| TSDT14 |
Signal Theory , 6 ECTS credits.
/Signalteori /
For:
COE
D
EI
I
Ii
Y
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Prel. scheduled
hours: 48
Rec. self-study hours: 112
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Area of Education: Technology
Subject area: Electrical Engineering
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Advancement level
(G1, G2, A): A
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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.
- 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.
- with some reliability be able to solve problems that demand integration of knowledge from different parts of the course.
- 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.
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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 non-programme students usually also include admission requirements for the programme and threshhold requirements for progression within the programme, or corresponding.
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Supplementary courses:
Telecommunication, Data compression, Image and audio coding, Data transmission, Radio communication, Error correcting codes, Information theory
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Organisation:
Teaching is given in the form of lectures, problem classes and laborations
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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 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.
- Case study: Reconstruction in CD players.
- Estimation of expectations, auto correlation function and power spectral density.
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Course literature:
Pursley: Random Processes in Linear Systems, Prentice Hall, 2002, ISBN 0-13-067391-9.
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Examination: |
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Written examination
Labratory work
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4 ECTS
2 ECTS
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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...".
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Course language is Swedish/English.
Department offering the course: ISY.
Director of Studies: Lasse Alfredsson
Examiner: Mikael Olofsson
Link to the course homepage at the department
Course Syllabus in Swedish
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