Cross-Correlation and Statistical Dependence between Envelope and Frequency Deviation of a Sine Wave plus Random Noise

Cross-correlation and statistical dependence between the envelope V(t) and angular frequency deviation Φ’(t) of a sine wave plus random noise are discussed with a view to possible application to frequency demodulation. In particular it is shown that the cross-correlation function RΦ’V(τ) vanishes because the joint probability density p2(Φ1’, V2; τ) turns out to be an even function of Φ1’. Besides, a short discussion on some features of the phase deviation allows not only to show that V(t) and Φ’(t), while uncorrelated, are not independent, but also, by a different method, to prove once more the vanishing of RΦ’V(τ)