Advanced chapters of signal processing (ETF TKO NPPS 4870)

General information

Module title

Advanced chapters of signal processing

Module code

ETF TKO NPPS 4870

Study

ETF-B

Department

Telecommunications

Year

1

Semester

2

Module type

Mandatory

ECTS

6

Hours

70

Lectures

28

Exercises

24

Tutorials

14

Module goal - Knowledge and skill to be achieved by students
  The goal of the course is to enable students to master basic terms in field of construction of filters and ways of filtering in communications, and then to gain and deepen basic knowledge in statistical signal processing and signal detection, with a view of adaptive modulation plans.

Syllabus
  Transfer function and forming of impulse: description of state space, Ways of realization (direct, standard cascade), sensitivity, Standard approximations: Butterworth, Tschebyscheff, Cauer and Bessel filters. Time discreet systems, FIR - Finite Impulse Response and IIR- Infinite Impulse Response systems. FIR filter, IIR filter. Stability, conditional stability. Adaptive signal processing; Channel estimation, correlations, LS - Least Squares, estimation, "unbiased" filtration with delay, Zero - Forcing algorithm, Adjusted filter, comparing the Zero - Forcing filter and adjusted filter, Wiener Kolmogorow filter, least square error, minimum mean square error using the Wiener filter, comparison with Zero - Forcing filter and adjusted filter. Statistical estimation theory - Fisher statistics and MLE - Maximum likelihood method, Fisher optimization theory in estimation – sufficient statistics, class of exponential probability distribution, Cramer-Rao border. Bayesian statistics, Bayesian estimation methods, MAP - Maximum A posteriori Probability and MMSE - Minimal Mean Square Error. Statistical theory of signal detection - Bayesian, Minimax, Neyman - Pearson. Kalman filter, linear MMSE estimation, orthogonal principle, Wiener - Hopf equation, adaptive modulation systems, transfer using variable speed and power, M-QAM transfer using variable speed and power, generalized M-ary modulations (continual adaptation and discreet adaptation).

Literature
Recommended
Additional

Didactic methods
  Course is performed through direct performed in an aula. Lectures are followed by solution of problems performed by lecturer with goal of enabling students to master mathematical instruments and methods introduced during the lectures and on which the analyzed filters and filtering method are based. <br>
During tutorials under tutor guidance and supervision, other examples and problems are solved, and ideas given for solution of problems presented during exercises. In this way even during the presentation of the study program it is possible to continually follow the achieved final exam preparedness level of students. <br>
As part of laboratory exercises students will be introduce with the basic features of software solution used in filtering of communications, and they also approach independent making of simple application in observed field <br>

Exams
  During the course students earn points according to the following system: <br>
- Attending classes and tutorials: 10 points, student with more then three absences from lectures and/or tutorials can not get these points. <br>
- Home assignments and laboratory exercises bring maximum of 10 points, assuming solving 5 to 10 assignments equally distributed throughout the semester. <br>
- Partial exams: two partial exams; each positively evaluated partial exam 20 points. Each partial exam lasts 90 minutes and it is structured as follows: <br>
- Answering to simple questions with goal of testing whether student has basic theoretical knowledge; students with correct answers to all such questions earn 5 points; <br>
- Solving an open answer problem, with correct answer bringing 10 points; <br>
- Solving problems with multiple answers offered, on of answers being the correct one; students with correct answers to all such questions earn 5 points; <br>
Students who earned less then 20 points during the semester must retake the course. Students who earned 40 or more points during the semester will take a final exam; This exam consists of discussion of problems from partial exams, home assignments and answers to simple questions related to course topics. <br>
Final oral exam provides maximum of 40 points. In order to get positive final grade, students must earn minimum of 20 points in this exam. Student failing to earn the minimum must take the makeup oral exam. Student who earned 20 or more, and less then 40 points during the semester, will have to take the makeup exam. <br>
The makeup exam is organized in the following manner: <br>
- Written part structured similarly to partial written exam, during which students solve problems in topics they failed on partial exams (less then 10 points); <br>
- Oral part structured the same as the oral part of the final exam. <br>
Only students who managed to earn total score of 40 or more points in written part of the makeup exam will be allowed to take the oral part of the makeup exam, where the mentioned score consists of points earned through attending lectures, solving home assignments, passing partial exams and passing the written part of makeup exam. Oral makeup exam provides maximum of 40 points. In order to achieve positive final grade students must earn minimum of 20 points in this exam. Student failing to earn the minimum will have to retake the course. Oral makeup exam gives maximum of 40 points. In order to achieve positive final grade students must achieve minimum of 20 points in this exam. Student failing to achieve the minimum will have to re-enroll for this course. <br>

Aditional notes
  1. During the written part of the exam students are allowed to use a list of formulas prepared by lecturers, which may be of use in solving problems. It is not allowed to use other notes, books, cell phones or other electronic devices. <br>
2. Problems, which students must solve during the exam, are of the same type solved during the lectures and tutorials. <br>