One embodiment of the present invention provides a system that reconstructs a high-resolution signal from a set of low-resolution quantized samples. During operation, the system receives a time series containing low-resolution quantized signal values which are sampled from the high-resolution signal. Next, the system performs a spectral analysis on the time series to obtain a frequency series for the low-resolution quantized signal values. The system next selects a subset of frequency terms from the frequency series which have the largest amplitudes. The system then reconstructs the high-resolution signal by performing an inverse spectral analysis on the subset of the frequency terms.