Algebraic representation for fractional Fourier transform on one-dimensional discrete signal models

Algebraic signal processing provides a general framework for studying theoretical problems (sampling, transform domain analysis etc.) in the classical signal processing. In this study, the<?show [AQ ID=Q1]?> authors extend algebraic representation for the conventional Fourier transform (FT) to the fractional FT (FRFT) domain, from which the algebraic structures for the FRFT on infinite and finite one-dimensional signal models are obtained. They show that FRFTs on the infinite and finite discrete-time (DT) signal models, respectively, are none other than the DTFRFT and the closed-form discrete FRFT. They also derive FRFTs on the infinite and finite discrete-nearest neighbour signal models, and finally they discuss their applications in optical and time-frequency signal processing.