Chebyshev approximation coefficients have been shown to be an accurate and compact representation of time-series datasets. However, for medical data, such as ECG beats, a clinician may require a time domain representation for medical intervention/diagnosis purposes. Thus, there is a need to accurately recreate these signals from the approximate Chebyshev coefficients - this is especially true in cases where the beat was captured using non-uniformly sampled signals. In this study, we show that a fast approach using an iterative algorithm can be used to reconstruct signals at any time point avoiding the use of interpolation in the reconstruction process resulting in improved accuracy. The average reconstruction error of our proposed algorithm compared to the direct approach is only 0.008%. We also show that this iterative approach can be implemented using a simple (two-pole) IIR filter and that this method can be applied to the reconstruction of any time-series data.