Biomedical Engineering Reference
In-Depth Information
can be recreated by simply mixing primary colors (red, green, and blue, or RGB) in the cor-
rect proportions. Television and computer displays often transmit signals as RGB, and these
signals are collated together to create colors much as a master painter would on a canvas. In
fact, the human visual system takes exactly the opposite approach. The retina decomposes
images and scenery from the outside world into purely red-green-blue signals that are inde-
pendently analyzed and processed by our brains. Despite this, we perceive a multitude of
colors and shades.
This simple color analogy is at the heart of Fourier's theory, which states that a complex
waveform can be approximated to any degree of accuracy with simpler functions. In 1807,
Fourier showed that an arbitrary periodic signal of period, T, can be represented mathemat-
ically as a sum of trigonometric functions. Conceptually, this is achieved by summing or
mixing sinusoids while simultaneously adjusting their amplitudes and frequency, as shown
for a square wave function in Figure 11.7.
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(b)
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(e)
FIGURE 11.7
A square wave signal (a) is approximated by adding sinusoids (B-E). (b) 1 sinusoid, (c) 2 sinu-
soids,
(d) 3 sinusoids,
(e) 4 sinusoids.
Increasing the number of sinusoids improves the quality of
the
approximation.
