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Course Catalog 2012-2013
SGN-2016 Digital Linear Filtering I, 5 cr |
Person responsible
Tapio Saramäki
Lessons
| Study type | P1 | P2 | P3 | P4 | Summer | Implementations | Lecture times and places |
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Requirements
Final examination.
Principles and baselines related to teaching and learning
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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? - There are numerous structures implementing the very same transfer function. - Advantages and drawbacks when comparing infinite-impulse response (IIR) and finite-impulse response (FIR) filters with each other. - Overall filter synthesis procedure in nutshell and various approximation criteria for the filter responses - The characteristics of the four types of linear-phase FIR filters, their use in practical applications, and their synthesis using the windowing technique and the Remez algorithm. - The characteristics of classical analog filters and their digital IIR equivalents; The synthesis of low-pass IIR filters by transforming analog filters to their digital equivalents using the bilinear transformation, and the synthesis of high-pass, band-pass, and band-stop filters by applying appropriate z-plane transformations to low-pass IIR filters. - 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 the probabilities of overflows and the output noises; Finite word-length effects on the variations in the filter coefficients and their impact on various kinds of oscillations in IIR filters. Several general-purpose MATLAB algorithms have been generated by the lecturer for the design of FIR and IIR filters. The students should be able to use these algorithms for designing filters to meet various predetermined specifications.
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 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. | The importance of making the phase delay response constant in the frequency band of interest for preserving the shape of an approximately periodic excitation, not considered in the existing textbooks. | 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. | ||
| 4. | The characteristics of the four types of linear-phase FIR filters, their use in practical applications, and their synthesis using the windowing technique and the Remez algorithm. | ||
| 5. | The characteristics of classical analog filters and their digital IIR equivalents; The synthesis of low-pass IIR filters by transforming analog filters to their digital equivalents by using the bilinear transformation, and the synthesis of high-pass, band-pass, and band-stop filters by applying appropriate z-plane transformations to low-pass IIR filters. | ||
| 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. |
Evaluation criteria for the course
Course is graded on the basis of answers to exam questions. Very good grade is obtained when exam questions are correctly answered. Course acceptance threshold is approximately half the maximum exam points.
Assessment scale:
Numerical evaluation scale (1-5) will be used on the course
Study material
| Type | Name | Author | ISBN | URL | Edition, availability, ... | Examination material | Language |
| Summary of lectures | Digital Linear Filtering I | Tapio Saramäki | English |
Prerequisites
| Course | Mandatory/Advisable | Description |
| SGN-1201 Signal Processing Methods | Mandatory | 1 |
| SGN-1251 Signal Processing Applications | Mandatory |
1 . Either SGN-1157 or SGN-1201 is required.
Prerequisite relations (Requires logging in to POP)
Correspondence of content
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More precise information per implementation
| Implementation | Description | Methods of instruction | Implementation |