SPECTRAL ANALYSIS OF SEQUENTIALLY SAMPLED SIGNALS FOR APPLICATIONS IN INFORMATION PROCESSING

N. FAGHIH, Ph.D., Department of Management and Accounting, College of Social Sciences, Shiraz University, Shiraz, I. R. of Iran

Abstract

This paper studies the sequential sampling scheme, as a solution to the problem of aliasing, where the sampling interval is restricted to a minimum allowable value DT. In the sequential sampling, the signal is sampled at intervals of DT, DT+Dt, DT+2Dt, DT+3Dt, ...; where Dt < DT and may be selected as desirable. The sequential sampling is, however, analyzed and it is proven that, when the ratio DT/Dt is an integral number, the associated spectral estimates give a Nyquist frequency . This sampling scheme can, therefore, be employed to yield a required cut-off frequency. The autocorrelation function estimation from the sequentially sampled data is then considered and the approach to this is discussed. Simulation studies are also used for empirical investigations of the sequential sampling. Furthermore, since with this sampling scheme no estimates of the autocorrelation coefficients are available in the initial time interval from 0 to DT, the initial autocorrelation coefficients estimation method is applied to solve this problem. This, in addition, provides some empirical studies of the latter approach. Moreover, the application of the autocorrelation function extrapolation method is considered, as a means of minimizing the sampling time and costs. The contribution of the sequential sampling in obtaining a desired cut-off frequency, is also demonstrated by data simulation.

Keywords - Sequential sampling, Spectral Analysis, Autocorrelation function, Aliasing, Fourier transform.