Algorithms for Noise Reduction in Signals: Theory and practical examples based on statistical and convolutional analysis

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The book concerns itself with higher order statistical analysis for reducing noise in signals, following a theoretical and practical approach using the least possible information to process the signal. The focus, based on a statistical analysis, is on a specific application of more general techniques in noise analysis from the point of view of a system that can be composed of one input and one output, or two inputs and one output in the case of adaptive models and artificial intelligence.

An introduction to the concept of signal processing in communication systems is presented, as well as algorithms applied to noise reduction and recovery of phase information. The remainder of the work focuses on noise reduction algorithms using statistical processing based on non-parametric estimates of statistical characteristics such as cumulants, moments and higher order spectra, demonstrating results from a practical point of view and including examples from real situations. The reader will benefit from both the theoretical foundations described in the book, and the practical examples including generic codes of all the functions described and modifiable for use in different applications.