The alternate capture and emission of electrons at an individual defect site generates discrete switching in resistance, referred to as a random telegraph signal (RTS). Recent experiments indicate that some defects might have two mutually exclusive emission modes with distinct emission rates, which result in the anomalous RTS: a rapid-switching RTS modulated in time by a slow-switching RTS of the same amplitude. The spectrum is calculated of the anomalous RTS by assuming that the emission mode for a captured electron is determined at the moment of capture of the electron, and the probability for a given mode is a constant p in each event of capturing. It is shown that a distribution in p might lead to a 1/f spectrum.