Functional conversion of signals in the study of relaxation phenomena
Signal Processing
Discrete-time signal processing (2nd ed.)
Discrete-time signal processing (2nd ed.)
Inverse filters for decomposition of multi-exponential and related signals
ISTASC'07 Proceedings of the 7th Conference on 7th WSEAS International Conference on Systems Theory and Scientific Computation - Volume 7
Sampling in relaxation data processing
ICS'06 Proceedings of the 10th WSEAS international conference on Systems
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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Decomposition of multi-exponential and related signals is generalized as an inverse filtering problem on a logarithmic time or frequency scale, and discrete-time filters operating with equally spaced data on a logarithmic scale (geometrically spaced on linear scale) are proposed for its implementation. Ideal prototypes, algorithms and types of filters are found for various time- and frequency-domain mono-components. It is disclosed that the ill-posedness in the decomposition originates as high sampling-rate dependent noise amplification coefficients arising from the large areas under the increasing frequency responses. A novel regularization method is developed based on the noise transformation regulation by filter bandwidth control, which is implemented by adaptation of the appropriate sampling rate. Algorithm design of decomposition filters is suggested joining together signal acquisition, regularization and discrete-time filter implementation. As an example, decomposition of a frequency-domain multi-component signal is considered by a designed filter.