Numerisch einfache Bezichungen zwischen Verlust- und Speicherkomponente des dynamischen dielektrischen Faktors

Digital signal processing for relaxation data conversion

“…4. The performance parameters of digital KK transformers versus the number of filter coefficients: (a) error E calculated according to (5) for a single Debye relaxation (solid line) and required input argument range d x (dashed line) and (b) noise coefficient S calculated according to (6). The horizontal line shows the theoretical noise coefficient for q = 2. investigated.…”

“…1). The tree stems from three roots representing the existing empirical and semi-empirical methods [2][3][4][5][6][7], the theory of digital filters [9,10], and the formal theory of relaxing systems [15]. In its turn, the formal theory of relaxing systems describing the formal causal relationships between input and output of the dynamic systems having monotonic decaying impulse responses breeds from the similar mathematics of the physical relaxation theories, such as dielectric [12,13], magnetic [14] and mechanic [11,12] ones, as well as from the general theory of signals and systems [10].…”

“…Such interpretation serves a base for: (i) considering relaxation data conversion as a specific filtering problem, and for (ii) identifying the existing numerical techniques, e.g. [2][3][4][5][6][7], as special cases of digital filters implemented in various -mainly non-classical ways. Thus, basic idea of the approach is to execute relaxation data conversion in the logarithmically transformed argument domain by digital filters, which due to their specific application ideology have been named as functional filters [8].…”

“…Despite of the fact that attention on the treatment of relaxation data has been paid for the long time beginning with the first relaxation experiments dated back nearly a century [1], the problem cannot be considered to be completely solved, especially looking from standpoint of the state-of-the-art of advanced digital signal processing. Mostly the methods [2][3][4][5][6][7] are based on empirical or semi-empirical approaches and are developed for highly specific applications without necessary generalization from the signal processing view.…”

“…Due to the specific relaxation behaviour, mostly methods of relaxation data conversion [2][3][4][5][6][7][11][12][13] exploit logarithmic transformation of time and frequency. The logarithmic transformation converts integral transform from the Mellin convolution type (1) into the Fourier convolution type with kernel depending on the difference of logarithmic arguments, which may be interpreted as an ideal filter operating on a logarithmic scale.…”