  In recent years there has been a renewed interest in finding fast algorithms
to compute accurately the linear canonical transform (LCT) of a given function.
This is driven by the large number of applications of the LCT in optics and
signal processing. The well-known integral transforms: Fourier, fractional
Fourier, bilateral Laplace and Fresnel transforms are special cases of the LCT.
In this paper we obtain an O(N*Log N) algorithm to compute the LCT by using a
chirp-FFT-chirp transformation yielded by a convergent quadrature formula for
the fractional Fourier transform. This formula gives a unitary discrete LCT in
closed form. In the case of the fractional Fourier transform the algorithm
computes this transform for arbitrary complex values inside the unitary circle
and not only at the boundary. In the case of the ordinary Fourier transform the
algorithm improves the output of the FFT.
