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T-61.181 – Biomedical Signal Processing. Chapters 3.4 - 3.5.2 14.10.2004. Overview. Model-based spectral estimation Three methods in more detail Performance and design patterns Spectral parameters EEG segmentation Periodogram and AR-based approaches. Model-based spectral analysis.

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t 61 181 biomedical signal processing

T-61.181 – Biomedical Signal Processing

Chapters 3.4 - 3.5.2

14.10.2004

overview
Overview
  • Model-based spectral estimation
    • Three methods in more detail
  • Performance and design patterns
  • Spectral parameters
  • EEG segmentation
    • Periodogram and AR-based approaches
model based spectral analysis
Model-based spectral analysis
  • Linear stochastic model
    • Autoregressive (AR) model
  • Linear prediction
prediction error filter
Prediction error filter
  • Estimation of parameters based on minimization of prediction error ep variance
estimation of model parameters
Estimation of model parameters
  • Parameter estimation process critical for the successful use of an AR model
  • Three methods presented
    • Autocorrelation/covariance method
    • Modified covariance method
    • Burg’s method
  • The actual model is the same for all methods
autocorrelation covariance method
Autocorrelation/covariance method
  • Straightforward minimization of error variance
  • Linear equations solved with Lagrange multipliers (constraint apTi=1)
levinson durbin recursion
Levinson-Durbin recursion
  • Recursive method for solving parameters
  • Exploits symmetry and Toeplitz properties of the correlation matrix
  • Avoids matrix inversion
  • Parameters fully estimated at each recursion step
data matrix
Data matrix
  • The correlation matrix can be directly estimated with data matrices
  • In covariance method the data matrix does not include zero padding, but the resulting matrix is not Toeplitz
  • In autocorrelation method the data matrix is zero-padded
modified covariance method
Modified covariance method
  • Minimization of both backward and forward error variances
  • Parameters from forward and backward predictors are the same
  • Correlation matrix estimate not Toeplitz so the forward and backward estimates will differ from each other
burg s method
Burg’s method
  • Based on intensive use of Levinson-Durbin recursion and minimization of forward and backward errors
  • Prediction error filter formed from a lattice structure
performance and design parameters
Performance and design parameters
  • Choosing parameter estimation method
    • Two latter methods preferred over the first
  • Modified covariance method
    • no line splitting
    • might be unstable
  • Burg’s method
    • guaranteed to be stable
    • line splitting
  • Both methods dependant on initial phase
selecting model order
Selecting model order
  • Model order affects results significantly
    • A low order results in overly smooth spectrum
    • A high order produces spikes in spectrum
  • Several criteria for finding model order
    • Akaike information criterion (AIC)
    • Minimum description length (MDL)
    • Also other criteria exist
  • Spectral peak count gives a lower limit
sampling rate
Sampling rate
  • Sampling rate influences AR parameter estimates and model order
  • Higher sampling rate results in higher resolution in correlation matrix
  • Higher model order needed for higher sampling rate
spectral parameters
Spectral parameters
  • Power, peak frequency and bandwidth
  • Complex power spectrum
  • Poles have a complex conjugate pair
partial fraction expansion
Partial fraction expansion
  • Assumption of even-valued model order
  • Divide the transfer function H(z) into second-order transfer functions Hi(z)
  • No overlap between transfer functions
eeg segmentation
EEG segmentation
  • Assumption of stationarity does not hold for long time intervals
  • Segmentation can be done manually or with segmentation methods
  • Automated segmentation helpful in identifying important changes in signal
eeg segmentation principles
EEG segmentation principles
  • A reference window and a test window
  • Dissimilarity measure
  • Segment boundary where dissimilarity exceeds a predefined threshold
design aspects
Design aspects
  • Activity should be stationary for at least a second
    • Transient waveforms should be eliminated
  • Changes should be abrupt to be detected
    • Backtracking may be needed
  • Performance should be studied in theoretical terms and with simulations
the periodogram approach
The periodogram approach
  • Calculate a running periodogram from test and reference window
  • Dissimilarity defined as normalized squared spectral error
  • Can be implemented in time domain
the whitening approach
The whitening approach
  • Based on AR model
  • Linear predictor filter “whitens” signal
  • When the spectral characteristics change, the output is no longer a white process
  • Dissimilarity defined similarly to periodogram approach
    • The normalization factor differs
  • Can also be calculated in time domain
dissimilarity measure for whitening approach
Dissimilarity measure for whitening approach
  • Dissimilarity measure asymmetric
  • Can be improved by including a reverse test by adding the prediction error also from reference window (clinical value not established)
summary
Summary
  • Model-based spectral analysis
    • Stochastic modeling of the signal
    • Is the signal an AR process?
  • Spectral parameters
    • Quantitative information about the spectrum
  • EEG segmentation
    • Detect changes in signal