Sampling in Relaxation Data Processing

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. Key-Words: Relaxation data, integral transforms, logarithmic sampling, convolution, functional filters