Advanced Digital Signal Processing Methods
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.
- explain time-frequency methods of signal processing
- analyze signals using continuous or discrete wavelet transform
- design filter bank of desired properties
- apply knowledge for features extraction, noise suppresion and for data compression
- evaluate and compare of the methods performance
- explain the connection between wavelets and filter banks
Forms of Teaching
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
|Type||Threshold||Percent of Grade||Threshold||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
- Introduction. Applications.
- Fourier transform: 4 variants. Resolution in time-frequency plane: concentration points, effective width. DFT matrix. Unitarity.
- Short time Fourier transform (STFT). Frame theory. Gabor expansion.
- Wavelet transform, continous and discrete (CWT, DWT).
- Perfect reconstruction conditions of decimated filter banks.
- Design of the perfect reconstruction filter banks.
- Wavelet filter banks. Limit scale function and wavelet function.
- Fast DWT. 2D DWT. Applications in signal and image analysis.
- Midterm exam.
- Applications in noise suppresion. Probability density estimation, regression.
- Polyphase representation of the filter banks.
- Lattice and ladder realization. Achievement of the desired decomposition properties.
- Applications in compression and communication. Applications in extrapolation and interpolation of signals and images. Applications in data fusion.
- Wavelet packets. Optimum trees. Efficient realizations.
- Project presentation. Final exam.