Stochastic Signals and Systems
2018/2019/1
In this semester the course is offered as a Guided Individual Study.
There will be one hour Lecture per week, and one hour Practical lesson.
The webpage of the Practical lessons.
Requirements and grading
- There will be three 30 minutes written tests sceduled for 10 Oct, 14 Nov and 12 Dec,
right before the Lectures.
They are worth
30 points each.
- Homework assignment: every week there will be 2 homework assignments:
one theoretical and the other one is a practical computation.
They are to be solved in writing within a week.
A total of at least 50% good solutions must be collected during the semester.
This is a necessary condition for end-term signature.
- Additional homework solutions in excess of the minimal requirements will be credited by 50% of its deserved score.
- Every week a short, 5 minutes test will be held at the beginning of the Practical lessons. They are
worth -1 or 0 or +1 point each.
The sum of these tests must be nonnegative. (If you miss a test, it is -1 point.)
- One of the written tests can be corrected during the first week of the exam period.
- The total score is the sum of the points of the three written tests, plus the score collected from the excess home
assignments.
- Requirement for the end-term signature is 36 points.
- There will be an oral exam at the end of the term.
Lecture slides
Lectures.
- 19 Sept. Wide sense stationary processes. The L_2 Hilbert space. Toeplitz matrix. Linear transformation.
Prediction based on finite past. LSQ predictor. Geometric approach. Normal equation.
- 26 Sept. Prediction on infinite past. Innovation process. AR process. SIngular process, an example.
Completely regular process. Wold decomposition of w.s.st. processes.
- 3. Oct. Fourier method for w.s.st. processes. Part 1.: Spectral representation of the autocovariance function.
Herglotz theorem. special case.
Homework exercises.
- 19 Sept. Exc. 1.7.
- 26 Sept. Exc. 2.8. or 2.7
- 3. Oct. Compute the spectral density function of an MA(1) process.
References
vago AT itk.ppke.hu