On Speedy Recognition of Non-Aliased Realization after Multifold Downsampling of an Oversampled Bandlimited Signal

Abstract

The aim of the given paper is the development of the criterion and some expressions for recognizing a nonaliased realization in the set of realizations obtained by multifold decimation (f ltering and downsampling) of any oversampled bandlimited signal that has been obtained at the beginning by periodic sampling of a continuous-time signal. For each nondecimated as well as decimated realization discrete-time Fourier series coeff cient values, located at Nyquist frequency are calculated, using speedy recursive expressions based on reverse order processing of the given realizations. In such a case, the summing calculation amount has been signif cantly reduced by applying the expressions that use, in each iteration, the respective values obtained by processing samples of a previously downsampled realization and some samples of the currently downsampled one. We formulate def nitions and prove the corollaries that refer to the recursive Fourier coeff cient calculation and present here an example. Finally, the simulation results for the bandlimited signal with a triangularshaped spectrum are presented.