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This paper is concerned with the definition of the continuous fractional Hartley transform. First, a general theory of linear fractional transform is presented to provide a systematic procedure to define the fractional version of any well-known linear transforms. Then, the results of general theory are used to derive the definitions of fractional Fourier transform (FRFT) and fractional Hartley transform (FRHT) which staisfiy the boundary conditions and additive property simultaneously. Next, andoi:10.1109/icassp.1998.681730 dblp:conf/icassp/PeiTYD98 fatcat:7cbxspcqyfformnv4vsbta6xxq