Wavelet-based representations for a class of self-similar signals with application to fractal modulation

A potentially important family of self-similar signals based upon a deterministic scale-invariance characterization is introduced. These signals, which are referred to as ´dy-homogeneous´ signals because they generalize the well-known homogeneous functions, have highly convenient representations in terms of orthonormal wavelet bases. In particular, wavelet representations can be exploited to construct orthonormal self-similar bases for these signals. The spectral and fractal characteristics of dy-homogeneous signals make them appealing candidates for use in a number of applications. As one potential example, their use in a communications-based context is considered. Specifically, a strategy for embedding information into a dy-homogeneous waveform on multiple time-scales is developed. This multirate modulation strategy, called fractal modulation, is potentially well-suited for use with noisy channels of simultaneously unknown duration and bandwidth.<>