Advanced Filter Design, ET2402

Course information

  • The course is given for: Master of Science Electrical Engineering
  • Number of Pts: 7,5 ECTS
  • Level: D, 61-80 pts
  • Subject: Electrical Engineering
  • Syllabus (swe),(eng)

Here you find information on which study periods the course is given: Contact the student help desk to register for the course.


Contact the teacher Benny Sällberg, if you have any questions regarding the course. 


Course overview

The purpose of the course is to give profound knowledge regarding properties and the design of digital filters, as well as giving an understanding to the term optimal filter design. Emphasis is given to the least squares- (LS) and the minimax-criterion for designing nonrecursive, Finite Impulse Response (FIR) filters. For example, the optimal window is defined by a compromise of the LS and minimax criterions. The course also covers filters with minimum delay, i.e. minimum phase filters and filters with arbitrarily specified amplitude and phase response.


Methods such as least squares, Remes exchange algorithm, linear and quadratic programming, and spectral factorization for designing FIR filters are parts of this course. The optimization methods are considered general design tools for construction of filters with arbitrary frequency specifications, i.e. by using design constraints on amplitude function, phase function, and group delay function. Other methods are also included in the course, such as a Cepstrum based method for minimum phase FIR filter design. The course focus on giving profound knowledge of the mathematical formulations and their solutions. A number of excercises are presented to illustrate the theory. These excersises constitute mandatory parts of the course, and tasks in the excercises should be presented in one report.


A course objective is to prepare students to research within the field or a specialized industrial application in the field.  


Course material

  • Course literature: "Digital Filter Design", T. W. Parks, C. S. Burrus, John Wiley & Sons, Inc., 1987. ISBN 0-471-82896-3
  • Material from the Department

List of assignments

List of assignments
Assignment Description
1 FIR filter with linear-phase, Least-Squares design
2 FIR filter with complex specification, Least-Squares Design
3 FIR filter with linear-phase, Minimax-Design using Linear Programming
4 FIR filter with linear-phase, Minimax-Design using Remes Algorithm
5 FIR filter with minimum-phase and optimal amplitude
6 FIR filter with Complex Specification, Minimax-Design
7 Groupdelay constraints
8 IIR filter, Elliptic filter, general design
9 Design of Halfband filters
10 The optimal window, quadratic programming
11 Minimum phase FIR filter design by Spectral Factorization
12 Digital Filter Design by Cepstrum Technique
13 Allpass Realization of Recursive Digital Filters
14 Quantized FIR filter using simulated annealing
15 Quantized FIR filter by deterministic annealing

Grade information

This course is a self study course. The student is supposed to solve a set of assignments and submit the solutions in one written report together with MATLAB m-scripts for their solutions.


It is possible to get the Swedish grades 5, 4, 3 and U (failed) or the ECTS grades A, B, C, D, E, and F (failed). The final grade on the course is based on the set of assignments that are solved, the quality of the submitted report and the corresponding MATLAB m-script files.


Please observe that you select yourself which assignments you want to solve and present according to the tables below. The tables are given for the swedish grades and the ECTS grades.

Selection of assignments (Swedish grade)


Grade Assignments
3 Select 8 assignments from assignments 2-10
4 Select 8 assignments from assignments 2-10,
2 assignments from assignments 11-13
5 Select 8 assignments from assignments 2-10,
2 assignments from assignments 11-13,
1 assignment from assignments 14-15

Selection of assignments (ECTS grade) 


Grade Assignments
E Select 8 assignments from assignments 2-10
D Select 8 assignments from assignments 2-10,
1 assignment from 11-13
C Select 8 assignments from assignments 2-10,
2 assignments from 11-13
B Select 8 assignments from assignments 2-10,
3 assignments from 11-13
A Select 8 assignments from assignments 2-10,
3 assignments from 11-13,
1 assignment from assignments 14-15


As a rule of thumb, up to grade 3 (ECTS grade E/D), the student can expect the teacher to help them with their codes, while for grade 5 (ECTS B/A) the student is expected to ask questions mainly related to theory.


Report submission

The written report should be submitted electronically, to the course teacher:

  • Report (PDF or DOC) describing Your solutions to Your selected assignments,
  • MATLAB m-script files for Your solutions, attached in a separate ZIP file.

After the student submits a report, the teacher examines the submitted material. The examination time after each submission is maximally two weeks, whereafter the student should expect a response from the teacher. The student will be given a chance to correct any mistakes in their analysis within an agreed time.

You may select assignments according to the guidelines under grade information, above.


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