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TSDT14 Signal Theory

Specification of course aims

Contents

General

One demand on examiners that is related to the Bologna process is that the course syllabus in the study guide (studiehandboken) must contain a few aims, and it must be clear how those aims are tested in the exam. All those aims must be tested at every examination opportunity. A consequence of this is that those aims are given a fairly vague formulation, and that those aims rather are section titles in a more traditional aim description.

For that reason, this page contains a specification of the aims in the study guide and how they are examined, grouped according to in what part of the exam they are treated.

TEN1: Written Exam

The Introductory Task

This task tests basic knowledge and abilities, i.e. the following aim. It contains three subtasks, and as partial fulfillment for passing the exam, you have to treat at least two of those three subtasks correctly. The following aims are examined with this task, one subtasks for each aim. Those aims are tested by samples within them.

  • be able to clearly define central concepts regarding stochastic processes, using own words.
    The following concepts can be treated here: Stochastic process, ensemble averages, strict and wide sense stationarity, exact predictable process, Gaussian process, white noise, all for both time-continuous and time-discrete processes.
  • be able to reliably perform standard calculations regarding stochastic processes, e.g. LTI filtering (both time continuous and time discrete), sampling and pulse amplitude modulation.
    This deals with linear operations. The aim is examined with a rather simple task that treats one of the examples mentioned in the aim. You are expected to handle relations between power spectral densities of the input output processes. Both one-dimensional and multi-dimensional signals and systems can occur.
  • be able to reliably perform standard calculations regarding stochastic processes being exposed to certain momentary non-linearities that are common in telecommunication, especially uniform quantization and monomial non-linearities of low degrees.
    This deals with non-linear operations. The aim is examined with a rather simple task that treats one of the examples mentioned in the aim. You are expected to handle relations between auto-correlation functions for squaring and "cubing", and also distortion calculations for quantization of a stochastic variable.

See also:

The Rest of the Tasks

Tasks number two to six on the exams examine the following aim.

  • with some reliability be able to solve problems that demand integration of knowledge from different parts of the course.
    This is where you find traditional exam tasks. This is the largest of the aims, and it should be related to the course contents, excluding the estimation and the case study.
    • Time continuous and time discrete stochastic processes: Probability distribution, probability density, expectation, ensemble expectation, auto correlation function, power spectral density, cross correlation function, cross spectral density, stationarity, ergodicity. Especially Gaussian processes and white processes. Multidimensional processes.
    • LTI filtering of stochastic processes: Relations between statistical properties of the input process and the output process. Especially matched filters and white Gaussian noise as input.
    • Amplitude and angle modulation of stochastic processes: Relations between statistical properties of the input process and the output process. Especially white Gaussian noise as input. Noise analysis of those modulation forms, primarily with white Gaussian noise as disturbance.
    • Non-linear momentary systems: Quantization and monomial non-linearities. Relations between statistical properties of the input process and the output process. Especially Gaussian processes as input. Properties of quantization noise.
    • Transformation between time continuous and time discrete stochastic processes: Sampling and pulse amplitude modulation, the sampling theorem, reconstruction and reconstruction error.
    You are expected to handle problems that incorporates several parts of the course. See previous exams for examples of what those tasks can look like. These five tasks can each give you at most five points, i.e. totally at most 25 points. Grade limits:
    • Grade 3: 10 points.
    • Grade 4: 15 points.
    • Grade 5: 20 points.

LAB1: Laborations

The laborations consist of three tasks. All of them deal with the estimation of auto-correlation functions and power spectral densities of processes. This is examined by a written report. This part examines the following aims:

  • be able to estimate the auto correlation function and power spectral density of a stochastic process based on a realization of the process. Also, clearly and logically account for those estimations and conclusions that can be drawn from them.
    The report should thus account for the measurements you have done, and estimations based on those measurements. Based on those measurements, you should be able to draw conclusions, such as if the studied system is an LTI system or not.
  • be able to account for the connection between different concepts in the course in a structured way using adequate terminology.
    This is really about comparing your estimations with theoretical analyses of corresponding situations, for instance by deriving power spectral densities of the output of a system.

See also:


Page responsible: Mikael Olofsson
Last updated: 2017 08 22   12:08