Provided are methods and systems for concealing missing segments and/or discontinuities in an audio signal, thereby restoring the continuity of the signal. The methods and systems are designed for and targeted at audio signals, are based on interpolation and extrapolation operations for sinusoids, and do not rely on the assumption that the sinusoids are harmonic. The methods and systems are improvements over existing audio concealment approaches in that, among other advantages, the methods and systems facilitate asynchronous interpolation, use an interpolation procedure that corresponds to time-domain waveform interpolation if the signal is harmonic, and have a peak selection procedure that is effective for audio signals.