Advanced Signal Processing Methods

Data is displayed for the academic year: 2024./2025.

Lecturers

Prof.
Mario Cifrek
PhD
Prof.
Igor Lacković
PhD
Prof.
Damir Seršić
PhD
Assoc. Prof.
Ana Sović Kržić
PhD

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.

Study Programmes

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. Explain the connection between wavelets and filter banks

Forms of Teaching

Lectures

Laboratory

Week by Week Schedule

  1. Lectures: Time- frequency transforms, Short-time Fourier transform, Laboratory: -, Seminar: -
  2. Lectures: Resolution in the time-frequency plane, Frame theory, Laboratory: Fourier transform: 4 variants. Resolution in time-frequency plain: energy concentration center and effetive width. DFT matrix, unitarity., , Seminar: Forming teams
  3. Lectures: Symmetric and periodic signal extension, Discrete cosine transform (DCT): 4 variants, Laboratory: Short time Fourier transform (STFT)., Seminar: -
  4. Lectures: Continous wavelet transform, Discrete wavelet transform, Laboratory: Wavelet transform (CWT), Seminar: Choice of the topic
  5. Lectures: Subband decompostition, Seminar: -
  6. Lectures: Decimation and interpolation; Multirate, Seminar: Workplan hand in
  7. Lectures: Perfect reconstruction, Laboratory: Filter banks: subband decomposition. Multirate systems, decimation and expansion., Seminar: -
  8. Lectures: Midterm exam, Laboratory: Midterm exam, Seminar: -
  9. Lectures: Scale and wavelet function, Laboratory: Perfect and imperfect reconstruction in multirate filterbanks., Seminar: -
  10. Lectures: Vanishing moments, Polynomial annihilation, Laboratory: Perfect reconstruction filterbank design., Seminar: Draft version
  11. Lectures: Denoising; Compression; Feature extraction, Laboratory: -, Seminar: -
  12. Lectures: Polyphase representation, Laboratory: Wavelet filterbanks. Applications in denoising., Seminar: -
  13. Lectures: Lattice and ladder realization, Laboratory: DWT of diskret signals. Applications in denoising., Seminar: -
  14. Lectures: Modified DCT and DCT filterbanks, Laboratory: Polyphase representation of filterbanks., Seminar: Presentation of the seminar
  15. Lectures: Final exam, Laboratory: -, Seminar: Final exam

Literature

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

General

ID 261531
  Winter semester
5 ECTS
L3 English Level
L1 e-Learning