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Z-plane, causality, and feedback
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Z-plane, causality, and feedback
LEAKY INTEGRATION
Plots
Two poles
SMOOTHING WITH BOX AND TRIANGLE
Smoothing with a rectangle
Smoothing with a triangle
CAUSAL INTEGRATION FILTER
The accuracy of causal integration
Examples of causal integration
Symmetrical double integral
Nonuniqueness of the integration operator
DAMPED OSCILLATION
Narrow-band filters
Polynomial division
Spectrum of a pole
Rational filters
INSTABILITY
Anticausality
Inverse filters
The unit circle
The mapping between Z and complex frequency
The meaning of divergence
Boundedness
Causality and the unit circle
MINIMUM-PHASE FILTERS
Mechanical interpretation
Laurent expansion
INTRODUCTION TO ALL-PASS FILTERS
Notch filter
PRECISION EXHAUSTION
MY FAVORITE WAVELET
IMPEDANCE FILTERS
About this document ...
Stanford Exploration Project
10/21/1998
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