Graphics Programs Reference
In-Depth Information
a certain period of time and therefore smoothes the natural signal. Similarly,
the measurement of magnetic susceptibility with the help of a loop sensor
introduces signifi cant smoothing since the loop integrates over a certain sec-
tion of the sediment core.
In most cases, the characteristics of these natural fi lters are diffi cult to de-
termine. Numerical fi lters, however, are designed with well-defi ned charac-
teristics. In addition, artifi cial fi lters are time invariant in most cases, while
natural fi lters, such as ocean mixing or bioturbation, may change with time.
An easy way to describe or predict the effect of a fi lter is to explore the
fi lter output of a simple input signal, such as a sine wave, a square wave, a
sawtooth, ramp or step function. Although there is an endless variety of such
signals, most systems or fi lters are described by their impulse response, i.e.,
the output of a unit impulse.
The chapter starts with a more technical section on generating periodic
signals, trends and noise, similar to Chapter 5.1. Chapter 6.3 is on linear
time-invariant systems, which provide the mathematical background for fi l-
ters. The following Chapters 6.4 to 6.9 are on the design, the realization and
the application of linear time-invariant fi lters. Chapter 6.10 then suggests
the application of daptive fi lters originally developed in telecommunication
automatically. Adaptive fi lters extract noisefree signals from duplicate mea-
surements on the same object. Such fi lters can be used in a large number of
applications, such as noise removal from duplicate paleoceanographic time
series or to improve the signal-to-noise ratio of parallel color-intensity tran-
sects across varved lake sediments (see Chapter 5, Fig. 5.1). Moreover, such
fi lters are also widley-used in geophysics for noise canceling.
6.2 Generating Signals
MATLAB provides numerous tools to generate basic signals that can be
used to illustrate the effects of fi lters. In the previous chapter we have gener-
ated a signal by adding together three sine waves with different amplitudes
and periods. In the following example, the time vector is transposed for the
purpose of generating column vectors.
t = (1:100)';
x = 2*sin(2*pi*t/50) + sin(2*pi*t/15) + 0.5*sin(2*pi*t/5);
plot(t,x), axis([0 100 -4 4])
Frequency-selective fi lters are very common in earth sciences. They are
used for removing certain frequency bands from the data. As an example,
