The fractional Fourier transform is a useful mathematical operation th
at generalizes the well-known continuous Fourier transform. Several di
screte fractional Fourier transforms (DFRFTs) have been developed, but
their results do not match those of the continuous case. We propose a
new DFRFT. This improved DFRFT provides transforms similar to those o
f the continuous fractional Fourier transform and also retains the rot
ation properties. (C) 1997 Optical Society of America.