# Spectral Processing of Signals

A schedule can be found here

## News:

2007-10-26: The fifth (and last) homework assignment has been corrected and is available in the out-box. You can see your results here.

2007-10-19: HW4 is now corrected and is available in the out box. The results are available online here. Note: You should NOT take the magnitude of the reconstructed signal when plotting it or using it to compute the MSE. Why so many people did this is a mystery to me...

2007-10-19: HW3 is now corrected and is available in the OUT-box. The results are available online here. (Note 1: Poles outside the unit circle does not matter when doing spectral analysis, since PSD = H(z)H^*(1/z^*). I.e., if the poles of H(z) are inside the unit circle, the poles of H^*(1/z^*) will be the mirrored poles of H(z) and thus outside the unit circle! Note 2: Always try to theoretically motivate your answers, e.g., if a method does not give proper results, explain why, do not just simply state that it does not work.)

2007-10-11: HW2 is now corrected and is available in the OUT-box. The results are available online here. (OBS: När ni studerar riktiga data så finns det inga exakta svar, utan det är era motiveringar som är det viktiga.)

2007-09-27: For HW2 you might want to use the file "armase.m" which handles the plotting of arma spectra. This function is available in the matlab package of the book, but it is "hidden" in the folder "extras" (or get it here).

2007-09-27: HW1 has been corrected, and is available in the OUT-box (no 45). The results are available online here. **This time, we have not reduced the number of points for small errors in the frequency axis. Next time we will, so make sure you plot all spectra correctly!**

2007-09-21: Note that some hints for the homeworks are available here.

2007-09-18: Track your progress on the homework and the labs from this page.

2007-09-10: Suggestions for the applications to present on lecture 10 have been added.

2007-09-06: The name of the box on the 2nd floor in house 2 where you will put your homeworks is now *Spectral proc. signals IN*.

2007-08-21: Course homepage updated with most important info.

Course Level | Study Period |
---|---|

Advanced | 1 |

## Educational programs:

Program | Course Code | Points | Application Code |
---|---|---|---|

Engineering physics | 1RT606 | 6hp | 11807 |

## Course moments:

Moment | Hours/Assignments | Instructors |
---|---|---|

Lectures | 10x2h | Peter Stoica |

Computer-lab sessions | 5x2h | Erik Gudmundson, Yngve Selén |

Homeworks | 5 | Erik Gudmundson, Yngve Selén |

For information about the location and time of the lectures and labs, please go

here

## Goal:

To provide the student with the knowledge necessary to think in the "frequency domain" and to introduce the state-of-the-art methods and algorithms for computer-aided spectral analysis of temporal and spatial signals with applications in communications, signal analysis, radar systems, emitter location, signal recognition, and others. More information is available on this page.

Click to download a popular desciption of the course in ps or pdf format.

## Prerequisites:

Linear algebra, Fourier analysis, Discrete-time signals and systems.

## Contents:

- Basic Definitions and the spectral estimation problem.
- Periodogram and correlogram methods.
- Improved periodogram-based methods.
- Parametric methods for rational spectra.
- Parametric methods for line spectra.
- Filter-bank methods.
- Spatial methods for array signal processing.

The course syllabus is available here. The course slides are available here (or locally in tar.gz-compressed format of in pdf format).

In lecture 10 the instructors will present several applications of spectral processing of signals. Similarly, the students have the possibility to get 20 credit points if they present short talks of approximately 20 minutes about some application of spectral processing of signals, either at their choice or by selecting one from the list below (NB: some of these paper might require being on the Uppsala University computer network in order to download):

- Use of Spectral Analysis in Defense Against DoS Attacks
- Spectral Analysis of Calcium Oscillations (The code and some more stuff can be found here)
- Application of model-based spectral analysis to wind-profiler radar observations
- Is Spectral Processing Important for Future WSR-88D Radar?
- High Resolution Analysis of Impact Sounds and Forces
- Winds under the Rain Forest Canopy: The Aerodynamic Environment of Gliding Tree Frogs
- A dynamical analysis of tennis: Concepts and data
- Frequency Spectrum of the Intracardiac and Body SurfaceECG during Ventricular Fibrillation - a Computer Model Study
- Heart-Rate Variability and Event-Related ECG in Virtual Environments
- A Spectral Analysis of the Frequency of Supermarket Visits

## Homework assignments:

Homework | Excercise (old/new book) | Deadline | Additional instructions |
---|---|---|---|

Periodogram methods | C2.20/C2.22 | Sept. 24 | Here |

Rational parametric methods | C3.18/C3.20 | Oct. 1 | Here |

Rational parametric methods for line spectra | C3.17/C3.18 | Oct. 8 | Here |

Parametric methods for line spectra | C4.10/C4.14 | Oct. 15 | Here |

Spatial methods | C6.14/C6.17 | Oct. 22 | Here |

(For information on the old/new book, see Literature below.)

The solutions should be put in the postbox marked *Spectral proc. signals IN* on floor 2 in house 2, and they will be returned via the adjacent OUT-box (box no:s 40 and 46).

The results will be continuously updated on this page.

For some general advice on the presentation etc of the homework assignments, please check this page.

Since the examination is based on the homeworks, discussing the solutions to the homework assignments with your colleagues or anybody else is **strictly forbidden**. Note that in grading the homework solutions we will put an emphasis on your interpretations of the results. Also, note that the **deadlines are strict**! This means that a homework which is handed in late may receive **no points** at all.

## Computer-Labs:

Lab | Excercise (old/new book) | Scheduled time | Instructions |
---|---|---|---|

Periodogram methods | C2.17/C2.19, C2.18/C2.20 | Sept 18, 15-17 | Lab1 |

Parametric methods for rational spectra | C3.16/C3.17 | Sept 20, 15-17 | Lab2 |

Parametric methods for line spectra | C4.9/C4.12 | Sept 24, 13-15 | Lab3 |

Filter bank methods | C5.13/C5.13 | Sept 28, 13-15 | Lab4 |

Spatial methods | C6.12/C6.15, C6.13/C6.16 | Oct 9, 15-17 | Lab5 |

(For information on the old/new book, see Literature below.)

For your progress so far, please check this page.

The computer-labs are mandatory. If you for some reason cannot attend a specific session, please, contact the person responsible for the lab well in advance. If your absence was not predicted, make this contact as soon as possible. Make sure that you come prepared (see the course syllabus) for descriptions of the different lab sessions).

All computer labs are scheduled to be in room 2315 (house 2, 3rd floor) at Pollacksbacken.

**IMPORTANT:** For access to the PC-labs at the department, an account at UpUnet-S (the university computer network for students) is required. * When logging in password C should be used! Make sure that you have this password!* Information about UpUnet-S can be found at http://www.student.uu.se/upunets/.

From the computer labs at the IT-department you can access matlab scripts for all the labs (so you don't have to do any programming yourself). Those lab-files can be found in two ways. If you have a `G:` drive mounted when you log into the system you find the files under `G:\Program\Systemteknik\Spektralanalys\`. If you don't have `G:` mounted you can either mount it yourself (using "Map Network Drive") or you can find the files directly under `"My Network Places"-"Entire Network"-"Microsoft Windows Network"-"It-Pclab"\Pegasus\Program\Systemteknik\Spektralanalys`.

## Examination:

The students are required to pass all five labs. The exam consists of solving the five homework assignments. Each homework assignment gives a maximum of 20 points. The points required for the different grades are as follows.

For Master of Science students:

Points | Grade |
---|---|

0-40 | Fail |

41-70 | 3 |

71-90 | 4 |

91-... | 5 |

For PhD students:

Points | Grade |
---|---|

0-74 | Fail |

75-... | G |

During the last lecture, up to 4 students may choose to present some applications of spectral analysis. Each presentation will last 25 minutes (including discussion) and its topic can be selected by the student or suggested by us. For each presentation a maximum of 20 points can be awarded.

## Literature:

P. Stoica and R. Moses, Spectral Analysis of Signals, Prentice-Hall, NJ, USA, 2005. Errata.

The old version of the book (P. Stoica and R. Moses, Introduction to Spectral Analysis, Prentice-Hall, NJ, USA, 1997) also includes everything needed for the course. A current list of corrections to this version is available here in ps or pdf format.