Smart Sensors and Systems by Chong-Min Kyung Hiroto Yasuura Yongpan Liu & Youn-Long Lin

Author:Chong-Min Kyung, Hiroto Yasuura, Yongpan Liu & Youn-Long Lin
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

10.4.1 Digital Filtering

Digital filters are central to all signal processing systems. Each sample of the digitized signal is passed through a specific type of filter. Digital filters are used to filter out unwanted noise or artifacts from the biosignal to enhance the quality of the signal and prepare it for closed-loop detection.

If input data x[n] enter the filter sequentially, the output data y[n] is the weighted sum of the current and past values, and is given by:

where x[n−i] is the past input data, y[n−i] is the past output data, the a i and b i parameters are the weights, and M and N are the numerical data lengths. The filtered output data have the same number of samples, in which the first sample of y[n] corresponds to the first sample of x[n]. Filters that depend on current and past data are known as causal filters. In real-time applications, causal filtering is necessary because future input and output data are not yet available. A simple example is the computation of a moving average. When computing a moving average, the signal passes through the filter, and the filter data is equal to the sum of the past input samples (N) each weighted by 1/N. This filter attenuates the high frequencies and preserves the low frequencies. The guidelines for developing closed-loop control demand low complexity and short latency. The sums of the past N consecutive samples have to be considered in the optimal range.

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