Estimation of modulation based on FM-to-AM transduction: two-sinusoid case

A method is described for estimating the amplitude modulation (AM) and the frequency modulation (FM) of the components of a signal that consists of two AM–FM sinusoids. The approach is based on the transduction of FM to AM that occurs whenever a signal of varying frequency passes through a filter with a nonflat frequency response. The objective is to separate the AM and FM of the sinusoids from the amplitude envelopes of the output of two transduction filters, where the AM and FM are nonlinearly combined in the amplitude envelopes. A current scheme is first refined for AM–FM estimation of a single AM–FM sinusoid by iteratively inverting the AM and FM estimates to reduce error introduced in transduction. The transduction filter pair is designed relying on both a timeand frequency-domain characterization of transduction error. The approach is then extended to the case of two AM–FM sinusoids by essentially reducing the problem to two single-component AM–FM estimation problems. By exploiting the beating in the amplitude envelope of each filter output due to the two-sinusoidal input, a closed-form solution is obtained. This solution is also improved upon by iterative refinement. The AM–FM estimation methods are evaluated through an error analysis and are illustrated for a wide range of AM–FM signals.