Estimating the Parameters of General Frequency Modulated Signals

A general frequency modulated (GFM) signal characterizes the vibrations produced by compressors, turbines, propellers, gears, and other rotating machines in a dynamic environment. A GFM signal is defined as the composition of a real or complex, periodic, or almost-periodic carrier function with a real, differentiable modulation function. A GFM signal therefore contains sinusoids whose frequencies are (possibly nonintegral) multiples of a fundamental; to distinguish a GFM signal from a set of unrelated sinusoids, it is necessary to track them as a group. This paper develops the general frequency modulation tracker (GFMT) for one or more GFM signals in noise using the expectation/conditional maximization (ECM) algorithm that is an extension of the expectation- maximization (EM) algorithm. Three advantages of this approach are that the ratios (harmonic numbers) of the carrier functions do not need to be known a priori, that the parameters of multiple signals are estimated simultaneously, and that the GFMT algorithm exploits knowledge of the noise spectrum so that a separate normalization procedure is not required. Several simulated examples are presented to illustrate the algorithm’s performance.