The Coronary Artery Disease (CAD) which is one among the major class of cardiovascular diseases is emerging as an epidemic in the society and has proven to be the leading cause for more number of deaths when compared to the other cardiovascular diseases. It is emerging as one of the threats to the economy. It has become very important to detect CAD in its early stage which can help society in a broader way by saving a significant number of lives. The proposed method is a novel efficient automated approach which is capable of detecting CAD among the large group of patients using Electrocardiogram (ECG) signal. The system design provides a complete model of pre-processing of ECG, finding the heart rate which is further decomposed up to 4 level sub-bands using analytic transformation based signal decomposition method. The signal decomposition method is used to analyze the low frequency components of the signal and to deal with non stationary nature of heart signals. Two Non-linear entropy estimators as K-Nearest Neighbor (K-NN) and Correlation entropy are applied to decomposed sub- bands obtained after applying Analytic wavelet transformation based flexible decomposition technique to extract non-linear dynamics. The clinical significant features from the large data set can be selected by employing wilcoxon ranking method which assigns ranks on the applied signal. Further, an entropy-based classification approach and a suitable classifier namely Linear support vector machine (L-SVM) is used to classify among CAD and normal class. The algorithm is simulated in MATLAB and it is found that the results matched closely with the available data. This computer-assisted automated system which characterizes the heart signal can serve as an aid for the cardiologists in their daily screening of a large number of patients and can be used in primary health care centers which help the physicians in the early detection of a CAD.