|   Preface to the third edition | |
| Introduction | |
| What is a digital filter? | |
| Why should we care about digital filters? | |
| How shall we treat the subject? | |
| General-purpose versus special-purpose computers | |
| Assumed statistical background | |
| The distribution of a statistic | |
| Noise amplification in a filter | |
| Geometric progressions | |
| The frequency approach | |
| Introduction | |
| Aliasing | |
| The idea of an eigenfunction | |
| Invariance under translation | |
| Linear systems | |
| The eigenfunctions of equally spaced sampling | |
| Summary | |
| Some classical applications | |
| Introduction | |
| Least-squares fitting of polynomials | |
| Least-squares quadratics and quartics | |
| Modified least squares | |
| Differences and derivatives | |
| More on smoothing: decibles | |
| Missing data and interpolation | |
| A class of nonrecursive smoothing filters | |
| An example of how a filter works | |
| Integration: recursive filters | |
| Summary | |
| Fourier series: continuous case | |
| Need for the theory | |
| Orthogonality | |
| Formal expansions | |
| Odd and even functions | |
| Fourier series and least squares | |
| Class of functions and rate of convergence | |
| Convergence at a point of continuity | |
| Convergence at a point of discontinuity | |
| The complex Fourier series | |
| The phase form of a Fourier series | |
| Windows | |
| Introduction | |
| Generating new Fourier series: the convolution theorems | |
| The Gibbs phenomenon | |
| Lanczos smoothing: The sigma factors | |
| The Gibbs phenomenon again | |
| Modified Fourier series | |
| The von Hann window: the raised cosine window | |
| Hamming window: raised cosine with a platform | |
| Review of windows | |
| Design of nonrecursive filters | |
| Introduction | |
| A low-pass filter design | |
| Continuous design methods: a review | |
| A differentiation filter | |
| Testing the differentiating filter on data | |
| New filters from old ones: sharpening a filter | |
| Bandpass differentiators | |
| Midpoint formulas | |
| Smooth nonrecursive filters | |
| Objections to ripples in a transfer function | |
| Smooth filters | |
| Transforming to the Fourier series | |
| Polynomial Processing in general | |
| The design of a smooth filter | |
| Smooth bandpass filters | |
| The Fourier integral and the sampling theorem | |
| Introduction | |
| Summary of results | |
| The Sampling theorem | |
| The Fourier integral | |
| Some transform pairs | |
| Band-limited functions and the Sampling theorem | |
| The convolution theorem | |
| The effect of a finite sample size | |
| Windows | |
| The uncertainty principle | |
| Kaiser windows and optimization | |
| Windows | |
| Review of Gibbs Phenomenon and the Rectangular window | |
| The Kaiser window: I subscript 0-sinh window | |
| Derivation of the Kaiser formulas | |
| Design of a bandpass filter | |
| Review of Kaiser window filter design | |
| The same differentiator again | |
| A particular case of differentiation | |
| Optimizing a design | |
| A Crude method of optimizing | |
| The finite Fourier series | |
| Introduction | |
| Orthogonality | |
| Relationship between the discrete and continuous expansions | |
| The fast Fourier transform | |
| Cosine expansions | |
| Another method of design | |
| Padding out zeros | |
| The spectrum | |
| Review | |
| 11 | |
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