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6 Signal Processing
6.1 Introduction
Signal processing refers to techniques for manipulating a signal to mini-
mize the effects of noise, to correct all kinds of unwanted distortions or to
separate various components of interest. Most signal processing algorithms
include the design and realization of filters. A fi lter can be described as a
system that transforms signals. System theory provides the mathematical
background for filter design and realization. A filter as a system has an input
and an output, where the output signal y(t) is modified with respect to the
input signal x(t) (Fig. 6.1). The signal transformation is often referred to as
convolution or, if filters are applied, fi ltering.
This chapter is on the design and realization of digital fi lters with the help
of a computer. However, many natural processes resemble analog fi lters that
act over a range of spatial and temporal scales. As an example, the perma-
nent mixing of the ocean and the atmosphere smoothes local weather and
climate conditions. 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 to deep-
sea sediment records. In addition to such natural fi lters, the fi eld collection
and sampling of geological data alters and smoothes the data with respect to
its original form. For example, a finite size sediment sample integrates over
Input signal Signal transformation Output signal
LTI System
Fig. 6.1 Schematic of a linear time-invariant (LTI) system. The input signal is transformed
into an output signal.
