## Mathematical Tools — from Fourier series to analysis of non-stationary signals

**Instructor:** Prof. Miroslav Vlček <vlcek@fd.cvut.cz>

**Lectures:** Tuesdays, 8:00–9:30 am; B106 Horská Bldg.

**Computer sessions:** Tuesdays, 9:45–11:15 am and 11:30–13:00 am; B106 Horská Bldg.

### Course description

Fourier Transform, short time Fourier Transform, and Wavelets have established themselves as an important tool in modern signal processing as well as in applied mathematics. The objective of this course is to establish the mathematical foundations necessary to understand and use basis functions, wavelets, and related constructions useful for signal processing. The course includes experimental and computer projects involving individual effort.

**Prerequisites:** Linear Algebra, MATLAB

### Texts

M. Vetterli, J. Kovacevic, and V. K. Goyal. “Fourier and Wavelet Signal Processing”. With permission of authors available from our webpage as PDF here.

S. Allen Broughton, and Kurt Bryan. ”Discrete Fourier Analysis and Wavelets”. John Wiley, 2009.

### Grading

The following table lists all possible scores that can be obtained:

Homeworks | 21 points |

- minimum homework points |
9 points |

Final project |
14 points |

- minimum from the project |
7 points |

Total |
30(+5) points |

Final grade is given by the total points obtained for homeworks and the final project. The grading scheme is as follows:

Total points | Grade | ECTS |
---|---|---|

27 to 30 | excellent | A |

24 to <27 | very good | B |

21 to <24 | good | C |

18 to <21 | satisfactory | D |

16 to <18 | sufficient | E |

less than 16 | failed |
F |