Phase-Magnitude Relations and Phaseless Reconstruction for Time-Frequency and Time-Scale representations
* Presenting author
We discuss the phase-magnitude (PM) relations for the short-time Fourier and wavelet transforms which are derived from analyticity of the respective transform, when an appropriate analysis window or wavelet is used. For the short-time Fourier transform, the PM relations were previously studied by Portnoff and later rediscovered by Auger et al. Recently, it was shown that these relations can be combined with an adaptive integration scheme to enable signal reconstruction from magnitude-only short-time Fourier measurements that often performs on par or better than more expensive, iterative algorithms for phaseless reconstruction. For wavelet transforms, similar relations hold that can be employed for phaseless reconstruction as well. We recall the phase-magnitude relations and the resulting algorithms in both settings and demonstrate their application in the audio domain.