Filter Design for Signal Processing Using MATLAB and Mathematica
Published on 15. September 2000
Book
Hardback
756 pages
978-0-201-36130-8 (ISBN)
Description
For courses in Digital Signal Processing.
This text opens up completely new vistas in basic analog and digital IIR filter design-regardless of the technology. By introducing exceptionally elegant and creative mathematical stratagems (e.g., accurate replacement of Jacobi elliptic functions by functions comprising polynomials, square roots, and logarithms), optimization routines carried out with symbolic analysis by Mathematica, and the advanced filter design software of MATLAB, it shows students how to design many types of filters that cannot be designed using conventional techniques. The filter design algorithms can be directly programmed in any language or environment such as Visual BASIC, Visual C, Maple, DERIVE, or MathCAD.
This text opens up completely new vistas in basic analog and digital IIR filter design-regardless of the technology. By introducing exceptionally elegant and creative mathematical stratagems (e.g., accurate replacement of Jacobi elliptic functions by functions comprising polynomials, square roots, and logarithms), optimization routines carried out with symbolic analysis by Mathematica, and the advanced filter design software of MATLAB, it shows students how to design many types of filters that cannot be designed using conventional techniques. The filter design algorithms can be directly programmed in any language or environment such as Visual BASIC, Visual C, Maple, DERIVE, or MathCAD.
More details
Language
English
Place of publication
United States
Publishing group
Pearson Education (US)
Target group
College/higher education
Dimensions
Height: 242 mm
Width: 185 mm
Thickness: 30 mm
Weight
1293 gr
ISBN-13
978-0-201-36130-8 (9780201361308)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Content
(NOTE: Most chapters conclude with Summary, MATLAB Exercises, and Mathematic Exercises.)
1. Signals.
Signal Classification. The Sampling Theorem. Basic Continuous-Time Signals-Functions. Basic Discrete-Time Signals-Sequences. Continuous-Time Signals in MATLAB. Sequences in MATLAB. Continuous-Time Signals in Mathematica. Sequences in Mathematica.
2. Systems.
Basic Definitions. Block Diagrams. System Properties. Linear Time-Invariant Systems.
3. Transforms.
Phasor Transformation. Fourier Series and Harmoni Analysis. Fourier Transform. Laplace Transform. Discrete Fourier Transform. The z Transform. Analysis of LTI Systems by Transform Method.
4. Classic Analog Filter Design.
Introduction to Analog Filters. Basic Filter Transfer Functions. Decomposition of Transfer Functions. Pole-Zero Pairing. Optimum Cascading Sequence. Sensitivity. Analog Filter Realizations. Op Amp Active RC Filters. Switched-Capacitor (SC) Filters. Passive RLC Filters. Operational Transconductance Amplifier (OTA) Filters. Current-Conveyor (CC) Filters.
5. Advanced Analog Filter Design Case Studies.
Basic Definitions. Specification of an Analog Filter. Approximation Problem. Design Space. Basic Design Alternatives. Visualization of Design Space. SC Filter Advanced Design Example.
6. Advanced Analog Filter Design Algorithms.
Introduction. Notation. Design Equations and Procedures. Design D1. Design D2. Design D3a. Design D3b. Design D4a. Design D4b. Design D5. Time Response and Frequency Response. Highpass Filter. Bandpass Filter. Bandreject Filter. Concluding Remarks.
7. Multicriteria Optimization of Analog Filter Designs.
Introduction. Notation. Objective Function. Constraints. Example Filter Designs. Validation and Verification of the Automated Framework. Conclusion.
8. Classic Digital Filter Design.
Introduction to Digital Filters. Basic Filter Transfer Functions. Decomposition of Transfer Functions. Pole-Zero Pairing. Optimum Cascading Sequence. Finite Wordlength Effects. Digital Filter Realizations. Comparison of Realizations.
9. Advanced Digital Filter Design Case Studies.
Basic Definitions. Specification of a Digital Filter. Approximation Step. Design Space. Basic Design Alternatives. Visualization of Design Space. Elliptic Half-Band IIR Filters. Hilbert Transformer. Multiplierless Elliptic IIR Filters. Linear Phase IIR Filters.
10. Advanced Digital Filter Design Algorithms.
Introduction. Notation. Design Equations and Procedures. Design D1. Design D2. Design D3a. Design D3b. Design D4a. Design D4b. Design D5. Frequency Response. Highpass Filter. Bandpass Filter. Bandreject Filter. Concluding Remarks.
11. Multicriteria Optimization of Digital Filter Designs.
Introduction. Notation. Objective Function. Constraints. Example. Conclusion.
12. Elliptic Functions.
Legendre Elliptic Integral. Jacobi Elliptic Functions. Periods of Elliptic Functions. Series Representation and Modular Constant. Chebyshev Polynomials. Elliptic Rational Function. Nesting Property of Jacobi Elliptic Functions. Poles of Normalized Transfer Function. Exact Formulas for Zeros of Elliptic Rational Functions. The Degree Equation. Elliptic Filters with Minimal Q-Factors.
13. Elliptic Rational Function.
Chebyshev Polynomials. Second-Order Elliptic Rational Function. Elliptic Rational Function of Order 2i. Third-Order Elliptic Rational Functions. Elliptic Rational Functions of Order 2i 3j. Fifth-Order Elliptic Rational Functions. Modified Elliptic Rational Functions. Poles, Zeros, and Selectivity Factor. Exact Formulas for Zeros. Approximate Determination of Zeros. Discrimination Factor. Selectivity Factor Versus Discrimination Factor. Transfer Function Poles. Transfer Function with Minimal Q-Factors.
Example Mathematica Notebooks.
Analysis by Transform Method of Analog LTI Circuits. Analysis by Transform Method of Discrete-Time LTI Systems. Switched Capacitor Filter-Mode 3a Analysis and Design. OTA-C General Biquad Analysis and Design. Lowpass-Medium-Q-Factor Active RC Filter Analysis and Design. General Purpose High-Q-Factor RC Filter Analysis and Design. Advanced Analog Filter Design Case Studies. Classical Digital Filters Transpose Direct Form II IIR 2nd-Order Realization. Advanced Digital Filter Design Case Studies. Jacobi Elliptic Functions. Elliptic Rational Function. Transfer Function with Minimal Q-Factors.
References.
Index.
1. Signals.
Signal Classification. The Sampling Theorem. Basic Continuous-Time Signals-Functions. Basic Discrete-Time Signals-Sequences. Continuous-Time Signals in MATLAB. Sequences in MATLAB. Continuous-Time Signals in Mathematica. Sequences in Mathematica.
2. Systems.
Basic Definitions. Block Diagrams. System Properties. Linear Time-Invariant Systems.
3. Transforms.
Phasor Transformation. Fourier Series and Harmoni Analysis. Fourier Transform. Laplace Transform. Discrete Fourier Transform. The z Transform. Analysis of LTI Systems by Transform Method.
4. Classic Analog Filter Design.
Introduction to Analog Filters. Basic Filter Transfer Functions. Decomposition of Transfer Functions. Pole-Zero Pairing. Optimum Cascading Sequence. Sensitivity. Analog Filter Realizations. Op Amp Active RC Filters. Switched-Capacitor (SC) Filters. Passive RLC Filters. Operational Transconductance Amplifier (OTA) Filters. Current-Conveyor (CC) Filters.
5. Advanced Analog Filter Design Case Studies.
Basic Definitions. Specification of an Analog Filter. Approximation Problem. Design Space. Basic Design Alternatives. Visualization of Design Space. SC Filter Advanced Design Example.
6. Advanced Analog Filter Design Algorithms.
Introduction. Notation. Design Equations and Procedures. Design D1. Design D2. Design D3a. Design D3b. Design D4a. Design D4b. Design D5. Time Response and Frequency Response. Highpass Filter. Bandpass Filter. Bandreject Filter. Concluding Remarks.
7. Multicriteria Optimization of Analog Filter Designs.
Introduction. Notation. Objective Function. Constraints. Example Filter Designs. Validation and Verification of the Automated Framework. Conclusion.
8. Classic Digital Filter Design.
Introduction to Digital Filters. Basic Filter Transfer Functions. Decomposition of Transfer Functions. Pole-Zero Pairing. Optimum Cascading Sequence. Finite Wordlength Effects. Digital Filter Realizations. Comparison of Realizations.
9. Advanced Digital Filter Design Case Studies.
Basic Definitions. Specification of a Digital Filter. Approximation Step. Design Space. Basic Design Alternatives. Visualization of Design Space. Elliptic Half-Band IIR Filters. Hilbert Transformer. Multiplierless Elliptic IIR Filters. Linear Phase IIR Filters.
10. Advanced Digital Filter Design Algorithms.
Introduction. Notation. Design Equations and Procedures. Design D1. Design D2. Design D3a. Design D3b. Design D4a. Design D4b. Design D5. Frequency Response. Highpass Filter. Bandpass Filter. Bandreject Filter. Concluding Remarks.
11. Multicriteria Optimization of Digital Filter Designs.
Introduction. Notation. Objective Function. Constraints. Example. Conclusion.
12. Elliptic Functions.
Legendre Elliptic Integral. Jacobi Elliptic Functions. Periods of Elliptic Functions. Series Representation and Modular Constant. Chebyshev Polynomials. Elliptic Rational Function. Nesting Property of Jacobi Elliptic Functions. Poles of Normalized Transfer Function. Exact Formulas for Zeros of Elliptic Rational Functions. The Degree Equation. Elliptic Filters with Minimal Q-Factors.
13. Elliptic Rational Function.
Chebyshev Polynomials. Second-Order Elliptic Rational Function. Elliptic Rational Function of Order 2i. Third-Order Elliptic Rational Functions. Elliptic Rational Functions of Order 2i 3j. Fifth-Order Elliptic Rational Functions. Modified Elliptic Rational Functions. Poles, Zeros, and Selectivity Factor. Exact Formulas for Zeros. Approximate Determination of Zeros. Discrimination Factor. Selectivity Factor Versus Discrimination Factor. Transfer Function Poles. Transfer Function with Minimal Q-Factors.
Example Mathematica Notebooks.
Analysis by Transform Method of Analog LTI Circuits. Analysis by Transform Method of Discrete-Time LTI Systems. Switched Capacitor Filter-Mode 3a Analysis and Design. OTA-C General Biquad Analysis and Design. Lowpass-Medium-Q-Factor Active RC Filter Analysis and Design. General Purpose High-Q-Factor RC Filter Analysis and Design. Advanced Analog Filter Design Case Studies. Classical Digital Filters Transpose Direct Form II IIR 2nd-Order Realization. Advanced Digital Filter Design Case Studies. Jacobi Elliptic Functions. Elliptic Rational Function. Transfer Function with Minimal Q-Factors.
References.
Index.