On sub-ideal causal smoothing filters

TL;DR

This paper introduces a family of causal smoothing filters for continuous-time processes that nearly achieve exponential damping of high-frequency energy while maintaining causality, balancing ideal filtering with practical constraints.

Contribution

It proposes a new class of sub-ideal causal filters with near-exponential high-frequency damping, addressing the trade-off between decay rate and causality.

Findings

Filters exhibit almost exponential damping of high frequencies.

The filters maintain causality despite near-ideal damping.

A faster decay would compromise causality.

Abstract

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.