🤖 AI Summary
This work addresses the limitations of existing filter design methods, which often lack flexibility and physical consistency, particularly in simultaneously enforcing spatial symmetry and diverse frequency-domain constraints. To overcome these challenges, the authors propose a general constrained optimization framework implemented in a Python library called pyDOF. This tool enables users to specify custom transfer function constraints and automatically synthesizes discrete forward and inverse filters that satisfy complex design requirements. The approach innovatively integrates adaptive template selection, van Cittert iterative deconvolution with controllable reconstruction order, and a highly configurable constraint mechanism, thereby transcending conventional design limitations. The framework efficiently generates filter coefficients for low-pass, high-pass, and multi-bandpass/bandstop configurations, demonstrating broad applicability in computational fluid dynamics and generalized signal processing tasks.
📝 Abstract
In this work, we present pyDOF, a Python-based software library which provides a domain-specific framework for the design of symmetric, physical-space, forward as well as inverse discrete filters. pyDOF is based on a constrained optimisation framework developed in our previous work [1, 2]. This framework allows the user to impose a wide range of constraints on the discrete filter transfer-function such as monotonicity, positivity, value-fixing, gradient-smoothing etc. amongst many others. pyDOF additionally includes an adaptive filter stencil selection option, and a van Cittert-based inverse-filter design with a user-controlled reconstruction order. The filter coefficients are computed automatically, and saved to a plain text file which can be readily parsed by any programming language. pyDOF can be used to design a wide range of low-pass, high-pass, multi band-pass/band-stop etc. discrete filters. In addition, due to its generality and abstraction, pyDOF can be used to design specific filters for user-defined target filter transfer functions. Although developed primarily for application to computational fluid dynamics simulations, pyDOF can be used to design discrete filters for a wide range of signal processing applications.