Mathematics in Independent Component Analysis

Chapter 20. Signal Processing 86(3):603-623, 2006 265
Synthetic s-EMG Source Signals [arbitrary units]
MU#1
MU#2
MU#3
MU#4
MU#5
Channel 1
Synthetic s-EMG signal [arbitrary units]
Channel 7 Channel 6 Channel 5 Channel 4 Channel 3 Channel 2
Channel 8
10
0
-10
10
0
-10
10
0
-10
10
0
-10
10
0
-10
20
0
-20
20
0
-20
20
0
-20
20
0
-20
20
0
-20
20
0
-20
20
0
-20
20
0
-20
50 100 150 200 250 300 350 400 450 500
Time [ms]
(a) synthetic source signals
50 100 150 200 250 300 350 400 450 500
Time [ms]
(c) generated s-EMG signals
Depth inside the arm [mm]
6
5
4
3
2
1
MU#1
MU#3
MU#4
MU#2
MU#5
Ch#1 Ch#2 Ch#3 Ch#4 Ch#5 Ch#6 Ch#7 Ch#8
0
-15 -10 -5 0 5 10
Electrode-Array surface [mm]
(b) source locations
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1
2
3
Channel
4
5
6
7
(d) mixing matrix
8
1
2
3
4
5
Source Signal
Fig. 2. Artificially created signals. (a) Five synthetic motor units action potential
trains (source signals, MUAPTs) generated by the model. (b) Artificial surface
electromyogram (s-EMG); location of the sources (motor units, encircled asterisks)
respect the electrodes location marked by an x. The y-axis represents the depth
inside the upper limb. (c) Artificially created mixture signal — only first 5000
samples (out of 15000) are shown. The eight-channel signal is generated from the
five source signals (a), using the mixing matrix illustrated in (d).
generated on the skin surface by the excitation of a single muscle fibre. The
potential distribution generated by the firing of a single motor unit can be
calculated as the linear superposition of the contributions of all its constitutive
muscle fibres, which are not located in one plane. The aforementioned
model can be considered as a linear instantaneous mixing process. In reality
however it is well-known that the model could exhibit slightly convolutive behavior,
which is due to the fact that the media crossed by the s-EMG sources
is anisotropic, provoking delayed mixtures of the same signals (convolutions)
rather than an instantaneous mixture of them. However, in the muscle model
used, the distances between the different muscle fibres have been increased
4