENF signal -140 100 -150 ENF matching result demonstrating similar variations in the ENF 9.6 9 6 10 10 10 4 10.4 10 8 10.8 signal extracted from video and from power signal recorded in India Frequency (in Hz)  When was the video actually shot? And where? Electric Network Frequency (ENF): 50/60 Hz nominal   Was the sound track captured at the same time as the  Was the sound track captured at the same time as the Varies slightly over time; main trends consistent in same grid Varies slightly over time; main trends consistent in same grid   picture? Or super-imposed afterward? Can be “seen” or “heard” in sensor recordings  Help determine recording time, detect tampering, etc.   Explore the fingerprint influenced by power grid onto  Explore the fingerprint influenced by power grid onto Other potential applications on smart grid & media management  sensor recordings  Ref: Garg et al. ACM Multimedia 2011, CCS 2012 and APSIPA 2012 UMD ENEE630 Advanced Signal Processing (v.1212) Aliasing Revisit: Aliasing Revisit: Downsample Downsample A Sinusoid A Sinusoid Tampering Detection Using ENF Tampering Detection Using ENF ENF matching result demonstrating the detection of video tampering based on the ENF traces ENF signal from Video equency (in Hz) 10.3 10.2 10.1 Inserted Fre 10 10 clip li 160 320 480 640 800 960 Time (in seconds) Ground truth ENF signal n Hz) 50.2 Frequency (in 50.1 50 49.9 160 320 480 640 800 Ti Time (in seconds) (i d ) “If the RF signal [white] is not sampled at least twice per cycle, aliasing will occur.  Adding a clip between the original video leads to discontinuity in But by properly adjusting the sampling interval [indicated by vertical lines], you can the ENF signal extracted from video down-convert the RF to whatever lower frequency is desired [blue and yellow].”  Clip insertion can also be detected by comparing the video ENF Cli i ti l b d t t d b i th id ENF IEEE Spectrum Magazine April 2009 “Universal Handset” – Alias Harnessed for software-defined radio signal with the power ENF signal at corresponding time http://spectrum.ieee.org/computing/embedded-systems/the-universal-handset/0/cellsb01 16 16 UMD ENEE630 Advanced Signal Processing (v.1212) Discussions [17] UMD ENEE630 Advanced Signal Processing (v.1212)