Measurement Theory

week

Synopsis

1.

1. Short summary of the subject Measurement Technology 2. The measurement procedure: Observation in case of deterministic channels. Observation in case of noisy channels. 3. Basics of decision theory: Bayesian Decision Theory

2.

3. Basics of decision theory: Bayesian Decision Theory (cont.) Examples: detection of a constant signal, detection of signal with varying magnitude, detection of signal with random magnitude in noise.

3.

4. Basics of estimation theory: The Bayesian Philosophy: minimum mean square error estimators, minimum absolute error estimators, maximum a posteriori estimators. Bayesian estimators in case of Gaussian PDF. Maximum likelihood estimator.

4.

4. Basics of estimation theory:  Gauss-Markov estimator. The Least Squares Approach. Examples: polinom fitting in discrete time, Fourier analysis, FIR filter, linear model fitting in case of colored noise, linear models with known components. 5. Model fitting: regression calculus. With totally specified statistics, with partially specified statistics, linear regression, polynomial regression, linear regression based on measured data. The adaptive linear combinator: Wiener-Hopf equation.

5.

5. Model fitting: (cont.) Proparties of the regression matrix: eigenvalue, eigenvector problem. Iterative model fitting methods: Newton, steepest descent, LMS, alfa-LMS, LMS-Newton, LMS-Newton together with the iterative estimation of the regression matrix. Iterative model fitting based on the Taylor expansion of the criterion function.  

6.

6. Basics of filtering theory: optimal non-recursive estimator: scalar Wiener filter. Recursive estimator from an optimal non-recursive estimator.

7.

6. Basics of filtering theory: (cont.) Optimal recursive estimator: scalar Kalman filter. Illustrative example. Optimal recursive predictor. General form of a Kalman filter.

8.

6. Basics of filtering theory: (cont.) General form of a Kalman predictor. 7. Model-Based signal processing. The basic concepts. Linear averaging. Exponential averaging. Sliding-window averaging. Behavior in time and frequency domains. Representation of signals in signal spaces: linear vector spaces, linear spaces, transformations. Observers for signal processing.

9.

Prep for the first mid-term exam: Examples and exercises related to the first 8 weeks

10.

Observers for signal processing (cont.):  Demodulation-integration-modulation versus band filtering. Derivation and characterization of the resonator/based structure. Relation to the Lagrange structure and the frequency sampling method.

11.

Observers for signal processing (cont.): A common structure for recursive discrete transforms. The resonator/based Fourier transformer. The resonator-based observer as a universal signal processor. Relation to the interpolation methods. The condition of passivity.

12.

Second-order, real-coefficient resonator blocks: direct, orthogonal and wave-digital forms. direkt, ortogonális, hullám-digitális. Properties of the orthogonal structures. Orthogonal transforms for data reduction. (KL transformation, principal component analysis.) 8. Basics of nonlinear signal processing: special test signals, special structures. Homomorf signal processing. Polynomial filters. Median filters.

13.

Prep for the second mid-term exam: Examples and exercises related weeks 10-12.

14.

Outlook: Reconfigurable systems, reconfiguration methods.