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Information
| Code | EE621 |
| Name | Multirate Filter Banks and Wavelets |
| Term | 2022-2023 Academic Year |
| Term | Spring |
| 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 | 4 |
| PLO06 | Bilgi - Kuramsal, Olgusal | To create a complete scientific text by compiling the information obtained from the research | 4 |
| 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 | 2 |
| PLO14 | Yetkinlikler - Öğrenme Yetkinliği | Adopting the ethical values required by both education and research aspects of academician | 1 |
| 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 | Discrete transformations (continued). Two band filter banks. | Reading from recommended textbooks and scientific journals. | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 4 | Two band filter banks (cont.). 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 | ||
| 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 and sample question solutions | 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 | 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 | ||