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The Approximation Problem
Introduction
Minimum Phase Transfer Functions
Equiripple Response Characteristics
Amplitude Approximations for Lumped Networks
Introduction
Maximally Flat Response
Chebyshev Response
Inverse Chebyshev Response
Elliptic Function Response
Synthesis of Ladder Networks
Explicit Formulas for Element Values in Chebyshev Filters
Summary of Results for Chebyshev and Maximally Flat Filters
Explicit Formulas for Element Values in Elliptic Function Filters
Summary of Results for Elliptic Function and Inverse Chebyshev Filters
Determination of the Degree of the Prototype Filter
Frequency Transformations and Impedance Scaling
Approximate Design Techniques for Band-stop and Band-pass Filters
Phase Approximations for Lumped Networks
Introduction
Maximally Flat Linear Phase Polynomial
Equidistant Linear Phase Polynomial
Equidistant Constant Phase Delay Polynomial
Arbitrary Phase Polynomials
Maximally Flat Logarithmic Phase Polynomial
All-pass Networks and Reflection Filters
Simultaneous Amplitude and Phase Approximations for Lumpec! Networks
Introduction
Constant Amplitude Filters with Phase Equalization
Linear Phase Filters with Amplitude Equalization
Optimum Maximally Flat Constant Amplitude and Linear Phase Response
Optimum Maximally Flat Constant Amplitude and Logarithmic Phase Response
Finite-band Approximations to Constant Amplitude and Arbitrary Phase Response
Prototype Synthesis Procedure for Transmission Type Filters
Amplitude Approximations for Distributed Networks
Introduction
Stepped Impedance Transmission Line Filters with Maximally Flat and Chebyshev Response Characteristics
Explicit Formulas for Element Values in Chebyshev Sepped Impedance Transmission Line Filters
Summary of Results for Chebyshev and Maximally Flat Distributed Prototype Filters
Interdigital Filters with Maximally Flat and Chebyshev Response Characteristics
Explicit Formulas for Element Values in Chebyshev Interdigital Filters
Summary of Results for Chebyshev and Maximally Flat Interdigital Filters
Fourier Coefficient Design Technique for Stepped Impedance Transmission Line Filters
Explicit Formulas for Element Values in Arbitrary Stepped Impedance Transmission Line Filters
Phase Approximations for Distributed Networks
Introduction
Exact Linear Phase Polynomials
Maximally Flat Distributed Linear Phase Polynomial
Equidistant and Arbitrary Distributed Linear Phase Polynomials
Distributed All-pass and Reflection Filters
Simultaneous Amplitude and Phase Approximations for Distributed Networks
Introduction
Constant Amplitude Filters with Exact Linear Phase
Constant Amplitude Filters with Phase Equalization
Linear Phase Filters with Amplitude Equalization
Optimum Constant Amplitude and Linear Phase Filters
Synthesis of Generalized Interdigital Filters
Digital Filters
Introduction
Basic Digital Wave Filters
Selective Linear Phase Filters
Appendix: Miscellaneous Amplitude Approximations
Generalized Chebyshev Functions with Prescribed Poles
Generalized Chebyshev Functions with Prescribed Zeros
Even Polynomials and Functions Equiripple over Two Bands
Maximally Flat Odd Polynomial Approximating Constant
Maximally Flat Odd Function Approximating Constant
Equiripple Odd Function Approximating Constant
Equiripple Two-band Odd Polynomial Approximating Zero
References