in this work, we further extend the recently developed adaptive data analysis method, the sparse time-frequency representation (stfr) method. this method is based on the assumption that many physical signals inherently contain am-fm representations. we propose a sparse optimization method to extract the am-fm representations of such signals. we prove the convergence of the method for periodic signals under certain assumptions and provide practical algorithms specifically for the non-periodic stfr, which extends the method to tackle problems that former stfr methods could not handle, including stability to noise and non-periodic data analysis. this is a significant improvement since many adaptive and non-adaptive signal processing methods are not fully capable of handling non-periodic signals. in particular, we present a simplified and modified version of the stfr algorithm that is potentially useful for the diagnosis and monitoring of some cardiovascular diseases.