A modified random telegraph signal with a 1/f PSD

A simple as possible random process - a random telegraph signal with independent amplitudes, and underpinned by a point process with inter-arrival times specified by a one sided Cauchy probability density function, is shown to have a 1/f power spectral density. Integral, and statistical, expressions for the number of points in a set interval, and the arrival time of the kth point, are specified. An approximate analytical expression for the zero crossing time probability density function is specified. Simulation results verify the theory.