Multirate operations for exact interpolation and iterative subdivision schemes

In this paper we examine the circumstances under which a discrete-time signal can be exactly interpolated given only every M-th sample. After pointing out the connection between designing an M-fold interpolator and the construction of an M-channel perfect reconstruction filter bank, we derive necessary and sufficient conditions on the signal under which exact interpolation is possible. Bandlimited signals are one obvious example, but numerous others exist. We examine these and show how the interpolators may be constructed. A main application is to iterative interpolation schemes, used for the efficient generation of smooth curves. Conventional bandlimited interpolators are not suitable in this context. We illustrate that a better criterion is to use interpolators that are exact for polynomial functions. We show how these may be designed for any polynomial degree N and any interpolation factor M