Systems and methods are described herein for applying a predefined functional shape to coefficients of a discrete Fourier transform of a waveform. The waveform may based, at least in part, on an electro-cardiogram (ECG). The predefined functional shape may be parabolic, and may be defined on a logarithmic scale. The application of a predefined functional shape may allow a more accurate reconstruction of a waveform to be generated at a lower sampling rate.
