Calculation of the Approximated Frequency Response of Sampled-Data Systems using Kranc Operators

A novel method for the approximation of the frequency response of a sampled data system is presented. Usually the frequency response calculation of sampled-data systems leads to use of the infinite dimension matrices of cumbersome mathematical treatment. The technique presented is based on the inclusion of a fictitious sampler in the continuous process output and on the signal flow analysis in the consequent Kranc operator multirate model obtained by switch decomposition. The main goal of this sampler is to get as much information as it can about the output continuous signal, but finite. The application of this tool will be demonstrated with the calculation of the frequency response of a dual-rate sampled data system, and its validity will be verified by looking correspondence of the results obtained with its time-domain response to a single frequency sine signal input.