Suppose I have an auto-correlation function $R_Y$ of a random process $Y$ which is
$$R_Y[t]=3 \delta[t] - 2(\delta[t+1] + \delta[t-1]) + u$$
where the $R_Y[\tau]=E[Y[t]Y[t+\tau]]$ and using the the Wiener–Khintchine theorem to get the power spectral density (PSD),
$$R_Y(t) \xrightarrow{\mathscr{F}} S_Y(f)$$
My question is for what values of $u$ is $R_Y$a valid autocorrelation function?
Looking at the Fourier transform of $R_Y$,
$$S_Y[f] = 3 - 4 \cos(2\pi f) + u \delta(f)$$
I believe there is no value of $u$ which makes this autocorrelation valid since any $u$ will result in $S_Y$ having negative values.
Is this correct?