MEASUREMENT THEORY AND SIGNAL THEORY Part II. The Analysis of Digitized Signals
Jaap van der Zanden · International Journal of General Systems · 1984
The relation between the continuum theory of matter and the concept of a sensor (measuring instrument) with finite resolution is described. Repeatability of an experiment, equivalence or instruments and refinement of instruments are described in procedural form and with help of simple mathematical tools for both deterministic and non-deterministic signals. Formulae are presented that relate the sampling frequency to the number of samples, and the number of digits per measurement. The attenuation characteristic and the cutoff frequency of a low-pass filter are taken into account. The finite discrete Fourier transform appears to be an adequate tool for signal analysis, which follows from a discussion of the estimation of variance, spectrum, and correlation function for stationary signals. There is no need to turn back or to refer to the infinite Fourier integral transform on continuous functions. If the number of samples increases indefinitely the sampling frequency approaches that of Nyquist's criterion and Shannon's theorem.