| TSDT14 |
Signal Theory , 6 ECTS credits.
/Signalteori /
For:
BME
D
ED
I
Ii
IT
MED
SY
U
Y
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Prel. scheduled
hours: 54
Rec. self-study hours: 106
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Area of Education: Technology
Main field of studies: 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, but also certain momentary non-linearities 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 LTI-filtering, modulation, sampling and non-linear filtering of stochastic processes, both one-dimensional and multi-dimensional.
- 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:
Digital Communication Continuation Course, Radio communication, Data compression, Image and audio coding, Communication systems CDIO.
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Organisation:
Teaching is given in the form of lectures, tutorial 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 Gaussian processes 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:
Mikael Olofsson, Signal Theory, Studentlitteratur, 2011, ISBN 978-91-44-07353-8.
Mikael Olofsson, Tables and Formulas for Signal Theory, Studentlitteratur, 2011, ISBN 978-91-44-07328-6.
Additional problems and Lab Memo will be distributed during the course.
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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: Klas Nordberg
Examiner: Mikael Olofsson
Link to the course homepage at the department
Course Syllabus in Swedish
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