# Linear Filtering Methods - Chapter 5

# G. D. Clifford

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.

__Links__:

- ECGtools - A selection of ECG analysis tools in Matlab including a self-explaining QRS detector, filtering tools and HRV analysis algorithms. Includes FIR, SVD, ICA and Wiener filtering code.
- 6.555 Materials related to Julie Greenberg's Biomed Signal & Image Processing course.
- Netlab -- A free set of pattern recognition & neural network tools in Matlab by Ian Nabney. the associated book is simply wonderful.
- HRV2006 - Harvard Course on Heart Rate Varaiability

__Contents__:

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