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The problem of defining and representing self-similar signals and systems in discrete time is examined and discussed.

Algorithms to design wavelets that match specified signals are discussed.

Wide-sense statistical self-similarity in continuous-time random processes is defined through invariance of its first-order and second-order statistics to scaling in time. Since scaling has an unambiguous definition in continuous-time but not in discrete-time, researchers have provided various definitions of discrete-time self-similarity without reference to scaling. This paper proposes a discrete-time continuous-dilation scaling operator and develops a framework based on it for formulating statistical self-similarity from first principles in a manner analogous to the continuous-time development. Relationship between the resulting model and fractional order transfer function systems is presented. The potential for using this model in applications involving long-range dependent phenomena is explored. [ABSTRACT FROM AUTHOR]

Deals with approximation and interpolation sampling systems. Interpolation and approximation sampling systems matched to the input process; Explanation on the perfect reconstruction circular convolution framework; Conclusion.