Instantaneous frequency and its periodicity for cyclostationary time-series

A statistical study of the instantaneous frequency (IF) for nonstationary time series exhibiting cyclostationarity is presented from a nonprobabilistic point of view. It is shown that second-order periodicity of a cyclostationary time series implies first-order periodicity of its IF, in both the pure periodic and almost periodic case. An explanation is given for the short-time periodicity in terms of IF that is exhibited by many signals of practical interest, including those which are not widely recognized as frequency-agile. This is illustrated through examples.