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This article concentrates on analysis of subtle ECG signal features associated with characteristic temporal variations in the repolarization phase of cardiac electrical activation (i.e., variations that are embedded within the T-wave). These variations are termed T-wave alternans (TWA) to connote larger similarity between T-wave shapes in every other beat than that in the adjacent beats that occur during regular heart rhythm of an increased rate. In an early work the concept of associating TWA with period-doubling bifurcation of the cardiac oscillator has been put forward and demonstrated on canine ECG traces. In this article we extend this idea and use it for quantification of TWA in human ECGs recorded from postinfarction patients. The purpose of this work is to show that: a statistically significant correlation exists for the analyzed ECGs between the TWA level computed by means of an inter-cycle synchronized sampling technique known as Poincare mapping (PM) and a widely used Fourier spectrum (FS) method, and that the PM method outperforms the widely used FS method for TWA analysis in a number of ways.