SIGNAL PROCESSING - Biomechanics and Motor Control of Human Movement - page 27

Jean-Baptiste-Joseph Fourier, a French mathematician who developed the
technique in 1807.
The knowledge of the frequency spectrum of any given signal is mandatory
in making decisions about collection and processing of any given signal. The
spectrum decides the sampling rate you must chose before an analog-to-digital
conversion is done, and it also decides the length of record that must be
converted. Also, the spectrum influences the frequency of filtering of the
data to remove undesirable noise and movement artifacts. All these factors
will be discussed in the sections to come.

2.2.2 Discrete Fourier (Harmonic) Analysis

1. Alternating Signals . An alternating signal (often called ac, for alter-
nating current) is one that continuously changes over time. It may be
periodic or completely random, or a combination of both. Also, any sig-
nal may have a dc (direct current) component, which may be defined
as the bias value about which the ac component fluctuates. Figure 2.9
shows example signals.
2. Frequency Content . Any of these signals can also be discussed in terms
of their frequency content. A sine (or cosine) waveform is a single
frequency; any other waveform can be the sum of a number of sine and
cosine waves.
Note that the Fourier transformation (see Figure 2.10) of periodic signals
has discrete frequencies, while nonperiodic signals have a continuous spec-
trum defined by its lowest frequency, f 1 , and its highest frequency, f 2 .To
analyze a periodic signal, we must express the frequency content in multiples

Figure 2.9 Time-related waveforms demonstrate the different types of signals that
may be processed.