Popis predmeta

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.

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

Live lectures, on-line lectures and recordings

Laboratory

Exercises are based on individual preparation work, group work in the laboratory, writing and handing in the reports.

Grading Method

Continuous Assessment Exam
Type Threshold Percent of Grade Threshold Percent of Grade
Laboratory Exercises 50 % 18 % 50 % 18 %
Class participation 0 % 2 % 0 % 2 %
Mid Term Exam: Written 50 % 20 % 0 %
2. Mid Term Exam: Written 50 % 20 % 0 %
3. Mid Term Exam: Written 50 % 20 % 0 %
Final Exam: Written 50 % 20 %
Exam: Written 50 % 80 %
Comment:

There are no separate thresholds on midterm and final exams, only on the overall score (50%).

Week by Week Schedule

  1. Time- frequency transforms, Short-time Fourier transform
  2. Resolution in the time-frequency plane, Frame theory
  3. Symmetric and periodic signal extension, Discrete cosine transform (DCT): 4 variants
  4. Continous wavelet transform, Discrete wavelet transform
  5. Subband decompostition
  6. Decimation and interpolation; Multirate systems
  7. Perfect reconstruction
  8. Midterm exam
  9. Scale and wavelet function
  10. Vanishing moments, Polynomial annihilation
  11. Denoising; Compression; Feature extraction
  12. Polyphase representation
  13. Lattice and ladder realization
  14. Modified DCT and DCT filterbanks
  15. Final exam

Study Programmes

University graduate
Audio Technologies and Electroacoustics (profile)
Elective Courses of the Profile (1. semester) (3. semester)
Communication and Space Technologies (profile)
Free Elective Courses (1. semester) (3. semester)
Computational Modelling in Engineering (profile)
Free Elective Courses (1. semester) (3. semester)
Computer Engineering (profile)
Free Elective Courses (1. semester) (3. semester)
Computer Science (profile)
Free Elective Courses (1. semester) (3. semester)
Control Systems and Robotics (profile)
Free Elective Courses (1. semester) (3. semester)
Data Science (profile)
Free Elective Courses (1. semester) (3. semester)
Electrical Power Engineering (profile)
Free Elective Courses (1. semester) (3. semester)
Electric Machines, Drives and Automation (profile)
Free Elective Courses (1. semester) (3. semester)
Electronic and Computer Engineering (profile)
Elective Courses of the Profile (1. semester) (3. semester)
Electronics (profile)
Free Elective Courses (1. semester) (3. semester)
Information and Communication Engineering (profile)
Elective Courses of the Profile (1. semester) Elective Coursesof the Profile (3. semester)
Network Science (profile)
Free Elective Courses (1. semester) (3. semester)
Software Engineering and Information Systems (profile)
Free Elective Courses (1. semester) (3. semester)

Literature

Damir Seršić (2015.), Valići i filtarski slogovi, Element
Gilbert Strang, Truong Nguyen (1996.), Wavelets and Filter Banks, SIAM
Jelena Kovacevic, Martin Vetterli (1995.), Wavelets and Subband Coding, Prentice Hall
P. P. Vaidyanathan (2006.), Multirate Systems And Filter Banks, Pearson Education India
Damir Seršić i Ana Sović Kržić (2021.), Napredne metode digitalne obrade signala, FER

For students

General

ID 222494
  Winter semester
5 ECTS
L3 English Level
L2 e-Learning
30 Lectures
22 Laboratory exercises

Grading System

88 Excellent
75 Very Good
62 Good
51 Acceptable

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

Live lectures, on-line lectures and recordings

Laboratory

Exercises are based on individual preparation work, group work in the laboratory, writing and handing in the reports.

Grading Method

Continuous Assessment Exam
Type Threshold Percent of Grade Threshold Percent of Grade
Laboratory Exercises 50 % 18 % 50 % 18 %
Class participation 0 % 2 % 0 % 2 %
Mid Term Exam: Written 50 % 20 % 0 %
2. Mid Term Exam: Written 50 % 20 % 0 %
3. Mid Term Exam: Written 50 % 20 % 0 %
Final Exam: Written 50 % 20 %
Exam: Written 50 % 80 %
Comment:

There are no separate thresholds on midterm and final exams, only on the overall score (50%).

Week by Week Schedule

  1. Time- frequency transforms, Short-time Fourier transform
  2. Resolution in the time-frequency plane, Frame theory
  3. Symmetric and periodic signal extension, Discrete cosine transform (DCT): 4 variants
  4. Continous wavelet transform, Discrete wavelet transform
  5. Subband decompostition
  6. Decimation and interpolation; Multirate systems
  7. Perfect reconstruction
  8. Midterm exam
  9. Scale and wavelet function
  10. Vanishing moments, Polynomial annihilation
  11. Denoising; Compression; Feature extraction
  12. Polyphase representation
  13. Lattice and ladder realization
  14. Modified DCT and DCT filterbanks
  15. Final exam

Study Programmes

University graduate
Audio Technologies and Electroacoustics (profile)
Elective Courses of the Profile (1. semester) (3. semester)
Communication and Space Technologies (profile)
Free Elective Courses (1. semester) (3. semester)
Computational Modelling in Engineering (profile)
Free Elective Courses (1. semester) (3. semester)
Computer Engineering (profile)
Free Elective Courses (1. semester) (3. semester)
Computer Science (profile)
Free Elective Courses (1. semester) (3. semester)
Control Systems and Robotics (profile)
Free Elective Courses (1. semester) (3. semester)
Data Science (profile)
Free Elective Courses (1. semester) (3. semester)
Electrical Power Engineering (profile)
Free Elective Courses (1. semester) (3. semester)
Electric Machines, Drives and Automation (profile)
Free Elective Courses (1. semester) (3. semester)
Electronic and Computer Engineering (profile)
Elective Courses of the Profile (1. semester) (3. semester)
Electronics (profile)
Free Elective Courses (1. semester) (3. semester)
Information and Communication Engineering (profile)
Elective Courses of the Profile (1. semester) Elective Coursesof the Profile (3. semester)
Network Science (profile)
Free Elective Courses (1. semester) (3. semester)
Software Engineering and Information Systems (profile)
Free Elective Courses (1. semester) (3. semester)

Literature

Damir Seršić (2015.), Valići i filtarski slogovi, Element
Gilbert Strang, Truong Nguyen (1996.), Wavelets and Filter Banks, SIAM
Jelena Kovacevic, Martin Vetterli (1995.), Wavelets and Subband Coding, Prentice Hall
P. P. Vaidyanathan (2006.), Multirate Systems And Filter Banks, Pearson Education India
Damir Seršić i Ana Sović Kržić (2021.), Napredne metode digitalne obrade signala, FER

For students

General

ID 222494
  Winter semester
5 ECTS
L3 English Level
L2 e-Learning
30 Lectures
22 Laboratory exercises

Grading System

88 Excellent
75 Very Good
62 Good
51 Acceptable