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Syllabus for

Academic year
TMA421 - Random processes
 
Owner: TELTA
3,0 Credits (ECTS 4,5)
Grading: TH - Five, Four, Three, Not passed
Level: B
Department: 11 - MATHEMATICAL SCIENCES


Teaching language: Swedish

Course module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 No Sp
0196 Examination 3,0 c Grading: TH   3,0 c   14 Dec 2005 am V,  19 Apr 2006 am V,  23 Aug 2006 am V

In programs

TKEFA CHEMICAL ENGINEERING WITH ENGINEERING PHYSICS, Year 4 (elective)
TIEKA INDUSTRIAL ENGINEERING AND MANAGEMENT - Systems and Mathematics, Year 3 (compulsory)
TTFYA ENGINEERING PHYSICS, Year 4 (elective)
TDATA COMPUTER SCIENCE AND ENGINEERING - Other elective courses, Year 4 (elective)
TDATA COMPUTER SCIENCE AND ENGINEERING, Year 3 (elective)
TM Teknisk matematik, Year 2 (elective)
TITEA SOFTWARE ENGINEERING, Year 4 (elective)
TITEA SOFTWARE ENGINEERING, Year 3 (elective)
EMMAS MSc PROGR IN ENGINEERING MATHEMATICS, Year 1 (elective)
TELTA ELECTRICAL ENGINEERING, Year 3 (elective)

Examiner:

Docent  Patrik Albin



Eligibility:

For single subject courses within Chalmers programmes the same eligibility requirements apply, as to the programme(s) that the course is part of.

Course specific prerequisites

Some basic course in mathematical statistics, basic
courses in mathematics, some experience of computer programming.

Aim

A "real" signal that depends on time, for example,
in electrical engineering or mathematical finance, but also in many
other contexts in science, can often be viewed as composed of a
deterministic signal part, and a random noise part. The added
observable signal is thus affected by randomness, that is, it is a
random or stochastic process.

The course teaches methodology for modelling and analysis of random
signals. In particular, models that are used, for example, in
biology, electrical engineering and mathematical finance are covered.

Random processes is a course at Mathematical Sciences with a mainly
theoretical content. Random processes is the basis for methodology
for analysis of time dependent phenomena in many areas in science,
for example, in various forms of signal processing in electrical
engineering and mathematical finance. The couse is a prerequisite
for many courses in signalprocessing at electrical engineering.

Content

THE COURSE TEACH methods for modelling and analysis of stochastic processes, that is, developments in time that are affected by or depends on chance. Further, it is seen how to make optimal decisions based on
observations of such processes. An important application is construction of
filters that remove as much noise as possible from an observed signal.

IMPORTANT PROCESSES as weakly and strictly staionary processes,
Gaussian processes, Wiener processes, Poisson processes, Levy processes, linear processes, AR and MA processes, discrete and continuous time white noise, shot noise.

ANALYTICAL QUANTITIES AND TOOLS as moment functions, spectral
ananysis (that is, Fourier analysis for stochastic processes), different
spectral distributions, impulse respone, frequency function, Hilbert filter and envelop.

STATISTICAL TOOLS for estimation of important analytical quatities and
process parameters from observed process data.

USE OF ANALYTICAL AND STATISTICAL TOOLS for optimal filetring,
linear prediction, and fitting of process parameters for different process
models.

Organisation

LECTURES: 28 hours

SEMINARS: 28 hours

LABORATIONPROJECT corrsponds to roughly one sixth of the course. There
are two or three projects to choose from. The project is examined by means of
one of the six tasks at examination. See also examination alternative 2 below.

Literature

LITERATURE:

"P. Albin: Stokastiska Processer" Studentlitteratur, 2003, and "A. Leon-Garcia: Probability and Random Processes for Electrical Engineering" Addison-Wesley, 1994. Either of the books cover the course on its own. Possibly, during the
course further course material will be put on the www-page of the course:
http://www.math.chalmers.se/Stat/Grundutb/Chalmers/TMA421/

Examination

EXAMINATION.

Alternative 1. Written tentamen. Test examination with two tasks that give
bonus on tasks 1 and 2 at examination.

Alternative 2. Two projects are reported in writing and orally before the
christmas break. Approved project reports together with a minimum score
of 4 points of a possible10 at the test examination (or on tasks 1 and 2 of
a later examination) gives grade 3.


Page manager Published: Thu 03 Nov 2022.