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EQ1220 Signal Theory 7.5 credits

Signalteori

The course gives a broad overview of modeling using stochastic processes in electrical engineering applications. Formulating problems using mathematical modeling is an important part of the course. Basics about continuous time an discrete time stochastic processes, especially weakly stationary processes. Definitions of probability distribution and density functions, statistical mean, mean power, variance, autocorrelation function, power spectral density, Gaussian processes and white noise. Linear filtering of stochastic processes, Ergodicity: Estimation of statistical properties from measurements. Sampling and reconstruction: Transformations between continuous and discrete time signals. Influence of sampling, sampling theorem. Pulse amplitude modulation. Errrors in the reconstruction of stochastic signals. Estimation theory: Linear estimation, orthogonality conditions. Prediction and Wiener filtering. Model based signal processing: Linear signal models, AR-models. Spectral estimation. Application of the above to simpler electrical engineering applications.

  • Educational level

    First cycle

  • Academic level (A-D)

    C

  • Subject area

    Electrical Engineering
    Techonology

  • Grade scale

    A, B, C, D, E, FX, F

Course offerings

Autumn 13 for programme students

Autumn 13 for programme students

  • Periods

    Autumn 13 P1 (7.5 credits)

  • Application code

    50400

  • Start date

    2013 week: 36

  • End date

    2013 week: 44

  • Language of instruction

    English

  • Campus

    KTH Campus

  • Number of lectures

    24 (preliminary)

  • Number of exercises

    24 (preliminary)

  • Tutoring time

    Daytime

  • Form of study

    Normal

  • Number of places *

    10 - 120

    *) The Course date may be cancelled if number of admitted are less than minimum of places. If there are more applicants than number of places selection will be made.

  • Schedule

    Schedule (new window)

  • Course responsible

    Tobias Oechtering

  • Teacher

    Tobias Oechtering

  • Target group

    Science without Borders

Learning outcomes

After passing the course you should be able to

  • Analyze given problems regarding properties of weakly stationary stochastic processes.
  • Analyze given problems in at least one of the areas filtering, sampling and reconstruction of weakly stationary processes.
  • Analyze given problems in estimation and/or optimal filtering.
  • Apply mathematical modeling tools to problems in electrical engineering. Develop simple software codes using, e.g., Matlab, and use this to simulate and analyze problems in the area. Report the methodology and results.
  • Use a given mathematical model, or formulate one on your own, to solve a given technical problem in the area, analyze the result and justify if it is reasonable.

If you are passing the course with higher grades, you should, in addition to the above, be able to

  • Analyze given problems in filtering, sampling and reconstruction of weakly stationary processes.
  • Analyze given problems in estimation and optimal filtering.
  • Formulate mathematical models which are applicable and relevant to a given problem formulation within the area. When vital information is missing, you should be able to judge and compare different possibilities as well as make reasonable assumptions to achieve a satisfactorily modeling performance.
  • Use a given mathematical model, or one formulated by yourself, to solve a problem in the area; e.g., a problem composed of several interacting sub-problems or other problems requiring a more complex modeling, analyze the result and its validity.

Course main content

The course gives a broad overview of modeling using stochastic processes in electrical engineering applications. Formulating problems using mathematical modeling is an important part of the course.

Basics about continuous time an discrete time stochastic processes, especially weakly stationary processes. Definitions of probability distribution and density functions, statistical mean, mean power, variance, autocorrelation function, power spectral density,

Gaussian processes and white noise. Linear filtering of stochastic processes, Ergodicity: Estimation of statistical properties from measurements. Sampling and reconstruction: Transformations between continuous and discrete time signals. Influence of sampling, sampling theorem. Pulse amplitude modulation. Errrors in the reconstruction of stochastic signals. Estimation theory: Linear estimation, orthogonality conditions. Prediction and Wiener filtering. Model based signal processing: Linear signal models, AR-models. Spectral estimation. Application of the above to simpler electrical engineering applications.

Eligibility

For single course students: General admission requirements, 120 credits and documented proficiency in English B or equivalent

Prerequisites

EQ1100 Signals and systems II, or equivalent
SF1901 Probability Theory and Statistics, or equivalent 
EL1150 Introductory Matlab Course, or equivalent.

Literature

Händel, Ottoson, Hjalmarsson, ”Signal Theory”, English edition.

Examination

  • PRO1 - Project, 1.0 credits, grade scale: P, F
  • PRO2 - Project, 1.0 credits, grade scale: P, F
  • TEN1 - Examination, 5.5 credits, grade scale: A, B, C, D, E, FX, F

Requirements for final grade

Written exam, (TEN1; 5,5 ECTS credits; Grading: A-F).
Project assignment 1 and 2 (PRO1; 1 ECTS credits PRO2; 1 ECTS credits; Grading: Pass/Fail).

Offered by

EES/Signal Processing

Contact

Tobias Oechtering

Examiner

Tobias Oecthering

Supplementary information

Equivalent to EQ1200/EQ1240 but given in English

Add-on studies

EQ2300 Digital Signal Processing

EQ2310 Digital Communications

Version

Course plan valid from: Autumn 07.
Examination information valid from: Autumn 07.