Smooth frame-path termination for higher order sigma-delta quantization

We study the perfomance of finite frames for the encoding of vectors by applying standard higher-order sigma-delta quantization to the frame coefficients. Our results are valid for any quantizer with accuracy epsilon > 0 operating in the no-overload regime. The frames under consideration are obtained from regular sampling of a path in a Hilbert space. In order to achieve error bounds that are comparable to results on higher-order sigma-delta for the quantization of oversampled bandlimited junctions, ive construct frame paths that terminate smoothly in the zero vector; that is, with an appropriate number of vanishing derivatives at the endpoint.