Linear Filtering Methods  - Chapter 5

G. D. Clifford

MLP Advanced Methods for ECG Analysis, (Eds. G. D. Clifford, F. Azuaje and P. E. McSharry),  Artech House, Boston, 2006.

This Chapter attempts to present a unified framework for advanced filtering methods, by describing methods for projecting data into a lower-dimensional set of basis functions, which allow signal/noise separation, then inverting the (lossy) transform. Comparative methods include Wiener and Wavelet filtering, Principal Component analysis and Independent Component Analysis. Detailed mathematical analysis is provided to show how these techniques can be reformulated as a neural network-based learning problem.     





5.2 Wiener Filtering


5.3 Wavelet filtering

5.3.1 The Continuous Wavelet Transform

5.3.2 The Discrete Wavelet Transform and Filterbanks

5.3.3 A Denoising Example: Wavelet Choice

5.4 Data-Determined Basis Functions

5.4.1 Principal Component Analysis

5.4.2 Neural Network Filtering

5.4.3 Independent Component Analysis for Source Separation and Filtering