Application of the Dirichlet transform in analysis of nonuniformly sampled signals

The authors introduce a method of spectrum analysis based on a Dirichlet transform which generalizes the Z-transform and is better suited to the analysis of nonuniformly sampled signals. The Dirichlet spectrum preserves information about sampling instants because a nonuniformly sampled signal is not treated as a sequence of samples but as a function of the sampling instants. Basic properties of the Dirichlet transform in case of periodical and nonperiodical nonuniform sampling are presented, and the inverse Dirichlet transform is shown. The authors suggest use of this transform in analysis of the nonuniformly sampled signals processed by digital filters with constant and varying delays, systems which modulate sampling instants, sampling jitter etc. Examples of Dirichlet transforms of several signals are given