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

2

3

4

Noisy Frequency Modulated Signal

e

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

0 10 20 30 40 50 60 70 80 90 100-4

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-2

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0

1

time

Ampl

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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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.

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-2

time

0.5

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Frequency Modulated Signal

Ampl

itude

AM MUSICAM MUSIC RESEARCHRESEARCH

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.