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Electrical bioimpedance spectroscopy in time-variant systems: Is undersampling always a problem?

Farhad Abtahi
Farhad Abtahi
, 
Fernando Seoane
Fernando Seoane
 e 
Kaj Lindecrantz
Kaj Lindecrantz
   | 18 apr 2014
Journal of Electrical Bioimpedance's Cover Image
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Article Category: Articles
Pubblicato online: 18 apr 2014
Pagine: 28 - 33
Ricevuto: 22 gen 2014
DOI: https://doi.org/10.5617/jeb.801
Parole chiave
© 2014 Farhad Abtahi, Fernando Seoane and Kaj Lindecrantz, published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Figure 1

System for acquisition of impedance signals. Current stimulation and measurement could be any method; frequency sweep, multi-sine, or other.
System for acquisition of impedance signals. Current stimulation and measurement could be any method; frequency sweep, multi-sine, or other.

Figure 2

Apparent frequencies of a signal with a 0.3 Hz actual frequency component, sampled at 0.2, 0.3, 0.4 and 0.5 Hz are depicted. It is clear that due to aliasing the apparent frequency differs from the actual frequency in all cases.
Apparent frequencies of a signal with a 0.3 Hz actual frequency component, sampled at 0.2, 0.3, 0.4 and 0.5 Hz are depicted. It is clear that due to aliasing the apparent frequency differs from the actual frequency in all cases.

Figure 3

Frequency responses of 5, 20,100 and 250 points average filters are shown by black plus, red star, green circle and purple solid lines, respectively.
Frequency responses of 5, 20,100 and 250 points average filters are shown by black plus, red star, green circle and purple solid lines, respectively.

Figure 4

Actual and apparent frequencies due to aliasing for 0.25 Hz and 0.35 Hz narrow band signals and (0.2-0.4 Hz) wideband signals are depicted in plots a, b and c, respectively. Sampling frequency is considered to be 0.33 Hz.
Actual and apparent frequencies due to aliasing for 0.25 Hz and 0.35 Hz narrow band signals and (0.2-0.4 Hz) wideband signals are depicted in plots a, b and c, respectively. Sampling frequency is considered to be 0.33 Hz.

Figure 5

Actual and apparent frequencies at sampling frequencies are illustrated. It is obvious that apparent and original frequencies are the same when the sampling frequency is equal to the Nyquist frequency. In general all sampling frequencies less than the Nyquist rate are causing aliasing. However, for lower sampling rates, i.e. sampling at 0.2 and 0.3 Hz, higher frequencies are folded into DC level and hence DC level cannot be recovered even by using the narrowest lowpass filter. Considering a maximum breathing rate of 25 breaths per minute (0.42 Hz) and sampling frequency of 0.5 Hz, the maximum frequency component (0.42 Hz) is folding on 0.08 Hz, as shown in the figure (dash-circle light blue line at X=0.42).
Actual and apparent frequencies at sampling frequencies are illustrated. It is obvious that apparent and original frequencies are the same when the sampling frequency is equal to the Nyquist frequency. In general all sampling frequencies less than the Nyquist rate are causing aliasing. However, for lower sampling rates, i.e. sampling at 0.2 and 0.3 Hz, higher frequencies are folded into DC level and hence DC level cannot be recovered even by using the narrowest lowpass filter. Considering a maximum breathing rate of 25 breaths per minute (0.42 Hz) and sampling frequency of 0.5 Hz, the maximum frequency component (0.42 Hz) is folding on 0.08 Hz, as shown in the figure (dash-circle light blue line at X=0.42).

Thoracic impedance; mean data with the standard deviation for the 12 subjects.

Frequency (kHz)Impedance (Ω) zRespiratory component (Ω) zrCardiac component (mΩ) zc
9.624.56±4.091.68±0.4398.4±33.0
19.223.93±4.101.66±0.4389.1±32.5
38.422.64±4.081.62±0.4279.4±32.7
76.821.04±3.961.55±0.4163.5±26.2
153.619.35±3.781.47±0.3954.1±22.5
307.217.8l ± 3.501.37±0.3640.4±17.9
611.115.70± 2.801.10±0.3028.2±12.4

Normal respiratory rates at different ages

RR (Breath/Minute)Frequency (Hz)
Newborns440.73
Infants20-400.33-0.66
Children18-300.30-0.5
Adults12-200.20-0.33
eISSN:
1891-5469
Lingua:
Inglese
Frequenza di pubblicazione:
Volume Open
Argomenti della rivista:
Engineering, Bioengineering and Biomedical Engineering, Biomedical Electronics, Life Sciences, Biophysics, Medicine, Biomedical Engineering, Physics, Spectroscopy and Metrology
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