SCALE PERIODICITY AND ITS SAMPLING THEOREM

The scale transform is a new representation for signals, offering pers pective that is different from the Fourier transform. In this correspo ndence, we introduce the notion of a scale periodic function. These fu nctions are then represented through the discrete scale series. We als o define the notion of a strictly scale-limited signal. Analogous to t he Shannon interpolation formula, we show that such signals can be exa ctly reconstructed From exponentially spaced samples of the signal in the time domain. As an interesting, practical application, we shaw how properties unique to the scale transform make it very useful in compu ting depth maps of a scene.