1. An artificial neural network training architecture comprising: source means for supplying at least one input data signal representing an input vector; a plurality of input terminals connected to said source means; an input multiplexer connected to each of said input terminals; N arithmetic and storage units, representing N sibling nodes, connected to said input multiplexer; N weight multiplier units connected to said N arithmetic and storage units; wherein each arithmetic and storage unit generates a Fourier series using an input data signal received from said input terminal through said input multiplexer as a variable of the Fourier series, said Fourier series having as arguments of the sine and cosine terms said input data signal and not a probability distribution function of said input data signal, and supplies an output data signal from said arithmetic and storage unit to said weight multiplier units; an adder unit connected to every one of said arithmetic and storage units through a plurality of said weight multiplier units; a weight initializer connected to each of said weight multiplier units; a weight changer connected to each of said weight multiplier units; wherein output signals, representing synaptic link weight values from said weight changer and said weight initializer are stored in said adder unit; an output multiplexer connected to said adder unit; at least one output node connected to each of said N weight multipliers through said adder unit and through said output multiplexer for generating at least one activation at said output node; means for connecting each said output node to a mid input terminal when said artificial neural network training architecture is performing as a lowpass, highpass, and bandpass filter; means for applying to said output node, as a target value, a noise corrupted signal associated with a noise signal at each said mid input terminal when said artificial neural network training architecture is performing as an in-band filter; a comparitor and error generator unit connected to said output node, and to said weight changer for generating an error measure signal when said activation is different from said signal at said output node; means for indicating the completion of training when said error measure becomes equal to a preset value; and means for storing the synaptic link weight values of said weight multiplier units in a records file when training of said artificial neural network training architecture is completed.