Titlebook: Spectral Analysis and Filter Theory in Applied Geophysics; Burkhard Buttkus Book 2000 Springer-Verlag Berlin Heidelberg 2000 Digital data

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Analogy

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Spectral Representation of Nonperiodic Processesined in most cases. If a function .(.) satisfies the Dirichlet conditions (see chapter 1) within an arbitrary interval and if the integral .converges, i.e., .(.) is an absolutely integrable function, .(.) can then be expressed as the Fourier integral.where.or as

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Characterization of Random Processes in the Time and Frequency Domainsds. It is not possible to describe such processes analytically. We are thus limited to describing them using statistical parameters. The objective of this is to characterize the process so that it can be analyzed and any alterations caused by transfer systems can be evaluated.

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Evaluation of Magnetotelluric Survey Datadata. The natural magnetic and electric fields at the surface of the Earth—covering a large range of frequencies—depend on the electrical conductivity in the ground. High-frequency fields are affected by the electrical conductivity of near-surface rocks, while fields with lower frequencies are influenced by deeper layers.

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Fourier Series Representation of Periodic FunctionsWith few exceptions, periodic functions can be expressed as a Fourier series of sine and cosine functions. If .(.)

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z-Transform Representation of Time SeriesIf a function .. is sampled at equidistant intervals Δ. at times . = .Δ., . = …, ?1,0,1,2,…, a discrete sequence of values .(.Δ.) is obtained. To simplify the notation, the values .(.Δ.) are represented by the index notation

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