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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Digital Imaging and Deconvolution: The ABCs of Seismic Exploration and Processing (SEG Geophysical References Series No. 15), covers the basic ideas and methods used in seismic processing, concentrating on the fundamentals of seismic imaging and deconvolution. Most chapters are followed by problem sets. Some exercises supplement textual material; others are meant to stimulate classroom discussions. Text and exercises deal mostly with simple examples that can be solved with nothing more than pencil and paper. The book covers wave motion; digital imaging; digital filtering; various visualization aspects of the seismic reflection method; sampling theory; the frequency spectrum; synthetic seismograms; wavelets and wavelet processing; deconvolution; the need for continuing interaction between the seismic interpreter and the computer; seismic attributes; phase rotation; and seismic attenuation. The last of the 15 chapters gives a detailed mathematical overview. Digital Imaging and Deconvolution, nominated for the Association of Earth Science Editors award for best geoscience publication of 2008–2009, will interest professional geophysicists, graduate students, and upper-level undergraduates in geophysics. The book also will be helpful to scientists and engineers in other disciplines who use digital signal processing to analyze and image wave-motion data in remote-detection applications. The methods described are important in optical imaging, video imaging, medical and biological imaging, acoustical analysis, radar, and sonar.