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

## TL;DR

This paper introduces an adaptive filtering method for impedance spectroscopy that improves noise immunity and outperforms Fourier transformation in high-noise conditions, enabling better interpretation of time-domain data.

## Contribution

It presents a novel adaptive filtering approach for impedance spectrum derivation, demonstrating its equivalence to traditional methods and superior noise-canceling capabilities.

## Key findings

- Adaptive filtering accurately derives impedance spectra in high-noise scenarios.
- The method outperforms Fourier transformation in noisy conditions.
- Practical application demonstrated with living-cell impedance measurements.

## 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.