I don't know about impulse response and signal filtering, but the Soviets did try to model their economy with linear models. Cosma Shalizi put up a good analysis [1] of why this is very very difficult. Simply put, any kind of "real" economy has so many variables (in the kinds of goods and services, their various quality levels, and the locations in both time and space that goods and services have to be) that any kind of linear programming quickly gets swamped by the sheer number of variables that have to be adjusted in order to compute an optimal outcome. So yes, in theory you can model an economy using a linear system. It's not even an NP problem. But in practice, the computational complexity is high enough (though still within P) that even toy economies with as few as a thousand elements become impossible to optimize with linear programming.
[1] http://crookedtimber.org/2012/05/30/in-soviet-union-optimiza...