TSDT14 
Signal Theory , 6 ECTS credits.
/Signalteori /
For:
BME
D
ED
I
Ii
IT
MED
SY
U
Y


Prel. scheduled
hours: 54
Rec. selfstudy hours: 106


Area of Education: Technology
Main field of studies: Electrical Engineering


Advancement level
(G1, G2, A): A


Aim:
After passing the course, the student should
 be able to clearly define central concepts regarding stochastic processes, using own words.
 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, but also certain momentary nonlinearities that are common in telecommunication.
 with some reliability be able to solve problems that demand integration of knowledge from different parts of the course, i.e. analysis of LTIfiltering, modulation, sampling and nonlinear filtering of stochastic processes, both onedimensional and multidimensional.
 be able to account for the connection between different concepts in the course in a structured way using adequate terminology.
 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.


Prerequisites: (valid for students admitted to programmes within which the course is offered)
From Calculus: Derivatives and integrals.
From Probability theory: Most, but with focus on binary distributions, rectangular distributions and Gaussian distributions.
From Signals and systems: Fourier transforms, LTI systems, convolution, amplitude modulation, sampling and pulse amplitude modulation. (all of it deterministic)
Note: Admission requirements for nonprogramme students usually also include admission requirements for the programme and threshhold requirements for progression within the programme, or corresponding.


Supplementary courses:
Digital Communication Continuation Course, Radio communication, Data compression, Image and audio coding, Communication systems CDIO.


Organisation:
Teaching is given in the form of lectures, tutorial and laborations


Course contents:
 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 Gaussian processes as input. Noise analysis of those modulation forms, primarily with white Gaussian noise as disturbance.
 Nonlinear momentary systems: Quantization and monomial nonlinearities. 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.
 Case study: Reconstruction in CD players.
 Estimation of expectations, auto correlation function and power spectral density.


Course literature:
Mikael Olofsson, Signal Theory, Studentlitteratur, 2011, ISBN 9789144073538.
Mikael Olofsson, Tables and Formulas for Signal Theory, Studentlitteratur, 2011, ISBN 9789144073286.
Additional problems and Lab Memo will be distributed during the course.


Examination: 

Written examination Labratory work 
4 ECTS 2 ECTS



At the exam, there will be an introductory task that examines the learning outcomes "be able to clearly define..." and " be able to reliably perform standard calculations...". This task has to be solved correctly, in order to pass the exam. The rest of the exam examines the learning outcome " with some reliability be able to solve problems...". The grade on the exam, and also on the course as a whole is based on this part.
The laborations are performed in small groups and is examined based on a report. This examines the last two learning outcomes, " be able to account for..." and " be able to estimate...".

Course language is Swedish/English.
Department offering the course: ISY.
Director of Studies: Klas Nordberg
Examiner: Mikael Olofsson
Link to the course homepage at the department

