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Book Chapter

Filtering

Published:
January 01, 2008

Abstract

What is digital filtering? The behavior of analog filters ordinarily is studied in the frequency domain. Digital filtering, on the other hand, is treated more fruitfully in the time domain. A digital filter is represented by its impulse response. The impulse response is made up of a sequence of numbers that act as weighting coefficients. The output of a digital filter is obtained by convolving the digitized input signal with the filter's impulse response.

The mechanics of digital filtering in the time domain can be described with the aid of Z-transform theory. The amplitude spectrum and the phase spectrum represent an important characterization of the filter. A digital filter is said to be causal if its output at time n depends only on its input at time n and on inputs at times before n. In Chapter 6, these ideas are related to the more familiar interpretation of filter behavior in the frequency domain.

What is a causal digital filter? As we just mentioned, a digital filter is represented by a sequence of numbers called its impulse response or its weighting coefficients. A digital filter is causal if its present output (at time n) depends only on present and past inputs (that is, depends only on inputs at times n, n − 1, n − 2, …, and so on). Another term for a causal filter is a realizable filter.

What is a constant digital filter? A constant filter is one that has a single constant weighting coefficient

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Contents

Society of Exploration Geophysicists Geophysical References Series

Digital Imaging and Deconvolution: The ABCs of Seismic Exploration and Processing

Enders A. Robinson
Enders A. Robinson
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Sven Treitel
Sven Treitel
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Society of Exploration Geophysicists
Volume
15
ISBN electronic:
9781560801610
Publication date:
January 01, 2008

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