Kernel approach to discrete-time linear scale-invariant systems

Zhao and Rao have proposed linear scale-invariant systems that operate with continuous dilation but in discrete-time. This was done through a discrete-time continuous-dilation operator which tacitly uses warping transforms such as bilinear transforms to implement conversion from discrete time frequency to continuous time frequency. This paper introduces a more general method based on kernels for effecting the dilation. It is shown that the warping function based scaling is a special case. The kernel approach results in an alternative formulation of discrete-time linear scale-invariant systems that possesses desirable properties not seen in the earlier formulation.