Articoli correlati a Digital Filters: Basics and Design
Sinossi
1 Continuous-Time Systems.- 1.1 Relations in the Time Domain.- 1.2 Relations in the Frequency Domain.- 1.2.1 The Laplace Transform.- 1.2.2 The Fourier Transform.- 1.3 Transfer Functions.- 2 Analog Filters.- 2.1 The Ideal Low-Pass Filter.- 2.2 Butterworth Filters.- 2.3 Chebyshev Filters.- 2.4 Inverse Chebyshev Filters.- 2.5 Elliptic Filters.- 2.6 Bessel Filters.- 2.7 Filter Fransformations.- 2.7.1 Low-Pass High-Pass Transformation.- 2.7.2 Low-Pass Bandpass Transformation.- 2.7.3 Low-pass Bandstop Transformation.- 2.7.4 Filter Transformations in Practice.- 3 Discrete-Time Systems.- 3.1 Discrete-Time Convolution.- 3.2 Relations in the Frequency Domain.- 3.3 The z-Transform.- 3.3.1 Definition of the z-Transform.- 3.3.2 Properties of the z-Transform.- 3.3.3 Examples.- 3.4 Stability Criterion in the Time Domain.- 3.5 Further Properties of the Unit-Sample Response h(n).- 4 Sampling Theorem.- 4.1 Introduction.- 4.2 Sampling.- 4.3 Band-Limited Signals.- 4.4 Practical Aspects of Signal Conversion.- 4.4.1 Analog-to-Digital Conversion.- 4.4.2 Digital-to-Analog Conversion.- 4.5 Mathematical Analysis of the D/A Conversion Process.- 5 Filter Structures.- 5.1 Graphical Representation of Discrete-Time Networks.- 5.2 FIR Filters.- 5.2.1 The Basic Structure of FIR Filters.- 5.2.2 Poles and Zeros of the FIR Filter.- 5.2.3 Linear-Phase Filters.- 5.3 IIR Filters.- 5.3.1 An Introductory Example.- 5.3.2 Direct-Form Filters.- 5.3.3 Poles and Zeros.- 5.4 Further Properties of Transfer Functions.- 5.4.1 Stability Considerations in the Frequency Domain.- 5.4.2 Minimum-Phase Filters.- 5.5 State-Space Structures.- 5.6 The Normal Form.- 5.7 Digital Ladder Filters.- 5.7.1 Lossless Networks.- 5.7.2 Realisability.- 5.7.3 Kirchhoff Ladder Filters.- 5.7.4 Wave Digital Filters.- 5.7.4.1 Wave Parameters.- 5.7.4.2 Decomposition of the Analog Reference Network into One-Ports and Multi-Ports.- 5.7.4.3 The Reflectance of Capacitor and Inductor.- 5.7.4.4 The Role of the Bilinear Transform.- 5.7.4.5 Observance of the Realisability Condition.- 5.7.4.6 Second-Order Wave Digital Filter Block.- 6 Design of IIR Filters.- 6.1 Introduction.- 6.2 Preservation Theorem of the Convolution.- 6.3 Approximation in the Time Domain.- 6.3.1 Impulse-Invariant Design.- 6.3.2 Step-Invariant Design.- 6.3.3 Ramp-Invariant Design.- 6.4 Approximation in the Frequency Domain.- 6.4.1 Difference Method.- 6.4.2 Bilinear Transform.- 6.4.3 Practical Filter Design Using the Bilinear Transform.- 6.4.4 IIR Filter with Bessel Characteristics.- 6.4.4.1 Design with Prescribed Delay t0.- 6.4.4.2 Design with Given 3-dB Cutoff Frequency.- 7 Design of FIR Filters.- 7.1 Introduction.- 7.2 Linear-Phase Filters.- 7.3 Frequency Sampling.- 7.4 Minimisation of the Mean-Square Error.- 7.4.1 Direct Solution.- 7.4.2 The Window Method.- 7.5 Chebyshev Approximation.- 7.5.1 The Remez Exchange Algorithm.- 7.5.2 Polynomial Interpolation.- 7.5.3 Introduction of a Weighting Function.- 7.5.4 Case 2, 3 and 4 Filters.- 7.5.5 Minimum-Phase FIR Filters.- 7.6 Maximally Flat (MAXFLAT) Design.- 8 Effects of Finite Register Length.- 8.1 Classification of the Effects.- 8.2 Number Representation.- 8.2.1 Fixed-Point Numbers.- 8.2.2 Floating-Point Numbers.- 8.3 Quantisation.- 8.3.1 Fixed-Point Numbers.- 8.3.2 Floating-Point Numbers.- 8.4 System Noise Behaviour.- 8.4.1 Signal-to-Noise Ratio.- 8.4.2 Noise Filtering by LSI Systems.- 8.4.3 Optimum Use of the Dynamic Range.- 8.5 Noise Optimisation with Fixed-Point Arithmetic.- 8.5.1 Noise Behaviour of First- and Second-Order Filter Blocks.- 8.5.2 Shaping of the Noise Spectrum.- 8.5.3 Noise in a Cascade of Second-Order Filter Blocks.- 8.6 Finite Coefficient Wordlength.- 8.6.1 Coefficient Sensitivity.- 8.6.2 Graphical Representation of the Pole Density.- 8.6.3 Increased Pole Density at Low and High Frequencies.- 8.6.4 Further Remarks Concerning Coefficient Sensitivity.- 8.6.5 A Concluding Example.- 8.7 Limit Cycles.- 8.7.1 Nonlinearities in Actual Implementations.- 8.7.2 Stability of the Linear
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