Abstract : Analyzing electrocardiogram (ECG) recordings is crucial to gathering useful information about a patient's heart condition in a noninvasive manner, with the consequent benefits in procedural time, cost and risk of complications relative to invasive diagnostic modalities. Signal processing can aid cardiologists to make informed decisions by revealing and quantifying underlying structures that may not be apparent in the observed data, especially when the redundancy inherent to the ECG leads hinders the expert's analysis. This chapter considers two such ECG signal processing problems, namely, T-wave alternans detection and atrial activity estimation during atrial fibrillation. The redundancy present in the ECG can effectively be exploited by decomposing the observed data into interesting signals or components that are often easier to analyze than the original recording. These components can be determined as appropriate linear combinations of the observed data according to different criteria such as principal component analysis (PCA) and independent component analysis (ICA). While PCA relies on second-order statistics and yields uncorrelated components, ICA achieves independence through the use of higher-order statistics. The main concepts as well as some advantages, limitations and success stories of these popular decomposition techniques are illustrated on real ECG data from the above cardiac signal processing problems.