Digital signal processing for relaxation data conversion

Determination of relaxation and retardation spectrum by inverse functional filtering

“…12. Effect of the random noise and smoothing on the spectrum recovered from the real part (kernel (2d)) by: (a) the six-point algorithm (see coefficients in Table 2); (b) the six-point algorithm with coefficients (12). See details in text.…”

“…In the presented paper, the problem of RRS determination is considered from the novel data processing perspective [11] by employing the functional filtering approach [12,13] and has been developed for interconverting the responses of relaxing materials. Motivation of this work was, first, to give comprehensive insight on the overall problem framework of RRS recovery in the up-to-date signal processing context, and, second to develop accurate, robust and computationally efficient algorithms.…”

Digital estimators of relaxation spectra

“…where j ¼ ffiffiffiffiffiffi ffi À1 p and parameter l named the Mellin frequency [5] represents the frequency of a function, whose independent variable is logarithmically transformed.…”

“…Deconvolution (5), which can be considered as an ideal DRT estimator, represents an ideal filter [1] operating on a logarithmic time-or frequency-domain. It may be implemented by a digital filter [1]…”

“…operating with equally spaced data on a logarithmic scale, which manifest as the data spaced according to geometric progression u n = u 0 q n on a linear scale (logarithmic sampling [5][6][7][8][9][10]). For the logarithmically sampled data, Eq.…”