This paper is concerned with the problem of sampling and interpolation involving derivatives in shift-invariant spaces and the error analysis of the derivative sampling expansions for fundamentally large classes of functions. A new type of polynomials based on derivative samples is introduced, which is different from the Euler-Frobenius polynomials for the multiplicityr> 1. A complete characterization of uniform sampling with derivatives is given using Laurent operators. The rate of approximation of a signal (not necessarily continuous) by the derivative sampling expansions in shift-invariant spaces generated by compactly supported functions is established in terms ofLp- average modulus of smoothness. Finally, several typical examples illustrating the various problems are discussed in detail.

Available upper limb active prosthetic devices lack any form of sensory feedback. This paper presents development of a vibrotactile sensory feedback system employing the sensory substitution method. Testing the device with amputees and improvement in overall experience of using the device with the developed system is also discussed.