  In this paper, a discrete LCT (DLCT) irrelevant to the sampling periods and
without oversampling operation is developed. This DLCT is based on the
well-known CM-CC-CM decomposition, that is, implemented by two discrete chirp
multiplications (CMs) and one discrete chirp convolution (CC). This
decomposition doesn't use any scaling operation which will change the sampling
period or cause the interpolation error. Compared with previous works, DLCT
calculated by direct summation and DLCT based on center discrete dilated
Hermite functions (CDDHFs), the proposed method implemented by FFTs has much
lower computational complexity. The relation between the proposed DLCT and the
continuous LCT is also derived to approximate the samples of the continuous
LCT. Simulation results show that the proposed method somewhat outperforms the
CDDHFs-based method in the approximation accuracy. Besides, the proposed method
has approximate additivity property with error as small as the CDDHFs-based
method. Most importantly, the proposed method has perfect reversibility, which
doesn't hold in many existing DLCTs. With this property, it is unnecessary to
develop the inverse DLCT additionally because it can be replaced by the forward
DLCT.
