The question is related to the optimallity of matched filter. The definition of matched filter is given in the link here: https://en.wikipedia.org/wiki/Matched_filter
Cosider that the signal is corrupt with a single frequency sinusoid along with the desired signal. This means the noise defined in the wikipedia link is a single frequency sinusoid (frequency is known)and some noise. In such case
a) is the matched filter alone is optimal or
b) a combination of a band pass filter and matched filter? The band pass filter is used before the matched filter to remove the unwanted sinusoid.
One can do simulation to find out some insight but can we proof something mathematically? In other words, the question: is the optimal condition is for added white noise only? Any help would be appreciated.
EDIT: The wiki link has the model x=s+v where s is the signal and v is the noise. The model I am talking about is x=s+v+one_sinusoid. The frequency of the sinusoid is known and is not in band with s.