The Energy Operator: A Useful Diagnostic Tool

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The Energy Operator A Useful Diagnostic Tool

• Balu Santhanam
• SPCOM Lab, Dept. of E.E.C.E.
• University of New Mexico
• Email bsanthan_at_eece.unm.edu

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Overview of Talk

• Energy Operator Primer

• Biomedical Applications

• Diagnostic Applications

• ECG Example

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Teager-Kaiser Energy Operator

• Continuous signals

• Discrete Signals

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Higher-order Energy Operators
Continuous Signals
Discrete Signals
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Energy Separation Algorithm

• Monocomponent AM-FM Signals

• Instantaneous Frequency (IF) and Amplitude (IA)

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Multi-band Demodulation

• Filter signal via a bandpass filter-bank with
  optimized center-frequency and bandwidth.

• Pick the most active branch based on the
  energy-operator output.

• Demodulate output of selected branch using the
  ESA into IA/IF signals.

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Features of E - Operators (1)

• The energy operator output for sinusoidal
  sources produces the normalized energy.

• For slowly time-varying sources, the energy
  operator tracks the energy of the source.

• Instantaneous behavior allows tracking of
  abrupt changes in energy.

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Features of E - Operators (2)

• Higher-order energy operators track higher-order
  energies of a signal source.

• For k 2 HOEO ? TKEO.

• Energy operators possess simplicity, efficiency
  and good time-resolution.

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Biomedical Applications

• Used to detect vocal-tract defects and
  pathologies

• Used to detect spikes in neural (EEG) output

• Used for EEG segmentation and abrupt event
  detection.

• Used for detection of heart murmurs, sleep
  apnea disorder, heart rate variability
  measurements.

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Vocal Tract Pathologies

• Improper glottal closure whisper phonation,
  creaky voice, glottal blow, etc.

• Pathologies polyps, papillomas, carcinoma,
  contact ulcers, nerve paralysis.

• Vocal tract asymmetry produces two different
  fundamental frequencies

• IA/IF estimates facilitate detection of
  normal/pathological cases.

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EEG Applications

• EEG provides a sensitive indicator of cerebral
  function.

• Spikes in the EEG output characterize epileptic
  seizures.

• IA and IF information from segmented EEG serve
  as a useful diagnostic tools.

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Cardio Applications (1)

• ECG signal exhibits quasi-periodicity producing
  regular peaks (R-waves)

• Respiratory sinus arythmia (RSA) constitutes
  frequency modulation in the ECG signal.

• The heart-IF (HIF) can be used to estimate
  heart-rate variability.

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Cardio Applications (2)

• Instantaneous energy and IF can be used to
  classify heart sound and murmurs.

• IA and IF of cardiac inter-beat times can be
  used to detect obstructive sleep-apnea (OSA).

• Two component chirp model used to model
  pulmonary and aortic components of second heart
  sound (dub)

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ECG Example 1
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ECG Example - 2
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ECG Example - 3
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ECG Example 4
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References 1
BaOh01 A. Barros and N. Ohnishi, Heart
Instantaneous Frequency (HIF) An alternative
Approach to Extract Heart Rate Variability, IEEE
Trans. On Biomed. Engg., Aug, 2001.
Miet00 J.E. Mietus et.al., Detection of
Obstructive Sleep Apnea from Cardiac Interbeat
Interval Time Series, Computers in Cardiology,
2000.
Shar00 Sharif et. al., Analysis and
Classification of Heart Sounds and Murmurs Based
on the Instantaneous Energy and Frequency
Estimations, Proceedings of TENCON, 2000.
MuRa98 S. Mukhopadhyay and G.C. Ray, A New
Interpretation of Nonlinear Energy Operator and
Its Efficacy in Spike Detection, IEEE Trans. On
Biomed. Engg. Feb. 2000.
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References - 2

• XDP01 J. Xu, L-G. Durand and P. Pibarot,
  Nonlinear Transient Chirp Signal Modeling of the
  Aortic and Pulmonary Components of the Second
  Heart Sound, IEEE Trans. On Biomed. Engg., March
  2001.
• XDP00 J. Xu, L-G. Durand and P. Pibarot,
  Extraction of the Aortic and Pulmonary
  Components of the Second Heat Sound Using a
  Nonlinear Transient Chirp Signal Model, IEEE
  Trans. On Biomed. Engg., July 2000.
• AgGo99 R. Agarwal and J. Gotman, Adaptive
  Segmentation of EEG Data Using A Nonlinear Energy
  Operator, 1999.
• HCK98 J.H.L. Hansen, L.G.-Ceballos, and J.F.
  Kaiser, A Nonlinear Operator-Based Speech
  Feature Analysis Method with Application to Vocal
  Fold Pathology Assessment, IEEE Trans. On
  Biomed. Engg., March 98