The correlation properties of noise fields when considered as a random superposition of elementary sources are derived as an extension of Rice's work on the shot effect [S. O. Rice, Bell System Tech. J.34, 282 (1944);24, 46 (1945)]. Next a formalism is derived which calculates the correlation properties of the response of a continuous, linear system when subject to an applied noise field. The requirements for solution are a knowledge of the impulse response of the system and the correlation function of the source. The latter may be obtained experimentally or from calculation.