Smoothing and filtering

Some methods for separation or extraction of usable information from the available data have been presented. First, optimum smoothing in state-space framework was discussed, which was to familiarize the reader with the various issues connected with smoothing. This was followed by studies on bidirectional filtering, which can be used to perform smoothing with minimum lag or phase shift. The bidirectional processing is a characteristic feature which is incorporated in many algorithms for bias-free processing; for example the fixed interval smoother uses similar forward-backward passes, and the centred moving average used in the time series analysis is also effectively similar in concept. Orthogonal transformation offers a numerically robust method of smoothing and signal extraction. The smoothing is performed through the elimination of insignificant on singular value decomposition (SVD). Besides smoothing, the potential of the SVD based methods in signal extraction and pattern estimation in a noisy environment was also demonstrated through application studies. The approach depends on the repetitive nature of the signal component of interest, and hence the data are appropriately configured for analysis. A case study on fetal ECG extraction from maternal ECG showed that extraction is possible with only one signal (i.e. the maternal ECG signal from the abdominal lead), and irrespective of low signal to noise ratio; the other available methods of fetal ECG extraction require one or more additional signals. The application of orthogonal transformation for smoothing and filtering is an area of active research, and the present study has been only a glimpse of its enormous potential.