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 linear-phase FIR and IIR filters, and the significant differences between IIR and linear-phase 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, least-squared, and maximally-flat 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, least-squared, and maximally-flat approximation criteria.	The characteristics of the four types of linear-phase 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 linear-phase FIR filters and their use in practical application. How to design minimum-phase FIR filters?	The lecture notes review various alternatives of synthesizing computationally-efficient linear-phase FIR filters.
5.	Design and implementation of IIR digital filters using both traditional approaches and more sophiscated approaches leading to efficient implementations.	An efficient Remez-type algorithm developed by the lecturer for designing classical IIR filters and their generalizations is described.
6.	Finite word-length effects in digital filters when using the fixed-point 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 cascaded-form IIR filters by using three commonly used scaling norms and the resulting trade-offs 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 word-length effects in practice: (a) How to easily quantize the coefficient values of direct-form linear-phase FIR filters?; (b) How to easily quantize the coefficient values of IIR filters, which are implemented as a cascade of second- and first-order 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.	Polynomial-based interpolation for signal processing and communications applications
9.	Design and implementation of multirate filter banks including conventional frequency-selective banks and discrete-time 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 Jovanovic-Dolocek, Idea Group Publishing, 2002, pp. 27-85.

Type	Name	Author	ISBN	URL	Additional information	Examination material
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. 2654-2677.	Tapio Saramäki			Only some parts are included in the study material.	Yes
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. 155-277.	Tapio Saramäki			Only some parts are included in the study material.	Yes
Other literature	Multirate Systems and Filter Banks, Chapter II in Multirate Systems: Design & Applications, edited by Gordana Jovanovic-Dolocek, Idea Group Publishing, 2002, pp. 27-85.	Tapio Saramäki and Robert Bregovic’			Only some parts are included in the study material.	Yes
Summary of lectures	Advanced Filter Design	Tapio Saramäki				Yes

Course	Corresponds course	Description
SGN-23006 Advanced Filter Design, 5 cr	SGN-2016 Digital Linear Filtering I, 5 cr + SGN-2056 Digital Linear Filtering II, 4 cr + SGN-2106 Multirate Signal Processing, 6 cr + SGN-2156 System Level DSP Algorithms, 4 cr