Which signals or set of signals is the most predictable or in other words most self-correlated (autocorrelation)?
I think one of them is $x(t)=c$, for all $t$, where $c$ is a scalar constant. The other one can be $x(t)=c$, for $t=t_0$ and $x(t)=0$, otherwise (a discrete signal with only one value). $t_0$ is a constant.
Here the book says: "the most predictable signal" is the sum of discrete cosine functions with random phases. Why? My two examples above seem to me more predictable!