Frequency-Domain Signal-to-Noise Ratios Illuminate the Effects of the Spectral Consistency Constraint and Griffin-Lim Algorithms

Stephen D. Voran and Jaden Pieper

Abstract:

The restoration of degraded audio signals is often performed on complex-valued frequency-domain (FD) representations. This requires manipulation of either magnitudes and phases or real and imaginary parts. In general, these manipulations do not produce consistent representations. The consequence is that the magnitudes and phases (or real and imaginary parts) of the restored time-domain signal (which are always consistent) do not match the generally inconsistent values imposed during FD restoration. In colloquial terms, “What we get is not what we asked for.” The enforcement of consistency is always heard in the resulting audio and is known in principle, but it can be better understood. We present two-dimensional FD SNR frameworks (e.g., magnitude/phase or real/imaginary) that visually reveal how consistency enforcement changes the applied FD restorations to arrive at the achieved FD restorations. We also show how extended Griffin-Lim algorithms can reduce and direct, but not eliminate, the changes produced by consistency enforcement. We apply objective estimators to connect this work to estimated speech quality and intelligibility. This work can inform machine learning training and architecture choices that must balance restoration efforts across two dimensions (e.g., magnitude and phase) to arrive at the best possible speech quality.

Keywords: frequency domain analysis; machine learning; signal processing algorithms; acoustics; signal to noise ratio; time-domain analysis; machine learning algorithms; training; conferences

(VoranPieperFD_SNRs_WASPAA2026.pdf)

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