On the Processing of Decimated Signals
The aim of the given paper is development of a recursive approach for calculating the statistics of decimated realizations of a basic discrete-time signal, obtained by sampling a continuous-time one. The statistics values are calculated without storing decimated realizations in the memory of a computer. In such a case, only all samples of the basic discrete-time signal are required. The summing calculation amount has been significantly reduced here by applying recursive expressions that use, in the current operation, the respective statistic obtained by processing the samples of a previous decimated realization. We prove the corollaries referring to recursive statistics calculation and present here an example. The results of calculation of the total quantity of computer operations for a different amount of decimated signals are also given and compared to that, determined by using the ordinary formulas.
processing decimation signals statistics realization computer operations nyquist frequency