Zotero Chunk RAG

Sensors 2019, 19, 959
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As these coefficients are implemented in fixed-point format, the denominators and numerators are
scaled and truncated. Figure 8 shows the transfer function for the highpass with the quantized coefficients:
GHP[z] = HPout[z]
HPin[z] = b[0] + b[1]z−1 + b[2]z−2
a[0] + a[1]z−1 + a[2]z−2 .
(5)
Table 2. Floating-point highpass filter coefficients.
Filter
a[0]
a[1]
a[2]
b[0]
b[1]
b[2]
20 Hz Che
1
−1.9836
0.9839
1
−2
1
30 Hz Che
1
−1.9754
0.9759
1
−2
1
40 Hz Che
1
−1.9664
0.9674
1
−2
1
50 Hz Che
1
−1.9580
0.9596
1
−2
1
60 Hz Che
1
−1.9496
0.9518
1
−2
1
70 Hz Che
1
−1.9418
0.9447
1
−2
1
80 Hz Che
1
−1.9333
0.9370
1
−2
1
90 Hz Che
1
−1.9247
0.9294
1
−2
1
100 Hz Che
1
−1.9168
0.9225
1
−2
1
20 Hz But
1
−1.9824
0.9825
1
−2
1
30 Hz But
1
−1.9733
0.9737
1
−2
1
40 Hz But
1
−1.9645
0.9651
1
−2
1
50 Hz But
1
−1.9556
0.9565
1
−2
1
60 Hz But
1
−1.9467
0.9481
1
−2
1
70 Hz But
1
−1.9378
0.9397
1
−2
1
80 Hz But
1
−1.9289
0.9314
1
−2
1
90 Hz But
1
−1.9201
0.9231
1
−2
1
100 Hz But
1
−1.9112
0.9150
1
−2
1
(a)
0
50
100
150
200
−60
−40
−20
0
Frequency (Hz)
|gHP[f]| (dB)
Chebyshev
(b)
0
50
100
150
200
−60
−40
−20
0
Frequency (Hz)
|gHP[f]| (dB)
Butterworth
20 Hz
30 Hz
40 Hz
50 Hz
60 Hz
70 Hz
80 Hz
90 Hz
100 Hz
Figure 8.
Transfer functions with quantization effects included.
(a) Chebyshev highpass filter;
(b) Butterworth highpass filter.
Highpass Filter Evaluation
To determine the optimal choice of filter characteristic and fC, we recorded EMG signals from
three subjects both at the left and at the right arm. A 50 Hz comb filter was implemented at the µC
for the measurements, but no highpass filter was implemented for the evaluation. Three contraction
and three artifact signals were recorded at each arm of each subject. Each measurement lasted 10 s,
but only 8 s were evaluated because the on-set of the contraction was not considered. The artifacts
were created by mechanical interferences, which might occur in real-world environments, such as
tapping, shifting or lifting of the sensor. By using these artifacts for the filter parameter evaluation,
the resulting system will be robust against this noise. The entire 10 s of the artifacts were evaluated.
The oscilloscope [42] was set to a sampling rate of 10 kHz.
The evaluation was performed in Matlab R⃝[39]. To this end, the filtering was carried out such that
the µC implementation was represented. The coefficients, the measurement values, the intermediate