Digital Low-Pass Differentiation for Biological Signal Processing

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Abstract
Digital low-pass differentiation is often required in processing various biological or biomechanical data. However, both the nature of biological signals and the use of micro-or minicomputers in such applications imply the need for simple, low-order, and fast differentiation methods, rather than sophisticated high-order algorithms. Responding to this need, we investigate here the low-pass first- and second-order digital differentiation from both theoretical and practical points of view, in order to achieve good and simple algorithms. In contrast with most of the research works previously done in this field, whose main aim was to achieve better accuracy even in the cost of using quite high-order algorithms, we restrict ourselves in this study only to low orders, being interested not only in the accuracy achieved, but also in the simplicity of the algorithm. After discussing the theoretical considerations concerning our optimum low-pass differentiation filters, we present our simple low-order filters and show them to be not only very convenient for use, but also almost optimum.