Signal Filtering and System Control

Abstract

During the recording of any signal, it is inevitable that some undesirable signals loosely termed “noise” are also picked up. This noise may be inherent in the measuring apparatus or it may be generated by other systems in the vicinity of the recording. In physiological measurement it is very common to find other physiological signals that provide undesirable noise to the measurement. If the signals are well separated in their frequency composition, it may be possible to use frequency filters that permit the passage of the desired signal while attenuating the other interfering signals. Such filtering is usually incorporated in the mechanical construction and analogue electronics of the signal recording apparatus. It is also possible to perform such filtering digitally after the signal is digitized. Quite often the frequency bands of the desired signal and the unwanted noise are not distinct, but exhibit appreciable overlap. In the case of recording EMG with interfering ECG, the frequency bands of the two signals are roughly 30–800 Hz and 0.05–80 Hz, respectively. In such situations, the question of how best to reduce the noise while retaining as much of the signal as possible is important. In this respect we can consider the design of a filter that is optimal for a particular measurement situation. If the signal x[n] and noise w[n] are not distinct in their frequency composition, the error cannot be made zero but can only be minimized. Since the signal as well as the noise are changing with every instant, the error will not be constant for any choice of filter function and the error can only be minimized in a statistical sense.