Digital IIR filters: Effective in edge preservation?

Abstract

Infinite Impulse Response (IIR) filtering stands as a fundamental technique in various signal processing applications. Despite its widespread use, the scientific community widely acknowledges the suboptimal nature of IIR filters in preserving edges or abrupt transitions in piecewise signals. In situations where meticulous preservation of abrupt signal transitions is crucial, signal processing practitioners often explore alternative methodologies tailored to specific application demands. Consequently, the effectiveness of digital IIR filters in preserving signal edges while filtering out undesirable noise components continues to be a topic of active debate.In response to this limitation (or answering the question posed by the above title), the paper demonstrates that the suboptimal nature of IIR filters in preserving edges arises from the conventional methodology used to compute the output of zero-phase IIR filters. The standard method of output computation equates to solving an unconstrained optimization problem with an ℓ2-norm penalty term. Following this analysis, the paper introduces a refined approach to compute the output of digital IIR filters, aiming to overcome the challenge of preserving abrupt signal transitions. This innovative proposal replaces the ℓ2-norm with an ℓ1-norm, resulting in the development of an IIR filter that dynamically adjusts its coefficients based on the input signal. As a result, this novel approach to output computation effectively preserves essential signal features while simultaneously reducing noise, highlighting the efficacy of digital IIR filters in edge preservation. Therefore, the answer to the aforementioned question greatly depends on the chosen method for computing the output. By employing the suggested approach, the answer is unequivocally yes.