EQ1220 Signal Theory 7.5 credits

Signalteori

Please note

The information on this page is based on a course syllabus that is not yet valid.

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.

  • Education cycle

    First cycle
  • Main field of study

    Electrical Engineering
    Technology
  • Grading scale

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

Course offerings

Autumn 18 for programme students

Autumn 18 Doktorand for single courses students

  • Periods

    Autumn 18 P1 (7.5 credits)

  • Application code

    10169

  • Start date

    27/08/2018

  • End date

    26/10/2018

  • Language of instruction

    English

  • Campus

    KTH Campus

  • Tutoring time

    Daytime

  • Form of study

    Normal

  • Number of places

    No limitation

  • Course responsible

    Tobias Oechtering <oech@kth.se>

  • Teacher

    Tobias Oechtering <oech@kth.se>

  • Target group

    For doctoral students at KTH

Intended 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

Recommended 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, ”Signalteori”, tredje upplagan.

Examination

  • PRO1 - Project, 1.0, grading scale: P, F
  • PRO2 - Project, 1.0, grading scale: P, F
  • TEN1 - Examination, 5.5, grading 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

EECS/Intelligent Systems

Contact

Tobias Oechtering

Examiner

Tobias Oechtering <oech@kth.se>

Supplementary information

Equivalent to EQ1200/EQ1240 but given in English

Add-on studies

EQ2300 Digital Signal Processing

EQ2310 Digital Communications

Version

Course syllabus valid from: Spring 2019.
Examination information valid from: Spring 2019.