Optimum kernels for oversampled signals

For an oversampled bandlimited acoustic signal, the sampling kernel is nonunique. Niland [R. A. Niland, J. Acoust. Soc. Am. 86, 1805–1812 (1989)] presents a formalism for constructing a kernel that is most concentrated near the origin. By exploiting the most general form for the sampling kernel, Niland’s result is seen to be nonoptimal. The form of the kernel which is in fact optimal by his measure is derived and illustrated.