Signal estimation from modified short-time Fourier transform

TLDR

The paper proposes an algorithm to reconstruct a signal from its modified short‑time Fourier transform. The method minimizes mean‑squared error between the estimated and modified STFT, and an iterative variant further refines the estimate using only DFT operations. Experiments show the iterative algorithm progressively reduces error, runs in real time, and yields high‑quality time‑scaled speech that outperforms current techniques.

Abstract

In this paper, we present an algorithm to estimate a signal from its modified short-time Fourier transform (STFT). This algorithm is computationally simple and is obtained by minimizing the mean squared error between the STFT of the estimated signal and the modified STFT. Using this algorithm, we also develop an iterative algorithm to estimate a signal from its modified STFT magnitude. The iterative algorithm is shown to decrease, in each iteration, the mean squared error between the STFT magnitude of the estimated signal and the modified STFT magnitude. The major computation involved in the iterative algorithm is the discrete Fourier transform (DFT) computation, and the algorithm appears to be real-time implementable with current hardware technology. The algorithm developed in this paper has been applied to the time-scale modification of speech. The resulting system generates very high-quality speech, and appears to be better in performance than any existing method.