Synthesis methods for frequency non-recursive numerical filters in spectral domain of arbitrary orthogonal basis

General theoretical grounds are considered to construct frequency nonrecursive numerical filters in spectral domain. Consideration includes the methods of filter description, statement and solution of their analytic synthesis task, choice of rational system of the basic functions in view of demands to the numerical filtration algorithm realisation. Computation complexity of the obtained fast algorithms is estimated. Results of theoretical research are illustrated by practical examples.