with Digital Filtering Applications

by Dr. Claude S. Lindquist


1 GENERAL CONCEPTS Digital versus Analog Filters, Digital Filter Components, Sampling - Uniform, Multirate, Nonuniform, Adaptive; Continuous, Series, and Discrete Transforms; Laplace Transform and Inverse Transform, Fourier Transform and Inverse Transform, Fourier Series, Discrete Fourier Transform and Series, Z-Transform, Inverse Z-Transform, Linearity, Causality, Stability, Signal Flow Graphs, Sensitivity, Root Locus, Random Signals.

2 FREQUENCY DOMAIN ANALYSIS Discrete Fourier, Chirp, and Zoom Transforms; Fast Fourier Transform, Time Domain Windowing, Frequency Domain Windowing; Walsh, Cal-Sal, Paley, Hadamard, Haar, Slant, and Karhunen-Lo\'eve Transforms; Relation Between Transform Coefficients, Two-Dimensional Transforms, Running Transforms.

3 TIME DOMAIN ANALYSIS Inverse Z-Transform, Fourier, Paley, Hadamard, Haar, Slant, and Karhunen-Lo\'eve Transforms; Simple Interpolators, Lagrange Interpolators, Ideal Lowpass Filter Interpolator, Fourier Series Interpolator, Generalized Series Interpolator, Nonzero Sample Duration Distortion, Signal Truncation Distortion, Window Size Adjustment, Constant Delay and Constant Magnitude Filters.

4 IDEAL FILTER RESPONSE Ideal Lowpass Filters, Classical Filters -- Butterworth, Chebyshev, Elliptic, Bessel; Optimum Filters; Adaptive Filters -- Distortion Balance, General Estimation, General Detection, Wiener Estimation, Pulse-Shaping Estimation, Correlation, Matched Detection, Inverse Detection, High-Resolution Detection, Transitional, Statistically Optimum Filters, Adaptation and Learning Process, Performance Measures; Class 1, 2, and 3 Adaptive Filters; Frequency Domain Smoothing, Adaptive Filters Using Feedback; Homomorphic Filters -- Multiplicative, Convolutional, Other Filters; Amplitude Domain Filters.

5 DIGITAL TRANSFORMATIONS S-Domain to Z-Domain Transformations, Numerical Integration Transforms H_{dmn}, Forward Euler Transform H_{111}, Backward Euler Transform H_{001}, Bilinear Transform H_{011}, Modified Bilinear Transform H_{MBDI} and H_{121}, Lossless Transform H_{LDI} and H_{112}, Optimum Transform H_{ODI} and H_{134}, Numerical Integration Filter Orders, Input-Invariant Transforms, Impulse-Invariant Transform, Step-Invariant Transform, Ramp-Invariant Transform, Sine, Cosine, and Complex Exponential Step-Invariant Transforms; Comparison of Transforms, Analog-to-Digital System Conversion.

6 FREQUENCY TRANSFORMATIONS Direct Analog Lowpass-to-Digital Highpass Transformations, Complementary Transformation, Direct Analog Lowpass-to-Digital Bandpass Transformations, Frequency Discriminator Transformations, Direct Analog Lowpass-to-Digital Bandstop Transformations, Lowpass-to-Allpass Transformations.


7 DIGITAL FILTER CLASSIFICATION Fast Transform Filters, Nonrecursive Filters, Recursive Filters, Selection of Implementation Form.

8 FAST TRANSFORM FILTER DESIGN Fast Transform Algorithms, Fast Fourier Transform Scalar Filters, FFT-Based Vector Filters, Fast Transform Vector Filters, Fast Transform Scalar Filters, Karhunen-Lo\'eve Scalar Filters, Time Domain Vector and Scalar Filters, Fast Transform Spectra.

9 FFT FILTER DESIGN Filter Structures, Estimation Filters, Adaptive Line Enhancers (ALE) and Noise Cancellers (ANC), Detection Filters, Correlation Filters, Delay Estimation Filters, Image Registration Filters, Image Enhancement Filters, Communication Filters, Radar Filters, Biomedical Filters, Filter Implementation.

10 NONRECURSIVE FILTER DESIGN Nonrecursive Filter Properties, Fourier Series Design (Integral Squared-Error Algorithm), Weighted Fourier Series Design (Windowing Algorithms), Frequency Sampling Design (Zero Point-Error Algorithm); Numerical Analysis Algorithms -- Interpolation, Differentiation Algorithms; Adaptive Nonrecursive Algorithms -- Search Methods, Newton's Method and Algorithms, Steepest Descent Method and Algorithms, LMS Algorithms, Frequency Domain Adaptive Nonrecursive Filters; Median Filters.

11 RECURSIVE FILTER DESIGN Recursive Filter Properties, Frequency Transformation Design (Frequency Domain Algorithms); Invariant Time Domain Response Design (Time Domain Algorithms) -- Impulse-Invariant Transform Design, Modified Impulse-Invariant Transform Design; Matched Z-Transform Design (Pole-Zero Mapping Algorithm); More Numerical Integration Transforms -- Single Integration, Multiple Integration and Differentiation Algorithms; Adaptive Recursive Algorithms -- Search Methods and Algorithms, Kalman Filters.

12 DIGITAL FILTER REALIZATION Canonical Structures, Multiple Feedback Realizations, Biquadratic Realizations, Cascade Realizations, Parallel Realizations, Lattice Realizations, Ladder Realizations, Analog Filter Simulations, Wave (Scattering Parameter) Realizations.

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