Derivation of the Optimal Matched Filter - Convolution vs. Correlation On the Wikipedia page for Matched Filters here, there is a matrix algebra derivation for an optimal matched filter. Now, considering the output of an LTI system is found using the convolution operator, why is the first step of the proof on the page is to consider:

$$ y = \sum_{k=-\infty}^{\infty} h^{*}[k]x[k] $$

instead of,

$$ y[n] = \sum_{k=-\infty}^{\infty} h[n-k]x[k] $$

the convolution operation? And is $h^{*}$ the complex conjugate of the impulse response?
Convolution commutes
$$
y[n]=\sum_k h[n-k]x[k]=\sum_k h[k] x[n-k]
$$
for $n=0$
$$
y[n=0]=\sum_k h[-k] x[k]
$$
If $H(e^{-\jmath \omega})$ is the Fourier Transform of $h[n]$, $H(e^{\jmath \omega})$  is the Fourier Transform of $h[-k]$, 

The maximization for the matched filter is at the point $n=0$.  

In communications $n=0$ corresponds to synchronization.

In a RADAR/SONAR problem the maximum output of the matched filter is the estimate of where $n=0$