Sinusoidal frequency modulated spectrum analysis

Abstract

We will analyze the stationary frequency modulated (FM) process with the additive ambient noise Zt =Yi+t:t =Acos(wct+X(t)+<P)+t:t, fortE Z where X(t) = B sin(wo t + cp) (1.2) is the sinusoidalmodulatingprocess, A and B are constants, wc, wo E [0, 1r] are, respectively, the carrier· and the modulating frequencies and cp and <P are uniformly distributed random variables on ( -1r, 1r] independent of each other and of the noise process {t:t}tEZ· We will consider the noise process as being Gaussian and white for simplicity of the exposition. However, the results are similar for any stationary and ergodic process with continuous spectral density function. Here we will estimate the relevant parameters A, B, wc and w0 by an updating procedure based on HOC (higher order correlations) sequences in the fine tuning of parametric filters. \\7e will use two different parametric families of time invariant linear filters: the alpha and complex filters. Here we alleviate the assumption of Gaussianity for the signal and we prove its stationarity and ergodicity under appropriate conditions.