On accuracy of periodic discrete finite-length signal reconstruction by means of a Whittaker-Kotelnikov-Shannon interpolation formula

Abstract

With the advent of digital transmission systems, the task of the discrete-time signal reconstruction became very important. Notice that the task of the discrete-time signals reconstruction is similar to the task of functions interpolation in numerical mathematics. In case of practical use of reconstruction methods one of the most important thing is to provide necessary accuracy of signal reconstruction. It depends both on type of the original analog signal and length of the discrete-time signal. This paper presents results of the research on the accuracy of the periodic discrete-time finite-length signal reconstruction by means of a Whittaker-Kotelnikov-Shannon interpolation formula. To estimate the accuracy of reconstruction the signal power to the error reconstruction power ratio has been employed. Two methods to increase the number of samples are considered. It is demonstrated that the formal increase in number of samples does not provide the of reconstruction error reduction every time. The conditions making reconstruction error on the dimensionless sampling rate ratio appear as the amount of the monotonic dependence with local extremums are defined. The ratio between the frequency of a signal, sampling rate and number of discrete samples providing minimum reconstruction error is determined.