Adaptive Filtering to Enhance Noise Immunity of Impedance and Admittance Spectroscopy: Comparison with Fourier Transformation

Daniil D. Stupin, Sergei V. Koniakhin, Nikolay A. Verlov, and Michael V. Dubina

Phys. Rev. Applied 7, 054024 – Published 30 May 2017

Abstract

The time-domain technique for impedance spectroscopy consists of computing the excitation voltage and current response Fourier images by fast or discrete Fourier transformation and calculating their relation. Here we propose an alternative method for excitation voltage and current response processing for deriving a system impedance spectrum based on a fast and flexible adaptive filtering method. We show the equivalence between the problem of adaptive filter learning and deriving the system impedance spectrum. To be specific, we express the impedance via the adaptive filter weight coefficients. The noise-canceling property of adaptive filtering is also justified. Using the RLC circuit as a model system, we experimentally show that adaptive filtering yields correct admittance spectra and elements ratings in the high-noise conditions when the Fourier-transform technique fails. Providing the additional sensitivity of impedance spectroscopy, adaptive filtering can be applied to otherwise impossible-to-interpret time-domain impedance data. The advantages of adaptive filtering are justified with practical living-cell impedance measurements.

Received 24 January 2017

DOI:https://doi.org/10.1103/PhysRevApplied.7.054024

Physics Subject Headings (PhySH)

Impedance Metrology Noise

Cells

Dielectric spectroscopy Electrical techniques Functional analytical methods Machine learning

Polymers & Soft MatterNetworksPhysics of Living SystemsCondensed Matter, Materials & Applied PhysicsInterdisciplinary PhysicsGeneral Physics

Authors & Affiliations

Daniil D. Stupin^1,*, Sergei V. Koniakhin¹, Nikolay A. Verlov^1,2, and Michael V. Dubina^1,3

¹St. Petersburg Academic University, Khlopina 8/3, 194021 St. Petersburg, Russia
²Petersburg Nuclear Physics Institute NRC “Kurchatov Institute,” Gatchina, St. Petersburg 188300, Russia
³Peter the Great St. Petersburg Polytechnic University, Polytechnicheskaya str. 29, 195251 St. Petersburg, Russia

^*Stu87@ya.ru, Stupin@spbau.ru

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Vol. 7, Iss. 5 — May 2017

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Images

Figure 1
Processing the IS on the basis of the AF method. The classical AF identification system with infinite impulse response (IIR) corresponds to the enabled IIR link (red) and disabled semi-IIR link (green). If the IIR link is disabled and if the semi-IIR link is enabled this scheme describes the semi-IIR model. If both links are disabled, the scheme describes the model with finite impulse response (FIR). The acronyms used in the figure are weight coefficients (WC), transfer function (TF), and immittance spectrum (IS).
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Figure 2
Setup for IS measurement using the time-domain technique. The operational amplifier is connected into the current-to-voltage converter circuit. Here, $Z$ is the unknown sample impedance, and $R_{0}$ is the feedback resistor.
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Figure 3
Frequency dependences of admittance obtained with AF and FFT for the high and low experimentally studied SNRs. Panels (a), (c), and (e) correspond to $SNR = 30 dB$ and show the admittance real and imaginary part spectra and the Nyquist plot, respectively. Panels (b), (d), and (f) correspond to $SNR = 3 dB$ . Light green is used to show the raw admittance spectrum obtained by the FFT, and dark green is used to show the CNLS fit of the corresponding spectra. The admittance spectra obtained by AF are shown in black, and the CNLS fit of it is shown in red. The CNLS fits for AF and FFT in panels (a), (c), and (e) are overlapping.
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Figure 4
Dependence of the obtained circuit elements ratings on the signal-to-noise ratio exhibiting the AF advances in noise immunity with respect to the FFT. Black squares are the results of the CNLS fit of the IS obtained by the FFT. Red circles denote the circuit element ratings obtained by AF. The statistics over four experiments for each SNR allow us to add the error bars (99.9% reliability). Panels (a), (c), and (e) are for the experimentally generated noise for resistance, capacitance, and inductance, respectively. Panels (b), (d), and (f) are for the digital artificial noise for resistance, capacitance, and inductance, respectively. AF gives correct results for all studied SNRs for both experimental noise and noise modeling. The FFT fails at 5 dB for experimental data and at 0 dB for noise modeling.
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Figure 5
Application AF for the biosensing EIS. (a) Photograph of the empty electrode. (b) Photograph of the electrode covered by the cell. The diameter of the electrodes is $30 μ m$ . (c) Nyquist plot of the obtained IS. Red and light green denote the IS obtained by AF of the empty and the covered by cell electrodes, respectively. Blue and dark green denote the IS obtained by FFT of the empty and the covered by cell electrodes, respectively. One sees that the AF IS is more informative with respect to the FFT IS; for example, it can be seen acceptance of the Giaever-Keese model [20]. The acronyms used in figure are immittance spectrum (IS) and fast Fourier transformation (FFT).
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