Budapest University of Technology and Economics, Faculty of Electrical Engineering and Informatics

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    Measurement Theory

    A tantárgy neve magyarul / Name of the subject in Hungarian: Méréselmélet

    Last updated: 2018. február 22.

    Budapest University of Technology and Economics
    Faculty of Electrical Engineering and Informatics
    Electrical Engineering MSc
    Course ID Semester Assessment Credit Tantárgyfélév
    VIMIMA17 1, 3 3/0/0/f 4  
    3. Course coordinator and department Dr. Péceli Gábor,
    Web page of the course
    4. Instructors Gábor Péceli, Department of Measurement and Information Systems
    5. Required knowledge Basics of signal and information processing.
    6. Pre-requisites
    NEM ( TárgyEredmény( "BMEVIMIM108" , "jegy" , _ ) >= 2
    TárgyEredmény("BMEVIMIM108", "FELVETEL", AktualisFelev()) > 0)

    A fenti forma a Neptun sajátja, ezen technikai okokból nem változtattunk.

    A kötelező előtanulmányi rendek grafikus formában itt láthatók.


    The subject is recommended to be completed within the first or the second semester of the MSc studies.

    7. Objectives, learning outcomes and obtained knowledge The subject discusses the theoretical background as well as the qualitative and quantitative characterization of the engineering methods used for studying the physical world around. It gives an overview of the basic methods of signal and system theory, estimation and decision theory, as well as of the most important data- and signal processing algorithms. The main goal of the subject is to show how different tasks such as complex measurement problems, modelling and information processing problems, etc. can be solved using this theoretical background. The knowledge discussed in the subject gives a general basis for solving research and development problems too.
    8. Synopsis




    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


    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.


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


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


    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.


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


    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.


    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.


    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.


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


    Outlook: Reconfigurable systems, reconfiguration methods.

    9. Method of instruction Lectures.
    10. Assessment Two in-term exams, and two home-works. Each item should be accomplished at least at 40% level.
    11. Recaps The mid-term exam can be repeated on an organized repeated mid-term exam during the repetition period, and on a 2nd organized repeated mid-term exam at the beginning of the examination period.
    12. Consultations

    Consultations are organized upon the explicit request of students taking into account personal and other resource availabilities.

    13. References, textbooks and resources 1. Lecture notes available on the web page of the subject.
    14. Required learning hours and assignment
    Contact lessons
    Preparing for lectures
    Midterm exam
    15. Syllabus prepared by

    Tamás Dabóczi

    István Kollár

    Géza Kolumbán

    Gábor Péceli

    László Sujbert