# Is match filter a solution of some differential equation?

Matched filter is very common and termed as optimal filter for detection purpose. The question is : can we formulate a differential equation and show that the solution is matched filter.

• sort of. Google Fredholm equations of the first kind – Stanley Pawlukiewicz Mar 12 at 2:50
• @StanleyPawlukiewicz Do you have specific kernel of Fredholm equation in mind to consider matched filter as solution. – Creator Mar 12 at 3:08
• @StanleyPawlukiewicz math.stackexchange.com/questions/3145674/… – Creator Mar 13 at 21:12

Note that as a degenerate case $$y(t) = x(t)$$ can also be considered to be a (useless) differential equation (of order zero?) but I think it's not what you mean by a differential equation.