Graphics Programs Reference
In-Depth Information
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 modifi ed with respect to the
input signal x
(
t
) (Fig. 6.1). The
signal transformation
is often referred to as
convolution or, if fi lters 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 fi nite 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.
