Evaluating deterministic errors in low - bandwidth digital filters using Taylor series expansions

A method is presented to show how deterministic errors in low-bandwidth digital filters may be expressed in terms of the input signal and its derivatives. By applying a Taylor series expansion to the delayed terms of the difference equation implemented by the digital filter, the difference equation may be written as a differential equation which allows easy computation of the deterministic errors, The paper also demonstrates the importance of performing error analysis as part of the digital filter design process.