Advanced Digital Signal Processing Methods

Course Description

This course gives knowledge on time-frequency transforms of signals, filter banks used in modern systems for compression, noise suppression and communications. Short-time Fourier transform (STFT). Wavelet transform, continuous and discrete (CWT, DWT). Resolution in the time-frequency plane. Frame theory. Filter banks: subband decomposition of signals. Multirate systems, decimation and interpolation. Perfect reconstruction conditions. Polyphase representation of filter banks. Lattice and ladder realization. Desired decomposition features through the filter bank structure. Wavelet filter banks. Limit scale and wavelet function. Wavelet packets. Optimum trees. Applications in feature extraction, communication, signal compression and suppression of noise. Efficient computer realizations. Arrays of distributed sensors, spatial filters.

General Competencies

The students will get acquainted with the concept of time-frequency signal processing. They will deeply understand the short time Fourier transform and wavelet transform - continuous and discrete, as well as the concepts of limit scale and wavelet functions. Students will be able to design multirate systems, perfect reconstruction filter banks, realized directly or in the polyphase domain, or using lifting steps. They will be able to denoise signals or images, to extract features or to preprocess data for lossy compression or for different communication applications using wavelets or wavelet packets.

Learning Outcomes

  1. explain time-frequency methods of signal processing
  2. analyze signals using continuous or discrete wavelet transform
  3. design filter bank of desired properties
  4. apply knowledge for features extraction, noise suppresion and for data compression
  5. evaluate and compare of the methods performance
  6. explain the connection between wavelets and filter banks

Forms of Teaching

Lectures

Course is divided in two cycles of lecturing. There are six weeks in the first cycle, and seven weeks lecturing in second cycle. Two weeks are reserved for midterm and final exam.

Exams

Midterm exam and final exam. Laboratory. Homeworks. Project.

Laboratory Work

Laboratory excercises are organized once a week. Homeworks are related to the laboratory excercises.

Seminars

Students work on project in a group or individually.

Other Forms of Group and Self Study

Homeworks.

Grading Method

Continuous Assessment Exam
Type Threshold Percent of Grade Comment: Percent of Grade
Laboratory Exercises 50 % 10 % 50 % 10 %
Homeworks 50 % 10 % 50 % 10 %
Seminar/Project 50 % 20 % 50 % 20 %
Mid Term Exam: Written 50 % 30 % 0 %
Final Exam: Written 50 % 30 %
Exam: Written 50 % 60 %

Week by Week Schedule

  1. Introduction. Applications.
  2. Fourier transform: 4 variants. Resolution in time-frequency plane: concentration points, effective width. DFT matrix. Unitarity.
  3. Short time Fourier transform (STFT). Frame theory. Gabor expansion.
  4. Wavelet transform, continous and discrete (CWT, DWT).
  5. Perfect reconstruction conditions of decimated filter banks.
  6. Design of the perfect reconstruction filter banks.
  7. Wavelet filter banks. Limit scale function and wavelet function.
  8. Fast DWT. 2D DWT. Applications in signal and image analysis.
  9. Midterm exam.
  10. Applications in noise suppresion. Probability density estimation, regression.
  11. Polyphase representation of the filter banks.
  12. Lattice and ladder realization. Achievement of the desired decomposition properties.
  13. Applications in compression and communication. Applications in extrapolation and interpolation of signals and images. Applications in data fusion.
  14. Wavelet packets. Optimum trees. Efficient realizations.
  15. Project presentation. Final exam.

Study Programmes

Electronic and Computer Engineering -> Electrical Engineering and Information Technology (Profile)

Information Processing -> Information and Communication Technology (Profile)

Information Processing -> Information and Communication Technology (Profile)

Literature

Strang G. and Nguyen T. (1996.), Wavelets and Filter Banks, Wellesley-Cambridge Press
Vetterly M. and Kovačević J. (1995.), Wavelets and Subband Coding, Prentice Hall
Vaidyanathan P.P. (1993.), Multirate Systems and Filter Banks, Prentice Hall
Seršić (2005.), Napredne metode digitalne obrade signala, FER

Lecturers in Charge

Grading System

4 ECTS
L2 English Level
L1 e-Learning
30 Lecturers
0 Exercises
0 Laboratory exercises

Grading

90 Excellent
75 Very Good
60 Good
51 Acceptable