EE 695G

Biomedical Signal Processing and System Identification

3 credit hours
every 3 semesters

instructor(s)
	S. B. Gelfand and P. C. Doerschuk

Prerequisites:
EE301, EE302 or permission of instructor

Text:
Lennart Ljung, "System Identification: Theory for the User,'' Prentice-Hall, 1987, 
plus papers from the biomedical engineering literature.

Description:
This course describes modern mathematical methods for the description
 and analysis of time-series data and the use of these methods on a range
 of biomedical engineering problems.  The diversity of goals and 
corresponding approaches is emphasized  A key part of the course is 
a project where the student analyzes data that has arisen in their own
 research or, alternatively, data from one of several standard sources
 using current software (especially Matlab and Mathematica).

Outline:
1.	Signals Systems and Models (5 weeks)
	(a)	Linear Time Invariant Systems
		Key issue: Stochastic versus deterministic models, models versus predictors
		i.	Input output models/ Transfer function models
			A.	Linear regression, ARX models (AR signal model)
			B.	Pseudolinear regression, ARMAX, ARIMAX models (ARMA, ARIMA 
		signal models)
			C.	Box Jenkins model
		ii.	State space models
			A.	Sampled  continuous time state space models
			B.	Canonical discrete time state space  models
			C.	Kalman filter as predictor for state space model
		iii.	Identifyibility, stability and stationarity of models 
	(b)	Linear Time Varying and Nonlinear System Models 
Key issue: Linear vs nonlinear models, nonlinear models as linear regressions
		i.	Polynomial and related models (Volterra, Hammerstein 
and Wiener models)
		ii.	Piecewise linear models
		iii.	Neural network models (multilayer perceptron nets,
 radial basis nets, recurrent 
	neural nets)
		iv.	NARX, NARMAX, NARIMAX input/output models
		v.	Nonlinear state-space models
		vi.	Markov models
2.	Methods and Issues in Identification (5 weeks)
	(a)	Nonparametric Methods
		i.	Impulse and frequency response methods
		ii.	Spectral analysis (periodogram, smoothing, windowing)
	(b)	Parametric Methods
		i.	Least squares
		ii.	Minimum prediction error
		iii.	Maximum likelihood
		iv.	Maximum entropy/ minimum information distance
		v.	Bayesian techniques
		vi.	Pseudolinear regression, instrumental variables
		vii.	Linear versus nonlinear models for identification
		viii.	Numerical methods for off-line implementations
		ix.	Recursive implementations
			A.	Identifying constant parameters
			B.	Tracking slowly varying parameters
			C.	Efficient implementation: matrix inversion lemma, matrix factorizations, 
		lattices
			D.	Detecting abrupt parameter changes: generalized likelihood ratio test 
		(detection of change in AR, ARMA process)
	(c)	Model Selection and Model Validation
	(d)	Other Methods in Identification and Validation
		i.	Higher order statistics
		ii.	Time frequency methods
3.	Applications (4 weeks)
	(a)	Pulmonary acoustics: input/output models.
	(b)	Pulmonary acoustics: distributed parameter acoustic models.
	(c)	EEG: auto- and cross-power spectral estimation.
	(d)	ECG: interpretation using Hidden Markov Models.
	(e)	ECG: inverse mapping of cardiac depolarization from body surface potential maps.
	(f)	Endocrine and metabolic physiology: nonlinear state space models.
	(g)	Speech as an interface for aids to the disabled.
4.	Project (concurrent)

For further information regarding the Biomedical Engineering Program at Purdue University contact the Biomedical Engineering Graduate Office at (317) 494-5730 bmeprogram@ecn.purdue.edu