### EE 678 – WAVELETS

**Course Offered In:**

Spring 2015

**Instructor:**

Prof. Vikram Gadre

**Motivation:**

Wavelets are useful in signal processing applications where the signal needs to be decomposed into high frequency components (details) and low frequency components (average). For example, one can use wavelet decomposition of a digital image, alter its high frequency components to store some secret information, while leaving the lower frequency components untouched. The result is an image which looks unchanged to the naked eye, while it actually contains the secret information we stored in the high frequency components. This was an example of hiding information in file, while it seems just the same (Steganography). Similarly, wavelet transform representation can be used to denoise an image, as the noise is generally contained in the higher frequency components. There are many other applications where breaking the signals into different resolutions enables interesting signal processing applications.

**Prerequisites:** None, although one is expected to know the basics of EE 210 (Signals and systems).

**Course content:**

- Introduction to Multiresolution Analysis (MRA), Vector spaces, Haar scaling function, Haar wavelet
- Two-band perfect reconstruction filter bank
- Conditions for perfect reconstruction in a general two-band perfect reconstruction filter bank
- Daubechies family of filter banks
- Time-bandwidth product and its properties, Uncertainty principle of Signal Processing
- Short-time fourier transform (STFT), Continuous wavelet transform (CWT), Admissibility condition for wavelets
- Axioms of MRA, Proof of Theorem of MRA
- 5/3 filter bank used in JPEG 2000

**Feedback on lectures:**

Attending the lectures is quite useful. The instructor uses the board and hence taking down notes is necessary.

Attendance is compulsory as a roll call is conducted at the end of every lecture. Students are supposed to keep a track of their own attendance, and present it during the exams. 5% marks are allotted for attendance, and if the number of lectures missed is more than a certain number, they are deducted accordingly.

Also, the instructor floats Challenges during the lectures, and students are awarded credit for posting solutions on Moodle. In some cases, grade improvements are awarded for consistent (and relevant 😛 ) moodle participation, and hence is highly recommended.

**Feedback on assignments and tutorials:**

The course has an application assignment which carries 30% weight, and is like a course project. Apart from that, tutorial sets are given for problem practice, but the students are not evaluated based on them directly. However, solving the tutorials is highly useful for exam preparation.

Challenges are floated during the lectures, and posting solutions on Moodle carries 5% weight. This may actually count for more than 5%, as the instructor award grade improvements for good moodle participation, and hence it is highly recommended

**Feedback on exams:**

There are no quizzes. Midsem and Endsem are conceptually easy, but computationally a bit tedious.

**Overall Difficulty level:**

Easy

**Grading:**

- Midsem : 25 %
- Endsem : 35 %
- Application assignment : 30 %
- Attendance : 5%
- Moodle participation : 5% (Can be more than 5%, grade improvements awarded in some cases)

AA: 15

AB: 15

AP: 2

AU: 1

BB: 26

BC: 24

CC: 6

CD: 1

DD: 2

FR: 1

**Reference books:**

None. The lecture notes are sufficient.

Reviewed by Akshay Sarode(akshay.sarode93@gmail.com)