19-10-2012, 05:38 PM
The Fundamentals of Signal Analysis
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Introduction
The analysis of electrical signals is
a fundamental problem for many
engineers and scientists. Even if the
immediate problem is not electrical,
the basic parameters of interest are
often changed into electrical signals
by means of transducers. Common
transducers include accelerometers
and load cells in mechanical work,
EEG electrodes and blood pressure
probes in biology and medicine, and
pH and conductivity probes in chemistry.
The rewards for transforming
physical parameters to electrical signals
are great, as many instruments
are available for the analysis of electrical
signals in the time, frequency
and modal domains. The powerful
measurement and analysis capabilities
of these instruments can lead to
rapid understanding of the system
under study.
The Time Domain
The traditional way of observing
signals is to view them in the time
domain. The time domain is a record
of what happened to a parameter of
the system versus time. For instance,
Figure 2.1 shows a simple springmass
system where we have attached
a pen to the mass and pulled a piece
of paper past the pen at a constant
rate. The resulting graph is a record
of the displacement of the mass
versus time, a time domain view of
displacement.
Such direct recording schemes are
sometimes used, but it usually is
much more practical to convert
the parameter of interest to an
electrical signal using a transducer.
Transducers are commonly available
to change a wide variety of parameters
to electrical signals. Microphones,
accelerometers, load cells,
conductivity and pressure probes are
just a few examples.
The Frequency Domain
It was shown over one hundred years
ago by Baron Jean Baptiste Fourier
that any waveform that exists in the
real world can be generated by
adding up sine waves. We have illustrated
this in Figure 2.5 for a simple
waveform composed of two sine
waves. By picking the amplitudes,
frequencies and phases of these sine
waves correctly, we can generate a
waveform identical to our
desired signal.
Conversely, we can break down our
real world signal into these same sine
waves. It can be shown that this combination
of sine waves is unique; any
real world signal can be represented
by only one combination of sine
waves.
Why the Frequency Domain?
Suppose we wish to measure the
level of distortion in an audio oscillator.
Or we might be trying to detect
the first sounds of a bearing failing on
a noisy machine. In each case, we are
trying to detect a small sine wave in
the presence of large signals. Figure
2.7a shows a time domain waveform
which seems to be a single sine wave.
But Figure 2.7b shows in the frequency
domain that the same signal is
composed of a large sine wave and
significant other sine wave components
(distortion components). When
these components are separated in
the frequency domain, the small
components are easy to see because
they are not masked by larger ones.