Application to biomedical signals - Practical Biomedical Signal Analysis Using MATLAB - page 174

biorthogonal spline wavelets were recommended for ECG reconstruction, which
was performed by keeping only the first approximation A 2 ( . The procedure is

equivalent in a way to low-pass filtering followed by resampling. However, the
wavelet transform approach seems to have advantages over conventional FIR filters,
which may produce oscillating structures in filtered signal (so called Gibbs oscilla-
tions) [Clifford, 2006]. In Figure 4.29 denoising by means of wavelet transform is
illustrated. The biorthogonal wavelets family is avaliable in MATLAB Wavelet Tool-
box. The wavelets in the family are named: biorJ.K ,where J and K correspond to
the number of vanishing moments in the low-pass and high-pass filters, respectively.
The wavelets with higher J and K seem to reproduce ECG signal structures better.

x )

FIGURE 4.29: Raw ECG with 50 Hz mains noise, IIR 50 Hz notch filtered ECG,
0.1-45 Hz bandpass filtered ECG and bior3.3 wavelet filtered ECG. The left most
arrow indicates the low amplitude P wave. Central arrows indicate Gibbs oscillation
in the FIR filter causing a distortion larger than the P wave. Reproduced by permis-
sion from author (Clifford, G., Advanced Methods and Tools for ECG Data Analysis ,
Norwood, MA: Artech House, Inc., 2006).

Other methods useful in removing the noise components from ECG are PCA and
ICA. It is an advantage of ICA that its subspace axes are not necessarily orthogo-
nal and the projections on them are maximally independent. ICA is a blind source