EXTENTION OF THE MUSIC ALGORITHM TO AM-FM SIGNALSusers.rowan.edu/~bouaynaya/Nidhal_UG_10.pdf ·...
Transcript of EXTENTION OF THE MUSIC ALGORITHM TO AM-FM SIGNALSusers.rowan.edu/~bouaynaya/Nidhal_UG_10.pdf ·...
EXTENTION OF THE MUSIC ALGORITHM TO AM-FM SIGNALSChristina Dunlap
Advisor: Dr. Nidhal BouaynayaDepartment of Systems Engineering, University of Arkansas at Little Rock
ABSTRACTABSTRACTTheThe goalgoal ofof thisthis projectproject isis toto extendextend thethe stationarystationaryMUltipleMUltiple SIgnalSIgnal ClassificationClassification (MUSIC)(MUSIC) algorithmalgorithmtoto nonnon--stationarystationary AmplitudeAmplitude andand FrequencyFrequencyModulatedModulated (AM(AM--FM)FM) signalssignals..Classical approaches to amplitude and frequency 1
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Noisy Frequency Modulated Signal
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THE EFFECT OF NOISETHE EFFECT OF NOISE BIOLOGICAL APPLICATIONBIOLOGICAL APPLICATIONThe proposed algorithm will be assessed using the AM-FMN calcium signaling response in lymphocite cells [1].AM-FM signaling modes can help us detect thedeleterious processes in cancerous cells for which thereClassical approaches to amplitude and frequency
estimation assume a stationary data model, i.e., boththe amplitude and frequency of the signal areconstant and do not vary with time. Non-stationaryharmonic signals are, however, ubiquitous in variousapplications such as speech, music, seismic, radar,sonar, and biology. We are particularly interested inbiological applications. Recent studies in cellbiology have shown that a number of cell types THE STATIONARY MUSIC ALGORITHMTHE STATIONARY MUSIC ALGORITHM
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itude deleterious processes in cancerous cells, for which there
is a discrepancy in either the amplitude or the period ofthe gene’s expressions between normal and cancerouscells.
biology have shown that a number of cell typesrespond to external stimulation by encoding cellularinformation in their amplitude (AM) and frequency(FM).
FORMS OF ANALOG FORMS OF ANALOG MODULATIONMODULATION
TheThe MUSICMUSIC algorithmalgorithm givesgives aa highhigh--resolutionresolution (higher(higher thanthan thethe spectrum)spectrum) estimationestimation ofof frequencyfrequency parametersparameters basedbasedonon thethe eigendecompositioneigendecomposition ofof aa givengiven stationarystationary signalsignal
( )
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x n A e w nω ϕ+
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AM MUSICAM MUSICCONCLUSIONS AND FUTURE CONCLUSIONS AND FUTURE
RESEARCHRESEARCH
Amplitude Modulated Signal THE PROPOSED AMTHE PROPOSED AM--FM MUSIC ALGORITHMFM MUSIC ALGORITHMOur approach relies on a basis decomposition of the time-dependent amplitude and frequencysignals. We show that the introduction of a basis representation reduces the non-stationaryestimation problem to a stationary one.
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Similarly to the stationary case, the AM and FMMUSIC have higher resolutions (in terms of frequencyseparation) than the non-parametric time-frequencydecomposition methods.
TheThe nextnext stepstep isis toto developdevelop thethe AMAM--FMFM MUSICMUSICalgorithmalgorithm..
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Amplitude and Frequency Modulated Signal
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We will, subsequently, investigate the statisticalproperties of the amplitude and frequency estimates bycomputing their respective Camer-Rao lower bounds(CRLB).
1k =
FM MUSICFM MUSIC
( [ ] )p
j∑
ACKNOWLEDGEMENTACKNOWLEDGEMENTWe would like to thank the Arkansas
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We would like to thank the ArkansasDepartment of Higher Education for theirfunding through a SURF grant 2010.
REFERENCESREFERENCES[1] M.J. Berridge, “The AM and FM of CalciumSignalling” Nature, vol. 386, pp. 759-760, 1997.