5.1 Introduction

In this chapter a basic knowledge of the ECG and signal processing is assumed, including time-domain infinite impulse response (IIR) filters, finite impulse response (FIR) filters, and basic Fourier theory. As background references, the reader is encouraged to read Chapter 7 in [1] and Chapter 3 in [2]. From this base, we will explore a range of modern filtering techniques including wavelets, principal component analysis, and independent component analysis. Furthermore, the selection of the appropriate filtering technique for a particular situation is not always obvious, and sometimes it is appropriate to cascade a series of filters. Methods and metrics for evaluating filters are therefore described both in this chapter and in the following chapter on nonlinear filtering techniques.

The simplest filtering of a time series involves the transformation of a discrete one-dimensional ( M = 1) time series x[ n], consisting of N points such that x[ n] = ( x ₁, x ₂, x ₃ x _N) ^T, into a new representation, y[ n] = ( y ₁, y ₂, y ₃ y _N) ^T. If x[ n] ( t = 1, 2, , N) is a column vector that represents a channel of ECG, then we can generalize this representation so that M channels of ECG, X, and their transformed representation Y are given by