Signal Reconstruction Based on the Relationship Between STFT Magnitude and Phase Spectra

Signal reconstruction by spectrogram inversion from short-time Fourier transform (STFT) magnitude spectrum has gained renewed interest since a few years. Actually, recent advances in compressive sensing made it possible to recover high quality signals from partial spectral data. In addition, recent theoretic works have revealed novel relationships between STFT magnitude and phase. Therefore, in this paper, a novel algorithm for signal reconstruction, based on the explicit relationship between STFT magnitude and phase is presented in many variants. Objective evaluation using signal-to-error ratio (\(SER_{dB}\)) shows the advantages and the limits of each variant.