In signal processing field, there are various measures that can be employed to analyse and represent the signal in order to obtain meaningful outcome. Sparse representation (SR) has continued to receive great attention as one of the well-known tools in statistical theory which among others, is used to extract specific latent temporal features that can reveal salient primitive and sparsely represented features of complex data signals, including temporal data analysis. Under reasonable conditions, many signals are assumed to be sparse within a domain, such as spatial, time, or timefrequency domain, and this sparse characteristics of such signals can be obtained through the SR. The ECG signal, for instance, is typically a temporal sparse signal, comprises of various periodic activities such as time delay and frequency amplitudes, plus additive noise and possible interference. Particularly challenging in signal processing, especially time series signals is how to reconstruct and extract the various features that characterized the signal. Many problems (e.g., signal components analysis, feature extraction/selection in signals, signal reconstruction, and classification) can be formulated as linear models and solved using the SR technique The reconstruction of signals through SR can offer a rich representation of the sparsified temporal structure of the original signal. Due to its numerous advantages, such as noise tolerance and widespread use in various signal processing tasks, this has motivated many researchers to adopt the use of this technique for various signal representation analysis for a better and richer representation of the original input signal. In line with this, therefore, the goal of this study is to propose a SR-based mathematical framework and a coherence function for reconstruction and feature extraction from signals for subsequent analysis. The time embedding principle was first applied to restructure the signal into tine delay vectors and then the proposed approach, referred to as temporal subsequence SR approach was used to reconstruct the noisy signals and provides a sparsified time dependent input signal representation, and then the coherence function is further used to compute and extract the correlational coefficient quantities between the temporal subsequence signals to form the final feature vectors representing the discriminative features for each of the signal. These final feature vectors representing the signal are further used as inputs to machine learning classifiers. Experiments are carried out to illustrate the usefulness of the proposed methods and to assess their impact on the classification performance of the SVM and MLP classifiers using the popular and widely used ECG time series benchmark dataset. This research study supports the general hypothesis that, signal reconstruction methods (datadriven approach) can be valuable in learning compact features from the original signals for classifications.