Sampled and discretized of short-time Fourier transform and non-negative matrix factorization: the single-channel source separation case

The Short-time Fourier transform (STFT) is a popular time-frequency representation in many source separation problems. In this work, the sampled and discretized version of Discrete Gabor Transform (DGT) is proposed to replace STFT within the single-channel source separation problem of the Non-negative Matrix Factorization (NMF) framework. The result shows that NMF-DGT is better than NMF-STFT according to Signal-to-Interference Ratio (SIR), Signal-to-Artifact Ratio (SAR), and Signal-to-Distortion Ratio (SDR). In the supervised scheme, NMF-DGT has a SIR of 18.60 dB compared to 16.24 dB in NMF-STFT, SAR of 13.77 dB to 13.69 dB, and SDR of 12.45 dB to 11.16 dB. In the unsupervised scheme, NMF-DGT has a SIR of 0.40 dB compared to 0.27 dB by NMF-STFT, SAR of -10.21 dB to -10.36 dB, and SDR of -15.01 dB to -15.23 dB.