KINESIOLOGICAL ELECTROMYOGRAPHY - Biomechanics and Motor Control of Human Movement - page 271

10.3.2 Linear Envelope
If we filter the full-wave rectified signal with a low-pass filter, we have what
is called the linear envelope . It can be described best as a moving average
because it follows the trend of the EMG and quite closely resembles the
shape of the tension curve. It is reported in millivolts. There is considerable
confusion concerning the proper name for this signal. Many researchers call
it an integrated EMG (IEMG). Such a term is quite wrong because it can be
confused with the mathematical term integrated , which is a different form of
processing.
There is a need to process the signal to provide the assessor with a pat-
tern that can be justified on some biophysical basis. Some researchers have
full-wave rectified the raw EMG and low-pass filtered at a high frequency
but with no physiological basis (Forssberg, 1985; Murray et al., 1985). If it
is desired that the linear envelope bear some relationship to the muscle force
or the joint moment of force, the processing should model the biomechanics
of muscle tension generation. The basic unit of muscle tension is the muscle
twitch, and the summation of muscle twitches as a result of recruitment is
matched by a superposition of m.u.a.p.'s. There is an inherent delay between
the m.u.a.p. and the resultant twitch waveform. If we consider the full-wave
rectified signal to be an impulse and the twitch to be the response, we can
define the transfer function of the desired processing. The duration of the
full-wave rectified m.u.a.p. is about 10 ms, while the twitch waveform peaks
at 50 - 110 ms and lasts up to 300 ms, so this impulse/response relationship
is close. Twitch waveforms have been analyzed and have been found to
be a second-order system, critically damped or slightly overdamped (Crosby,
1978; Milner-Brown et al., 1973). The cutoff frequency of these second-order
responses ranged from 2.3 Hz to 7.8 Hz. Figure 10.16 is presented to show
the linear envelope processing of the EMG to model the relationship between
the m.u.a.p. and the twitch. A critically damped second-order low-pass filter
has a cutoff frequency f c , which is related to the twitch time T as follows:

f c = 1 / 2 π T (10.8)

Thus, the table in Figure 10.16 shows the relationship between fc and T
for the range of twitch times reported in the literature. The soleus muscle with
a twitch time ≈ 106ms would require a filter with f c = 1 . 5 Hz. The reader is
referred back to Section 9.0.5 for information on the twitch shape and times.
Good correlations have been reported between the muscle force and
linear envelope waveforms during isometric anisotonic contractions (Calvert
and Chapman, 1977; Crosby, 1978). Readers are also referred back to
Section 9.3.1 and Figure 9.20, which modeled the muscle contraction as
a mass-spring-damper system that was critically damped. The critically
damped low-pass filters described earlier have exactly the same response
as this previously described mechanical system. Thus, the matching of the
muscle force waveform with that from the model is exactly the same as