Geoscience Reference
In-Depth Information
6 Signal Processing
Trace fossils several centimeters long in
Cambrian sediments exposed in the Äleklinta
clif on the island of Öland, Sweden. Such
benthic mixing (or bioturbation) causes
signii cant distortions in sedimentary records
as it changes both the amplitude and the
phase of environmental signals. In order to
reconstruct the original signal such records
need to be deconvolved, i.e., the ef ect of the
bioturbation i lter needs to be reversed.
6.1 Introduction
Signal processing involves techniques for manipulating a signal in order to
minimize the ef ects of noise, to correct all kinds of unwanted distortions,
and to separate out various components of interest. Most signal processing
algorithms include the design and realization of i lters. A
i lter
can be
described as a system that transforms signals.
System theory
provides the
mathematical background for i lter design and realization. A i lter has an
input and an output, with the
output signal
y
(
t
) being modii ed with respect
to the
input signal
x
(
t
) (Fig. 6.1). h e
signal transformation
can be carried
out through a mathematical process known as
convolution
or, if i lters are
involved, as
i ltering
.
h is chapter deals with the design and realization of
digital i lters
with
the help of a computer. Many natural processes, however, resemble
analog i lters
that act over a range of spatial dimensions. A single rainfall
event is not recorded in lake sediments because short and low-amplitude
events are smeared over a longer time span. Bioturbation also introduces
serious distortions, for instance in deep-sea sediment records. In addition
to such natural i lters, the i eld collection and sampling of geological data
