# A new mother wavelet for fetal ECG to achieve optimal denoising and compressing results

## S. Almagro, M.M. Elena, Martin J. Bastiaans, and J.M. Quero

A de-noise and compress algorithm based on wavelet transformation (WT) for abdominal electrocardiograms (AECG) signals is designed. This is done at the first stage before extracting the fetal electrocardiogram (FECG) from the AECG. Since the FECG is mixed with the MECG into the AECG and has much lower amplitude than the maternal electrocardiogram (MECG), it is impossible to have a non-invasive method which measures FECG alone. The goal at this stage is to design an algorithm which achieves an AECG with minimal noise and high compression rate while keeping the AECG quality at a visually and clinically acceptable level.

The algorithm uses a new mother wavelet that is especially designed in this study for AECG analysis. The first part of the algorithm is based on the design of a mother wavelet. Higher compression in WT is achieved when greater correlation exists between the mother wavelet and the signal which is transformed into wavelet coefficients. Hence, the shape of the mother wavelet should resemble the shape of a normal AECG. The algorithm can also be used to design mother wavelets for other purposes.

After deriving the WT using the new mother wavelet, the second part of the algorithm consist in calculating the wavelet coefficients. The algorithm used ensures real time monitoring of an AECG signal, since the wavelet coefficients are calculated with a fixed delay of N (number of scales used to represent the wavelet coefficients) multiplied by the AECG sample frequency and by a variable delay (linear to the length of the AECG signal) which depends on the time needed to produce a reduced row echelon form of an N*N matrix. Hence, the algorithm can be implemented by a chip which has the ability to produce accurate and fast reduced row echelon forms of matrices. No complex low and high pass reconstruction and decomposition filters, with orthogonal or bi-orthogonal properties, are needed as is traditionally the case.

The algorithm is evaluated by real AECG data from the Database for the Identification of Systems (DaISy) showing a low MSE (0.118 %), RMS (6.570 microvolt) and excellent visual similarity between the original and the reconstructed AECG. Better results can be achieved by using greater accuracy in calculating the necessary parameters and improving the correlation between the mother wavelet and the AECG signal.

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To: Papers by Martin J. Bastiaans