Abstract
For nonperiodic processes, a discrete spectral representation using Eq. (1.9) is not possible. However, a continuous spectral distribution can be obtained in most cases. If a function x(t) satisfies the Dirichlet conditions (see chapter 1) within an arbitrary interval and if the integral \( \int_{{ - \infty }}^{\infty } {\left| {x\left( t \right)\left| {dt} \right.} \right.} \) converges, i.e., x(t) is an absolutely integrable function, x(t) can then be expressed as the Fourier integral
where
or as
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© 2000 Springer-Verlag Berlin Heidelberg
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Buttkus, B. (2000). Spectral Representation of Nonperiodic Processes. In: Spectral Analysis and Filter Theory in Applied Geophysics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-57016-2_3
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DOI: https://doi.org/10.1007/978-3-642-57016-2_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-62943-3
Online ISBN: 978-3-642-57016-2
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