ET2402 Advanced Filterdesign

The course aims at giving the students deepened knowledge of digital filters, their characteristics and construction and also at giving meaning to the concept of optimal filter design. In particular, the least-square- and minimax criteria will be studied and compared. The purpose is to provide the students with an understanding of the mathematical formulation and its solution and also to provide knowledge and experience that is useful at the choice of filter type and optimization criterion. The students will also get an introduction to modern methods for filter design that can be used, among other things, for the construction of filters that have a complex specification or minimum phase.

Prerequisites

For admission to the course the following courses are required: Signal Processing II ET1303 7,5 credit points.

Content

Central items of the course are:
• Characteristics of FIR filters:
• The four types of linear-phase FIR filters
o Construction of linear-phase FIR filters:
o least-square approximation
o the Chebyshev approximation
o the Remes algorithm
o Linear programming
o Quadratic programming
• Minimum-phase and complex approximation
• Optimal amplitude Chebyshev design
o Minimum phase
o Complex least-square approximation
o Complex Chebyshev approximation
• Construction of IIR filters
o Butterworth,
o Chebyshev
o Inverted Chebyshev
o Elliptic filters
• Construction of half-band filters
• Filter construction with spectral factorization
• Optimal windows
• Filter design with Cepstrum technique
• All-pass realization of IIR filters
• Simulated annealing
• Deterministic annealing

Learning outcomes

On completion of the course the student will:

• be able to understand and use the various filter construction methods for both FIR- and IIR filters
• be able to understand and use the various optimization methods
• know which optimization method and filter type to use for solving a problem

Generic Skills

The following generic skills are trained in the course:
• Skill in analysis and synthesis
• Skill in applying knowledge in practice
• Solution of problems
• Academic writing

Course literature and other teaching material

Course literature and other teaching material

Learning methods

The course is a self-instruction course based mainly on a number of compulsory hand-in assignments. The hand-in assignments must be handed in individually by each participant and may consist of a theoretical problem and/or programming assignments. Upon request some introductory lectures/exercises/opportunities to ask questions may be given in order for the students to familiarize themselves with the subject. The instruction is carried out entirely or partly in English.

Work placement

No work placement is included in the planned learning activities. BTH is aiming for a close contact with the surrounding community when developing courses and programmes.

Teachers

Examiner
Benny Sällberg

Course Manager
Benny Sällberg

Planned learning activities

Exercises and laboratory sessions.

Time allocation

On average, a student should study 200 hours to reach the learning outcomes. This time includes all the various available learning activities (lectures, self studies, examinations, etc.). This estimation is based on the fact that one academic year counts as 60 ECTS credits, corresponding to an average student workload of 1 600 hours. This may vary individually.

Assessments

Code	Title	ECTS credits	Grade
1010	Assignment1	7.5	F/P/3/4/5

¹ Determines the final grade for the course, which will only be issued when all components have been approved.

Grading

The course will be graded Fail, Pass, 3, 4 or 5 .

On request grades according to ECTS will be given.

Future exams

No upcoming, centrally coordinated, examinations for this course were found.

To participate in a centrally coordinated examination, you must enroll in Student's Portal, no later than fifteen days before the examination.

Time and location for the examination will be published about 5 days in advance.

There might be other scheduled examinations. Information concerning these examinations are available in It's Learning or at other places that the person who is responsible of the course will refer to.

Course Evaluation

The course manager is responsible for the views of students on the course being systematically and regularly gathered and that the results of the evaluations in various forms affect the form and development of the course.