Algorithms for Reconstruction of Impedance Spectra from Non-uniformly Sampled Step Responses

Fast and reliable bioimpedimetric measurements are of growing importance in many practical applications. In this work we used a measurement method in time domain by processing the step response of the biological system under test. In order to decrease the data volume and computation time while retaining all relevant information the step response is sampled non-uniformly. Consequently, fast Fourier transform cannot be directly used for spectrum calculation and non-conventional data processing algorithms for transforming measured data into the frequency domain are required. In this paper we present corresponding computational methods. They are split into two groups. The first group is oriented on calculating the local approximation of the measured step response with a set of proper functions and calculating its spectrum via analytical Fourier transform, thus yielding a relatively versatile approach for estimating the impedance spectrum. In this case, the choice of approximating functions that suit known a priori properties of the measured signals are of great importance. A second group of methods relies on the evaluation of important signal parameters directly in the time domain. In this case we use a priori information about the measurement object in the form of an underlying model. After that the model is fitted to the measured data and thus, parameter values are extracted. Practical aspects, advantages and drawbacks of all considered data processing steps are revealed when applying them to the measurements made with real biological objects.