Each year 400,000 North Americans die from sudden cardiac death (SCD). T- wave alternans (TWA) refers to an alternating pattern in the T-wave portion of the surface electrocardiogram (ECG) and has been shown as a risk stratifier for SCD. These subtle changes in the T-waves are in the micro-volt scale and ambulatory ECG recordings usually contain biological noise. Also, data non-stationarity owing to heart rate variability and the amplitude variability in TWA magnitude can limit the accuracy of the detection techniques. This necessitates the need for robust detection algorithms for processing such non-stationary data. In this thesis, we have proposed an Empirical Mode Decomposition (EMD) based scheme combined with the Instantaneous Frequency (IF). EMD decomposes the signal into several monocomponent signals called Intrinsic Mode Functions (IMFs). IF extracted from these IMFs provides an accurate estimate of time varying frequency components and hence can aid during characterization of TWAs. In order to validate the performance of the proposed detection technique, the feature vectors extracted from the IMFs were fed to a linear discriminant analysis (LDA) classifier. The performance assessment was carried out using two datasets: (a) Synthetic TWAs: 72 signals obtained from publicly accessible Physionet database and (b) TWAs from patients: 55 ambulatory ECG signals obtained from the Toronto General Hospital. Using an unbiased leave-one-out cross validation strategy, maximum overall classification accuracies of 86.1% and 81.8% were achieved for TWA detection from synthetic and ambulatory ECG recordings respectively. In addition, the usability of the proposed technique has been investigated to assess its suitability for addressing another cardiovascular problem stroke. Atrial Fibrillation (AF) has been identified as a risk factor to increase the chances of stroke. The most common method in studying the complex AF electrograms is to employ dominant frequency (DF) analysis; however, due to signal non-stationarity DF does not always provide the best estimate of the atrial activation rate. As a result, analyzing the electrograms via EMD and IF has been investigated as the second contribution of this work.