Fluctuation of autocorrelation of a signal due to signal's noise I have a question about the fluctuation of autocorrelation of a signal due to signal's noise.

I have a signal defined in $-1\leq t \leq 1$ as the following:
$V(t)=kt+R(t)$, where $R(t)$ is the random noise, and $k$ is non-negative.

Then, when I calculate the autocorrelation of $V(t)$, $G(\tau)=\int_{-1}^{1-\tau} V(t)V(t+\tau)dt$ (using the commend CorrelationFunction of Mathematica), I could observe that the fluctuation of $G(\tau)$ reduces as $k$ increases from zero. Could you explain the origin of this observation? Is it because as $k$ becomes larger, there is more autocorrelation and $R(t)$'s contribution to $G(\tau)$ is diminished?
If you view $V(t)$ as desired signal $kt$  affected by noise $R(t)$, the clearly as you keep increasing $k$, this has the effect of increasing signal energy. Hence if the noise power is kept constant then $V(t)$ tends towards being more deterministic (in a loose sense) with improving SNR, and autocorrelation hence is more deterministic with reduced fluctuations.