Suppose we have an added discrete noise signal defined as:
$$y[n]=x[n]+w[n], $$ where $w$ is zero mean white Gaussian noise.
When we say white noise, is it sufficient to say that it is always be uncorrelated with signal $x$, no matter what the distribution of signal is? (I think yes)
Can we conclude that both $x$ and $w$ are independent IF noise is white Gaussian BUT the signal have unknown distribution ? (I am Confused about it)
Lastly, What the information we glean-out of the model (intuitively) if we are informed about noise that besides being zero mean, white and Gaussian, it is circular symmetric complex as well? (I do know white noise has impulse auto-correlation but confused with circular-symmetric term).