1/f fluctuation in a discrete one-dimensional diffusion system

A one-dimensional diffusion system is considered to be a convenient tool to generate 1/f fluctuations by a computer, since its frequency response to t he driving force concentrated at one point is proportional to 1/root f. How ever, the frequency response of a discrete diffusion system depends not onl y on the spatial increment and time step but also on the type of finite dif ference used to approximate the derivative. In the present paper, we specif y the conditions under which a discrete diffusion system has a frequency re sponse strictly proportional to 1/root f.