**2.5.3 Overlapping window**

228 Recurrent Neural Networks and Soft Computing

)n(x).n(e.2)n()1n( <sup>3</sup>

The LMF has a faster convergence than the LMS algorithm. It has generally a lower weight noise than the LMS algorithm, with the same speed of convergence. It was shown to have 3 dB to 10 dB lower mean-squared error (MSE) than the LMS algorithm (Wallach and Widrow, 1984). Adaptive LMF-based quadratic and cubic Volterra structures have been

A major limitation of the back-propagation algorithms is the slow rate of convergence to a global minimum of the error-performance surface because the algorithm operates entirely on the gradient of the error-performance surface with respect to the weights in the singlehidden-layer perceptron. The back-propagation learning process is accelerated by incorporating a momentum term. The use of momentum introduces a feedback loop which prevents the learning process from being stuck at a local minimum on the errorperformance surface of the single-hidden-layer perceptron. The classifier is a single-hiddenlayer perceptrion based on a modified Back-Propagation technique. The modified backpropagation algorithm has a momentum term which helps to avoid local minima. One hundred and sixty one-dimensional TOC slices have been used as templates for the desired

2. *Detect the maternal QRS-complexes –* Read the ECG recording sequentially, and process each of the 90% overlapping windows (length 250 msec) to compute the diagonal or wall slice TOC. The slice is matched to the templates until a maternal QRS-complex is detected. An auxiliary subroutine is used to pinpoint the position of the R-wave. If the second successive segment detects a maternal QRS-complex then it is discarded because it is the same complex detected in the adjacent window. The whole process of TOC template matching is repeated until the second maternal QRS-complex is detected and its R-wave is pinpointed. The maternal heart rate is accurately calculated from the

3. *Detect the fetal cardiac cycles –* The search begins from the position of the detected maternal R-wave. Window overlapping, each with fetal cumulant template matching, continues until the first, second, and possibly third fetal ECG TOC diagonal and wall slice signatures have been matched to one template for each one of them. Once the slices have been matched, the window will be flagged as a detection window. If the next overlapping window detects a fetal heartbeat, it will be discarded because it is the same fetal heartbeat that has just been detected in the previous window. The number of fetal heartbeats detected within the maternal cardiac cycle is counted. The instantaneous maternal heart rate is previously known with some degree of accuracy, and the relative fetal to maternal heartbeat is also known within the maternal cardiac cycle. Hence, the averaged fetal heart rate can be calculated within each maternal cardiac cycle.

Operations 2 and 3 are repeated for all individual maternal cardiac cycles.

developed and shown to outperform LMS-based Volterra by 6-7 dBs (Zgallai, 2007).

**2.4 Neural network classifiers** 

**2.5 The proposed algorithm** 

1. *Create ECG cumulant database* 

**2.5.1 TOC detection** 

signals in the Artificial Neural Network (ANN) classifier.

knowledge of the current and previous R-wave positions.

<sup>i</sup> <sup>i</sup> <sup>i</sup> **a a** . (2.5)

When detecting the fetal heartbeat within the maternal transabdominal cardiac cycle, 90% overlapping windows, each of 250 msec duration, are scanned at a rate of 100 Hz with a sampling rate of 0.5 KHz. The overlapping percentage should be carefully chosen to compensate for the apparent loss of temporal resolution due to a lengthy window which is dictated by the maximum threshold of the variance of the TOCs. The average fetal QRScomplex duration is 60 msec. This may be encountered at the beginning, middle, or end of the flag window. Hence by using a window overlapping of 90%, any fetal QRS-complex which may be missed because it starts to evolve, say, 20 msec before the end of a window, can definitely be picked up by the next one or two overlapping windows when it completes its full duration of 60 msec and has definitely reached its full peak (the R-wave). If this particular QRS-complex has enough strength to be picked up by two successive overlapping windows, the algorithm will count it as one FHB. It has been found that reducing the overlapping below 90% yielded missed fetal heartbeats.
