Functional conversion of signals in the study of relaxation phenomena
Signal Processing
Spectrum analysis and synthesis of relaxation signals
Signal Processing
Discrete-time signal processing (2nd ed.)
Discrete-time signal processing (2nd ed.)
FIR Kramers-Kronig transformers for relaxation data conversion
Signal Processing - Fractional calculus applications in signals and systems
Decomposition of multi-exponential and related signals: functional filtering approach
WSEAS Transactions on Signal Processing
Nonlinear extension of inverse filters for decomposition of monotonic multi-component signals
WSEAS Transactions on Signal Processing
Nonlinear decomposition filters with neural network elements
ICS'08 Proceedings of the 12th WSEAS international conference on Systems
Measurement systems for distribution of relaxation and retardation times
Proceedings of the 15th WSEAS international conference on Systems
Proceedings of the 15th WSEAS international conference on Systems
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It is shown that the conventional sampling schemes are of limited use for conversion of monotonic long-time-interval and wide-frequency-band data of relaxation experiments, which can be measured over many decades of time or frequency. The problem of sampling is considered in combination with designing the discrete-time algorithms for relaxation data conversion has been generalized as a convolution on a logarithmic scale, for which implementation discrete-time filters with the logarithmic sampling are proposed. It is demonstrated that the sampling rate has a direct influence on the performance of the discrete-time filters to govern the potential accuracy and noise behaviour. A pragmatic approach is proposed for choosing sampling rate based on ensuring the maximum accurate output signal with the acceptable random error (noise). The optimum sampling is searched for an inverse filter executing the ill-posed inversion of an integral transform for determination of relaxation spectrum where sampling rate plays also a role of regularization.