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
Decomposition of multi-exponential and related signals: functional filtering approach
WSEAS Transactions on Signal Processing
Nonlinear decomposition filters with neural network elements
ICS'08 Proceedings of the 12th WSEAS international conference on Systems
Sampling in relaxation data processing
ICS'06 Proceedings of the 10th WSEAS international conference on Systems
Activity index variance as an indicator of the number of signal sources
WSEAS Transactions on Signal Processing
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The article is devoted to improving quality of decomposition of monotonic multi-component time-and frequency-domain signals. Decomposition filters operating with data sampled at geometrically spaced times or frequencies (at equally spaced times or frequencies on a logarithmic scale) are combined with artificial neural networks. A nonlinear processing unit, which can be considered as a deconvolution network or a nonlinear decomposition filter, is proposed to be composed from several linear decomposition filters with common inputs, which outputs are nonlinearly transformed, multiplied by weights and summed. One of the fundamental findings of this study is a square activation function, which provides some useful features for the decomposition problem under consideration. First, contrary to conventional activation functions (sigmoid, radial basis functions) the square activation function allows to recover sharper peaks of distributions of time constants (DTC). Second, it ensures physically justified nonnegativity for the recovered DTC. Third, the square activation function transforms the Gaussian input noise into the nonnegative output noise with specific probability distribution having the standard deviation proportional to the variance of input noise, which, in most practical cases when noise level in the data is relatively low, increases radically the noise immunity of the proposed nonlinear algorithms. Practical implementation and application issues are described, such as network training, choice of initial guess, data normalization and smoothing. Some illustrative examples and simulations are presented performed by a developed deconvolution network, which demonstrate improvement of quality of decomposition for a frequency-domain multi-component signal.