On the Characterization of Slowly Varying Sinusoids

We give a brief discussion on the amplitude and frequency variation rates of the sinusoid representation of signals. In particular, we derive three inequalities that show that these rates are upper bounded by the 2nd and 4th spectral moments, which, in a loose sense, indicates that every complex signal with narrow short-time bandwidths is a slowly varying sinusoid. Further discussions are given to show how this result helps providing extra insights into relevant signal processing techniques.