On sub-ideal causal smoothing filters

Smoothing causal linear time-invariant filters are studied for continuous time processes. The paper suggests a family of causal filters with almost exponential damping of the energy on the higher frequencies. These filters are sub-ideal meaning that a faster decay of the frequency response would lead to the loss of causality.

► A family of smoothing causal linear time-invariant filters for continuous time processes is suggested such that the frequency response approximates the real unity uniformly on an arbitrarily large interval.
► In addition, almost exponential damping of the energy on the higher frequencies is ensured.
► These filters are sub-ideal meaning that a faster decay of the frequency response would lead to the loss of causality.