Sampling and series expansion theorems for fractional Fourier and other transforms
Signal Processing - Special issue: Fractional signal processing and applications
A fast Mellin and scale transform
EURASIP Journal on Applied Signal Processing
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The scalar transform is a new representation for signals, offering a perspective that is different from the Fourier transform. We introduce the notion of a scalar periodic function. These functions are then represented through the discrete scale series. We also define the notion of a strictly scale-limited signal. Analogous to the Shannon interpolation formula, we show that such signals can be exactly reconstructed from exponentially spaced samples of the signal in the time domain. As an interesting, practical application, we show how properties unique to the scale transform make it very useful in computing depth maps of a scene