A new technique for instantaneous frequency rate estimation

This letter introduces a two-dimensional bilinear mapping operator referred to as the cubic phase (CP) function. For first-, second-, or third-order polynomial phase signals, the energy of the CP function is concentrated along the frequency rate law of the signal. The function, thus, has an interpretation as a time-frequency rate representation. The peaks of the CP function yield unbiased estimates of the instantaneous (angular) frequency rate (IFR) and, hence, can be used as the basis for an IFR estimation algorithm. The letter defines an IFR estimation algorithm and theoretically analyzes it. The estimation is seen to be asymptotically optimal at the center of the data record for high signal-to-noise ratios. Simulations are provided to verify the theoretical claims.