For our purposes, an analog filter is any filter which operates on continuous-time signals. In other respects, they are just like digital filters. In particular, LTI analog filters can be characterized by their (continuous) impulse response , where is time in seconds. Instead of a difference equation, analog filters may be described by a differential equation. Instead of using the z transform to compute the transfer function, we use the Laplace transform. Every aspect of the theory of digital filters has its counterpart in that of analog filters. In fact, one can think of analog filters as simply the limiting case of digital filters as the sampling-rate is allowed to go to infinity.
In the real world, analog filters are usually electrical models, or ``analogues'', of mechanical systems working in continuous time. If the physical system is linear and time-invariant (LTI) (e.g., consisting of elastic springs and masses which are constant over time), an LTI analog filter can be used to model it. Before the widespread use of digital computers, physical systems were simulated on so-called ``analog computers.'' An analog computer was much like an analog synthesizer providing modular building-blocks (``integrators'') that could be patched together to build models of dynamic systems.