As indicated in the previous section, instead of digitizing a differential equation by finite differences, one can often formulate a filter design problem. This is ideal when all that matters is the input-output response of the physical system, and the physical system is linear and time-invariant (LTI). When the desired transfer function spans more than one system element, non-physical models are usually obtained, so we will not consider such models further. However, digital filter design methods optimizing perceptually motivated error criteria are extremely effective in spectral modeling and audio compression applications . They are also good choices for subsystems which are to remain fixed over time, such as cello bodies, piano soundboards, and the like.