EE621 Multirate Filter Banks and Wavelets

6 ECTS - 3-0 Duration (T+A)- . Semester- 3 National Credit

Information

Code EE621
Name Multirate Filter Banks and Wavelets
Term 2023-2024 Academic Year
Term Fall
Duration (T+A) 3-0 (T-A) (17 Week)
ECTS 6 ECTS
National Credit 3 National Credit
Teaching Language İngilizce
Level Doktora Dersi
Type Normal
Mode of study Yüz Yüze Öğretim
Catalog Information Coordinator Prof. Dr. SAMİ ARICA
Course Instructor
1


Course Goal / Objective

To teach multi-resolution signal processing methods. To teach methods of making time-frequency maps of signals, separating them into frequency bands (components). To ensure that they have the knowledge and equipment to use these methods in the analysis of signals and images.

Course Content

Filters. Up and down sampling. Half band filter banks. M-band uniform filter banks and reconstruction conditions. Approximate and detail components of a sign. Multi-resolution analysis. Wavelet transform, scaling function and its relationship with half-band filter banks. Applications.

Course Precondition

There are no prerequisites for the course.

Resources

Multiresolution Signal Decomposition: transforms, subbands and wavelets. Ali N. Akansu. Academic Press Wavelets and Filter Banks. Gilbert Strang. Wellesley Cambridge Press

Notes

No suggested additional course notes.


Course Learning Outcomes

Order Course Learning Outcomes
LO01 A students can apply finite and infinite impulse response filters.
LO02 A student learns and applies the methods of reducing and increasing the sampling rate.
LO03 A student can decompose the signals into subbands and analyze and process each subband separately.
LO04 A student can perform time-frequency analysis with M-band filter band and wavelet transform.
LO05 A student can design an M-band filter bank construct scaling and wavelet functions.


Relation with Program Learning Outcome

Order Type Program Learning Outcomes Level
PLO01 Bilgi - Kuramsal, Olgusal Being able to specialize in at least one of the branches that form the foundations of Electrical and Electronics Engineering by increasing the level of knowledge beyond the master's level 5
PLO02 Bilgi - Kuramsal, Olgusal To comprehend the integrity of all the subjects included in the field of specialization. 5
PLO03 Bilgi - Kuramsal, Olgusal Having knowledge of the current scientific literature in the field of specialization to analyze the literature critically 5
PLO04 Bilgi - Kuramsal, Olgusal To comprehend the interdisciplinary interaction of the field with other related branches, to suggest similar interactions. 4
PLO05 Bilgi - Kuramsal, Olgusal Ability to do theoretical and experimental work
PLO06 Bilgi - Kuramsal, Olgusal To create a complete scientific text by compiling the information obtained from the research
PLO07 Bilgi - Kuramsal, Olgusal To work on the thesis topic programmatically, following the logical integrity required by the subject within the framework determined by the advisor. 4
PLO08 Bilgi - Kuramsal, Olgusal To search for literature in scientific databases, particularly the ability to correctly and accurately scan databases and evaluate and categorize listed items. 4
PLO09 Bilgi - Kuramsal, Olgusal Having a command of English and related English jargon at a level that can easily read and understand a scientific text written in English in the field of specialization and write a similar text 4
PLO10 Bilgi - Kuramsal, Olgusal Ability to write a computer program in a familiar programming language, generally for a specific purpose, specifically related to the field of expertise. 4
PLO11 Bilgi - Kuramsal, Olgusal Ability to plan and teach lessons related to the field of specialization or related fields 3
PLO12 Bilgi - Kuramsal, Olgusal Being able to guide and take the initiative in environments that require solving problems related to the field 3
PLO13 Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği Ability to communicate with people in an appropriate language
PLO14 Yetkinlikler - Öğrenme Yetkinliği Adopting the ethical values required by both education and research aspects of academician
PLO15 Yetkinlikler - Öğrenme Yetkinliği To be able to produce projects, policies, and processes in the field of expertise and to evaluate these elements 3
PLO16 Yetkinlikler - Öğrenme Yetkinliği Ability to research new topics based on existing research experience 3


Week Plan

Week Topic Preparation Methods
1 Linear time-invariant systems. Fourier and z-transforms. An overview. Reading from digital signal processing textbooks Öğretim Yöntemleri:
Anlatım
2 Decimator and Interpolator. Discrete transformations. Reading from recommended textbooks. Reading from scientific journals. Öğretim Yöntemleri:
Anlatım, Alıştırma ve Uygulama
3 Two band filter banks. Reading from recommended textbooks and scientific journals. Öğretim Yöntemleri:
Anlatım, Alıştırma ve Uygulama
4 Two-band orthogonal filter bank design. Reading from recommended textbooks and scientific journals. Öğretim Yöntemleri:
Anlatım, Alıştırma ve Uygulama
5 Binary tree structures. Decomposition of the signals into approximate and detail components. Division of images into four bands by seperable transformation. Tree structures for two-dimensional signals. Reading from recommended textbooks and scientific journals. Öğretim Yöntemleri:
Anlatım, Alıştırma ve Uygulama
6 Type 1 and 2 polyphase decomposition. Multi-resolution noble identities. Frequency and z-domain equivalents of decimation and interpolation. Incoperation of polyphase decomposition to decimation and interpolation processes. Reading from recommended textbooks and scientific journals. Öğretim Yöntemleri:
Anlatım, Alıştırma ve Uygulama
7 General review and sample question solutions. Reading and reviewing lecture notes. Öğretim Yöntemleri:
Soru-Cevap, Alıştırma ve Uygulama
8 Mid-Term Exam Reading and reviewing lecture notes. Problem solving. Ölçme Yöntemleri:
Yazılı Sınav
9 M-band uniform filter banks. Deriving perfect reconstruction condition in the z-domain. Reading from recommended textbooks and scientific journals. Öğretim Yöntemleri:
Anlatım, Alıştırma ve Uygulama
10 Recontruction condition of M-band filter banks in terms of polyphase components Obtaining the perfect reconstruction condition in the time domain Reading from recommended textbooks and scientific journals Öğretim Yöntemleri:
Anlatım, Alıştırma ve Uygulama
11 Wavelet transform in continuous time, conditions that wavelet transform must satisfy. Inverse wavelet transform. Time-scale (frequency) map of signals. Dyadic sampling of the transform plane and reconstruction from these samples. Reading from recommended textbooks and scientific journals. Öğretim Yöntemleri:
Anlatım, Alıştırma ve Uygulama
12 Multi-resolution analysis. Approximation and detail spaces. Decomposition of sşgnals into The scaling and wavelet functions of the signals and their approximate and detail components. separation. with the scaling and wavelet functions. Reading from recommended textbooks and scientific journals. Öğretim Yöntemleri:
Anlatım, Alıştırma ve Uygulama
13 Relation of scaling and wavelet functions of two-band orthogonal quadature mirror filter bank with low and high pass filters. Constructing scaling and wavelet function from these filters. Reading from recommended textbooks and scientific journals. Öğretim Yöntemleri:
Anlatım, Alıştırma ve Uygulama
14 Two-dimensional non-separable filter banks. Up and down sampling on the sampling grid in two dimensions. Two-dimensional two-band filter bank. Reading from recommended textbooks and scientific journals. Öğretim Yöntemleri:
Anlatım, Alıştırma ve Uygulama
15 General review for final Reading and reviewing lecture notes. Öğretim Yöntemleri:
Soru-Cevap, Alıştırma ve Uygulama
16 Term Exams Reading and reviewing lecture notes. Problem solving. Ölçme Yöntemleri:
Yazılı Sınav
17 Term Exams P2 Reading and reviewing lecture notes. Problem solving. Ölçme Yöntemleri:
Yazılı Sınav


Student Workload - ECTS

Works Number Time (Hour) Workload (Hour)
Course Related Works
Class Time (Exam weeks are excluded) 14 3 42
Out of Class Study (Preliminary Work, Practice) 14 6 84
Assesment Related Works
Homeworks, Projects, Others 7 4 28
Mid-term Exams (Written, Oral, etc.) 1 2 2
Final Exam 1 2 2
Total Workload (Hour) 158
Total Workload / 25 (h) 6,32
ECTS 6 ECTS

Update Time: 11.05.2023 11:22