Signal Processing in Relaxation Experiments

Signal processing problems arising in the study of the linearly viscoelastic behavior of polymers and composites are considered. It is shown that the great amount of data conversions is associated with integral transforms using kernels which depend on the ratio or product of arguments for monotonic long-time-interval and wide-frequency-band functions (signals). A unified method of carrying out these integral transforms is developed by combining a logarithmic transformation of the signal time scale with digital filtering. For integral transforms leading to ill-conditioned inverse problems, a method of regularization is proposed based on choosing a sampling rate which ensures an acceptable error variance of the output signal. The specific features of the functional filters used for performing the functional (integral) transforms are discussed. Examples of performing the Heaviside-Carson sine transform and an inherently ill-conditioned problem of inverting the integral transform for determining the relaxation spectrum are represented by digital functional filters.