On FM Correlation System

Abstract

In terms of FM correlation system, we mean an analog correlation system which consists of two channels, containing a FM detector in each channel. This paper presents a detailed analysis of the output for FM correlation system when two input signals to be correlated have the arbitrary time difference and magnitude, and are superimposed by the statistically independent stationary Gaussian random noises. First, the expressions are derived for the output of FM correlation system when each channel input is a frequency-modulated signal with constant amplitude superimposed by random noise, and the features of FM correlation system are shown in comparison with the conventional correlation system. Second, we analize the output of FM correlation system for the following two cases: namely, the one in which each channel input consists of an amplitude-limited narrowband Gaussian random signal X_L1(t) (X_L2(t)) and random noise, and the other case in which each channel input consists of a no-limited one X₁(t) (X₂(t)) and random noise, and show the difference in the effect of input carrier-to-noise ratio for the output of FM correlation system for the two cases. In addition, it is shown by σ, the rms band-width of X(t), that we are able to regard the band-width as ±(3∼4) σ, for X_L(t) and X(t) under the condition of equal mean power.