Course detail
Digital Filters
FEKT-KCIFAcad. year: 2011/2012
The course covers the whole range of the digital signal processing, from real-time implementation of digital systems, through methods of the analysis of one-dimensional digital systems, up to the basic methods of designing one-dimensional digital filters: representation of numbers, floating- and fixed-point arithmetic, the Harvard architecture of digital signal processors, very long instruction word (VLIW) architecture, programming processors in the assembler and in the C language(intrinsic functions, pragma directives, pre-processor directives, linker), real-time communication with off-chip peripherals, characteristics of digital systems (transfer function, impulse response, frequency response), stability and causality of digital systems, finite and infinite impulse response, the structures of digital systems, signal flow graphs, the effect of quantization on the digital system characteristics, methods of designing one-dimensional digital filters, systems with multiple sample rates, filter banks.
Language of instruction
Czech
Number of ECTS credits
6
Mode of study
Not applicable.
Guarantor
Department
Learning outcomes of the course unit
Student will gain:
* Overview of the technical devices in which the digital systems are implemented,
* overview of the various generations of digital signal processors and their properties,
* experience with the implementation of digital signal processing algorithms using fixed-point arithmetic,
* experience with the programming microcontrollers in the C language,
* practical experience with the implementation of real-time digital signal processing,
* practical experience with the design of digital filters.
Experience can be in particular utilized:
* When optimizing digital signal processing algorithms,
* when programming the microprocessor,
* when the development of telecommunication equipment.
* Overview of the technical devices in which the digital systems are implemented,
* overview of the various generations of digital signal processors and their properties,
* experience with the implementation of digital signal processing algorithms using fixed-point arithmetic,
* experience with the programming microcontrollers in the C language,
* practical experience with the implementation of real-time digital signal processing,
* practical experience with the design of digital filters.
Experience can be in particular utilized:
* When optimizing digital signal processing algorithms,
* when programming the microprocessor,
* when the development of telecommunication equipment.
Prerequisites
The basic knowledge of the digital signal processing (sampling, representation of discrete-time signals, description of discrete-time systems, etc.) and of microprocessor technology (principles of microprocessors, registers, memory, programming in the C language, debugging) are required. Appropriate courses, in which this knowledge can be obtained, are compulsory and optional specialised courses of Teleinformatics study area or equivalent:
* Computers and Programming 2 (KPC2),
* Signals and Systems Analysis (KASS),
* Digital Circuits and Microprocessors (KDOM).
* Computers and Programming 2 (KPC2),
* Signals and Systems Analysis (KASS),
* Digital Circuits and Microprocessors (KDOM).
Co-requisites
Not applicable.
Planned learning activities and teaching methods
Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations.
Tutorials have the explanation of basic principles, methodology of the discipline problems and their solutions.
Practice proceeds on digital signal processor development kits and Matlab.
Tutorials have the explanation of basic principles, methodology of the discipline problems and their solutions.
Practice proceeds on digital signal processor development kits and Matlab.
Assesment methods and criteria linked to learning outcomes
Evaluation of study results follows Rules for Studies and Examinations of BUT and Dean's Regulation to the Rules for Studies and Examinations of BUT.
Solution of the seven homeworks max. 40 marks
Written examination max. 60 marks
Solution of the seven homeworks max. 40 marks
Written examination max. 60 marks
Course curriculum
1. Technical devices for the implementation of digital systems, Von Neumann architecture of microcontrollers, Harvard architecture of digital signal processors, digital signal processor generation, interfaces for real-time debugging.
2. Programming processors in the C language, the compilation process, the pre-processor directives, linking stage, intrinsic functions, assembler language, linking assembler and the C language.
3. The communication of the digital signal processor with off-chip peripherals, connecting the A / D and D / A converters, circular buffering, double buffering, interrupt handling, the controller program.
4. Description of digital system, difference equations, transfer functions, zeros, poles, state-space description, signal flow graph, Mason's rule, the basic characteristics of digital systems, frequency response, impulse response, stability.
5. Floating-point arithmetic, fixed-point arithmetic, dynamic range, saturation, quantization noise, arithmetic logical unit, analysis of quantization effects on the transfer function and other characteristics of digital systems, limit cycles.
6. Structures for the realization of digital systems, canonical forms of realization, the classification of digital systems, digital systems with finite impulse response (FIR) and infinite impulse response (IIR).
7. Hardware cycles, address generation unit, addressing modes, utilization of addressing modes in the C language and assembler, optimization of digital systems, code profiling.
8. Design of FIR digital filters: Window method, frequency sampling method, optimum equiripple linear phase filter design method, Remez's algorithm.
9. Design of IIR digital filters: a method of bilinear transformation, method of impulse invariance. Conversion to the second-order section.
10. Inverse filtering, Wiener optimal filtering, the Wiener-Hopf equation. Adaptive filters, LMS algorithm, RLS algorithm, properties and applications of adaptive filters.
11. Multi-rate systems, decimation and interpolation, sampling-rate conversion by a rational number, polyphase filter structures.
12. Filter banks, DFT filter bank, filter bank modulated by cosine function, two-channel filter bank, perfect reconstruction condition, quadrature mirror filters.
13. Fundamentals of nonlinear digital signal processing, filters based on sorting, homomorphic filtering, cepstral analysis.
2. Programming processors in the C language, the compilation process, the pre-processor directives, linking stage, intrinsic functions, assembler language, linking assembler and the C language.
3. The communication of the digital signal processor with off-chip peripherals, connecting the A / D and D / A converters, circular buffering, double buffering, interrupt handling, the controller program.
4. Description of digital system, difference equations, transfer functions, zeros, poles, state-space description, signal flow graph, Mason's rule, the basic characteristics of digital systems, frequency response, impulse response, stability.
5. Floating-point arithmetic, fixed-point arithmetic, dynamic range, saturation, quantization noise, arithmetic logical unit, analysis of quantization effects on the transfer function and other characteristics of digital systems, limit cycles.
6. Structures for the realization of digital systems, canonical forms of realization, the classification of digital systems, digital systems with finite impulse response (FIR) and infinite impulse response (IIR).
7. Hardware cycles, address generation unit, addressing modes, utilization of addressing modes in the C language and assembler, optimization of digital systems, code profiling.
8. Design of FIR digital filters: Window method, frequency sampling method, optimum equiripple linear phase filter design method, Remez's algorithm.
9. Design of IIR digital filters: a method of bilinear transformation, method of impulse invariance. Conversion to the second-order section.
10. Inverse filtering, Wiener optimal filtering, the Wiener-Hopf equation. Adaptive filters, LMS algorithm, RLS algorithm, properties and applications of adaptive filters.
11. Multi-rate systems, decimation and interpolation, sampling-rate conversion by a rational number, polyphase filter structures.
12. Filter banks, DFT filter bank, filter bank modulated by cosine function, two-channel filter bank, perfect reconstruction condition, quadrature mirror filters.
13. Fundamentals of nonlinear digital signal processing, filters based on sorting, homomorphic filtering, cepstral analysis.
Work placements
Not applicable.
Aims
Improve students' knowledge of the digital signal processing (DSP) obtained in previous courses. Acquaint students with the basic principles of implementation on technical devices (digital signal processors and microcontrollers). Acquaint students with the programming digital signal processors in the assembler and in the C language. Acquaint students with the differences and the problems of implementation of digital signal processing methods using floating- and fixed-point arithmetic.
Specification of controlled education, way of implementation and compensation for absences
Tutorials are not duly
Computer exercise are duly
Surrender of separate tasks is duly
Computer exercise are duly
Surrender of separate tasks is duly
Recommended optional programme components
Not applicable.
Prerequisites and corequisites
Not applicable.
Basic literature
PROAKIS, J. G.;MANOLAKIS, D. G.:Digital Signal Processing. Prentice Hall: New Jersey, 1996. 3 edition. 966 p. ISBN 0-13-373762-4 (EN)
VÍCH,R., SMÉKAL,Z.: Digital Filters (Číslicové filtry). Academia, Praha 2000. ISBN 80-200-0761-X (In Czech) (CS)
VÍCH,R., SMÉKAL,Z.: Digital Filters (Číslicové filtry). Academia, Praha 2000. ISBN 80-200-0761-X (In Czech) (CS)
Recommended reading
Not applicable.
Classification of course in study plans
Type of course unit
Lecture
39 hod., optionally
Teacher / Lecturer
Syllabus
1. Properties of one-dimensional digital filters (DF). Linear differential equation and its solution. Transfer function, impulse response, pole-zero plot. Stability and causality, frequency properties. Systems of the type of FIR and IIR and their basic properties.
2. Realization structures of DF. Avalysis of DF properties, using matrices and signal flow graphs, Mason's Gain Rule. Canonical and non-canonical realization structures. Design methods for type FIR digital filters. Quantization of transfer function coefficients, quantization of intermediate results of arithmetic operations. Quantization of input signal. Limiting the effect of quantization. Optimum method of uniformly rippled approximations, the Remez algorithm. Method of window sequences and sampling frequency characteristic.
3. Design methods for type IIR filters. Design based on analog prototype, method of signal invariance, method of bilinear transformation. Wavelet digital filters. Design by the LSM.
4. Adaptive DF. Preconditions of adaptive algorithm selection. Adaptive filter structures, type LMS alllgorithms, their application. Multirate Digital Signal Processing. Decimation, interpolation. Change in the sampling frequency in the form of rational fraction. Application of these systems in digital filtering.
5. Filter banks and poly-phase filters. Wavelet transform and principle of multiple resolution. Methods of signal analysis and compression by filter bank. Homomorphous signal processing and non-linear digital filters. Generalized principle of superposition. Complex and real cepstrum. Cepstrum application in speech and image processing.
2. Realization structures of DF. Avalysis of DF properties, using matrices and signal flow graphs, Mason's Gain Rule. Canonical and non-canonical realization structures. Design methods for type FIR digital filters. Quantization of transfer function coefficients, quantization of intermediate results of arithmetic operations. Quantization of input signal. Limiting the effect of quantization. Optimum method of uniformly rippled approximations, the Remez algorithm. Method of window sequences and sampling frequency characteristic.
3. Design methods for type IIR filters. Design based on analog prototype, method of signal invariance, method of bilinear transformation. Wavelet digital filters. Design by the LSM.
4. Adaptive DF. Preconditions of adaptive algorithm selection. Adaptive filter structures, type LMS alllgorithms, their application. Multirate Digital Signal Processing. Decimation, interpolation. Change in the sampling frequency in the form of rational fraction. Application of these systems in digital filtering.
5. Filter banks and poly-phase filters. Wavelet transform and principle of multiple resolution. Methods of signal analysis and compression by filter bank. Homomorphous signal processing and non-linear digital filters. Generalized principle of superposition. Complex and real cepstrum. Cepstrum application in speech and image processing.
Laboratory exercise
26 hod., compulsory
Teacher / Lecturer
Syllabus
1. Implementation structures of digital filters.
2. Design methods of digital filters.
2. Design methods of digital filters.