Explicit consistency constraints for STFT spectrograms and their application to phase reconstruction

By Jonathan Le Roux, Nobutaka Ono, S. Sagayama. 2008

95 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

Wave-U-Net: A Multi-Scale Neural Network for End-to-End Audio Source Separation (2018, methodology): “Alternatively, the Grifﬁn-Lim algorithm can be applied to ﬁnd an approximation to a signal whose magnitudes are equal to the estimated ones, but this is slow and often no such signal exists [8].”
SIGNAL RECONSTRUCTION FROM STFT MAGNITUDE : A STATE OF THE ART (2011, methodology): “This was illustrated by Le Roux in [18], with the example of designing an inconsistent STFT H ∈ CN×M so that ∑ |H| > 0 but STFT (STFT−1(H)) = 0 only for a given analysis/synthesis window pair.”
Phase Processing for Single-Channel Speech Enhancement: History and recent advances (2015, background): “[18], whose key idea was to bypass the time domain altogether and reformulate the problem within the time-frequency domain.”
Universal Sound Separation (2019, methodology): “Since we measure loss in the time domain, gradients are backpropagated through the synthesis transform and its overlap-add layer, so STFT consistency [26, 32] is implicitly enforced when using the STFT.”
Deep Learning Based Phase Reconstruction for Speaker Separation: A Trigonometric Perspective (2018, background): “To resolve this sign ambiguity, we think that inter-T-F unit phase relations such as group delay (GD) or instantaneous frequency [11] and phase regularizations such as phase consistency [12] could help.”
PhaseNet: Discretized Phase Modeling with Deep Neural Networks for Audio Source Separation (2018, background): “One approach to phase estimation is to promote consistency [18, 19], where it modiﬁes the mixture phase depending on the results of the estimated magnitude such that the mod-iﬁed phase satisﬁes consistency .”
Consistent Wiener Filtering for Audio Source Separation (2013, methodology): “If the inverse STFT (iSTFT) is defined in such a way that time-domain signals can be exactly reconstructed from their STFT through iSTFT without additional time-varying normalization, a necessary and sufficient condition for an element S of S to be consistent is that it is equal to the STFT of its i”
Equalization matching of speech recordings in real-world environments (2016, methodology): “Multiplying directly the STFT frames with an arbitrary zero-phase spectral weighting for separation (with |L(ω, t)|) or EQ (with |G(ω)|) corresponds to using non-realizable filters [9], resulting in time-aliasing artifacts and non-consistent STFTs [18, 19, 20].”
Beyond NMF: Time-Domain Audio Source Separation without Phase Reconstruction (2013, background): “[7] proposed a cost function that evaluates the inconsistency of a complex spectrogram and derived an efficient algorithm for minimizing the cost function [8].”