A centrosymmetric matrix based technique for the interpolation of a Hermitian signal

This work is concerned with the signal interpolation problem, i.e., given only samples of a signal, a method is derived for evaluating its samples on finer grids. The derivation is based on a discrete-time decimation formula. In the special case where the known samples have the Hermitian property, two schemes are presented and mathematically proved to result in interpolated points having the same property. The first scheme does not utilize the known sample at the origin and results in a square system of equations to be solved for the unknown interpolated points of the signal. The second scheme has the merit of utilizing all the known samples, but it results in an overdetermined system of equations to be solved by the least squares method. The exploitation of the elegant properties of the involved centrosymmetric matrices is central to the treatment presented here.