
Course Catalog 20142015
SGN23006 Advanced Filter Design, 5 cr 
Person responsible
Tapio Saramäki
Lessons
Study type  P1  P2  P3  P4  Summer  Implementations  Lecture times and places 








Requirements
Final examination and 2 assignments out of 3.
Learning Outcomes
After finalizing the course with a good grade, the student will be really aware of, among others, on the following aspects:  What is a digital filter and how to analyze its performance using its transfer function and frequency response as well as its magnitude, phase, group delay, and phase delay responses?  Advantages and drawbacks when comparing infiniteimpulse response (IIR) and finiteimpulse response (FIR) filters with each other. – Four types of linearphase FIR filters and their use in practice.  Design and implementation of FIR digital filters using both traditional approaches and more sophisticated approaches leading to efficient implementations  Design and implementation of IIR digital filters using both traditional approaches and more sophisticated approaches leading to efficient implementations  Various finite wordlength effects in the implementation digital filters in both theory and practice: (a) output noise due to multiplication roundoff errors; (b) filter scaling; (c) finite word length effects on the variations in the filter coefficients as well as their impact on various kinds of oscillations in IIR filters.  When and why is it beneficial to utilize multirate filtering when generating DSP algorithms?  Design and implementation of various kinds of decimators or interpolators for various practical applications.  Basic characteristics of various kinds of Nthband FIR and IIR decimators and interpolators as well as their optimization and use in practical applications  How to use the modified Farrow structure for interpolation by an arbitrary factor and the transposed modified Farrow structure for decimation by an arbitrary factor.  What are multirate filter banks, transmultiplexers, and discretetime wavelet filter banks and how to synthesize them for practical application?
Content
Content  Core content  Complementary knowledge  Specialist knowledge 
1.  What is a digital filter and how to analyse its performance with the aid of various responses such as its transfer function and frequency response as well as its magnitude, phase, group delay, and phase delay responses? Various structures to implement the very same transfer function.  Introductory filtering examples, the roles of the poles and zeros in providing their contributions to various responses of linearphase FIR and IIR filters, and the significant differences between IIR and linearphase FIR filters for shaping the passband response of the filter, namely, the poles of IIR filters accomplish efficiently this shaping, whereas FIR filters have only zeros to perform this duty.  During the lectures, some extra information not included in the lecture notes is given. 
2.  Filter synthesis procedure in nutshell, including typical criteria for filter responses along with examples, and illustrative descriptions on the use of minimax, leastsquared, and maximallyflat approximation criteria.  The lecture notes provide a review on those various structures, which are commonly used for implementing digital filters, to make students aware of the terminologies, which are used about these structures.  
3.  Filter synthesis procedure in nutshell, including typical criteria for filter responses along with examples, and illustrative descriptions on the use of minimax, leastsquared, and maximallyflat approximation criteria.  The characteristics of the four types of linearphase FIR filters and their use in practical application.  
4.  Design and implementation of FIR digital filters using both traditional approaches and more sophiscated approaches leading to efficient implementations.  The characteristics of the four types of linearphase FIR filters and their use in practical application. How to design minimumphase FIR filters?  The lecture notes review various alternatives of synthesizing computationallyefficient linearphase FIR filters. 
5.  Design and implementation of IIR digital filters using both traditional approaches and more sophiscated approaches leading to efficient implementations.  An efficient Remeztype algorithm developed by the lecturer for designing classical IIR filters and their generalizations is described.  
6.  Finite wordlength effects in digital filters when using the fixedpoint two's complement arithmetic; Attractive properties of the two's complement arithmetic; The commonly used model for estimating the output noise due to the multiplication roundoff errors; Scaling of the cascadedform IIR filters by using three commonly used scaling norms and the resulting tradeoffs between probabilities of the overflows and resulting output noises; Finite word length effects on the variations in the filter coefficients as well as their impact on various kinds of oscillations in IIR filters.  Finite wordlength effects in practice: (a) How to easily quantize the coefficient values of directform linearphase FIR filters?; (b) How to easily quantize the coefficient values of IIR filters, which are implemented as a cascade of second and firstorder blocks?; (c) How to easily quantize the coefficient values of IIR filters, which are implemented as a parallel connection of two allpass filters?; (d) The validity of the noise model, which is commonly used to estimate the output noise due to the multiplication roundoff errors.  
7.  Design and implementation of efficient decimators and interpolators  A comprehensive review  
8.  Polynomialbased interpolation for signal processing and communications applications  
9.  Design and implementation of multirate filter banks including conventional frequencyselective banks and discretetime wavelet banks  A comprehensive review  More information on multirate filter banks can be found in T. Saramäki and Robert Bregovic', Multirate Systems and Filter Banks," Chapter II in Multirate Systems: Design & Applications, edited by Gordana JovanovicDolocek, Idea Group Publishing, 2002, pp. 2785. 
Instructions for students on how to achieve the learning outcomes
Course is graded on the basis of answers to exam questions. Very good grade is obtained when exam questions are correctly answered and 2 of 3 homeworks are accepted. Course acceptance threshold is approx. half of the maximum exam points. The third homework is a volunteer work and is prized with increasing the exam result by one grade provided that the threshold is passed.
Assessment scale:
Numerical evaluation scale (15) will be used on the course
Study material
Type  Name  Author  ISBN  URL  Edition, availability, ...  Examination material  Language 
Other literature  Design of computationally efficient FIR fillters using periodic subfilters as building blocks in The Circuits and Filters Handbook, Second Edition, edited by W.K. Chen, CRC Press, Inc., 2002, pp. 26542677.  Tapio Saramäki  Only some parts are included in the study material.  Yes  English  
Other literature  Finite impulse response filter design, Chapter 4 in Handbook for Digital Signal Processing, edited by S. K. Mitra and J. F. Kaiser, John Wiley and Sons, New York, 1993, pp. 155277.  Tapio Saramäki  Only some parts are included in the study material.  Yes  English  
Other literature  Multirate Systems and Filter Banks, Chapter II in Multirate Systems: Design & Applications, edited by Gordana JovanovicDolocek, Idea Group Publishing, 2002, pp. 2785.  Tapio Saramäki and Robert Bregovic’  Only some parts are included in the study material.  Yes  English  
Summary of lectures  Advanced Filter Design  Tapio Saramäki  Yes  English 
Prerequisites
Course  Mandatory/Advisable  Description 
SGN11000 Signaalinkäsittelyn perusteet  Mandatory  
SGN11006 Basic Course in Signal Processing  Mandatory  
SGN21006 Advanced Signal Processing  Mandatory 
Additional information about prerequisites
Either SGN11000 Signaalinkäsittelyn perusteet, SGN11006 Basic Course in Signal Processing, or SGN21006 Advanced Signal Processing.
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