Intuitive Approach to Active Digital Filter Design. Part I: Principle of First-order Filters

Analog signals are usually digitized and further processed using various algorithms and procedures for digital data analysis. In digital signal processing (DSP), digital filtering is a crucial signal processing task that is used to enhance signal quality and increase the signal-to-noise ratio of a processed stream. This paper presents an original, intuitive, and easy-to-implement approach to the design of integrator-based closed-loop infinite-impulse-response filters, namely active digital filters. The approach is based on the feedback control theory and uses digital integrators to build stable negative feedback DSP systems that allow easy implementation of various filtering functions: low-pass, high-pass, etc. The filter cutoff frequency can be controlled using a single coefficient and adapted to the application needs. The presented active filters offer the simplest possible architecture and are well-suited for many DSP applications.