SoudenMVDR

class torchaudio.transforms.SoudenMVDR

Minimum Variance Distortionless Response (MVDR [Capon, 1969]) module based on the method proposed by Souden et, al. [Souden et al., 2009].

Given the multi-channel complex-valued spectrum \(\textbf{Y}\), the power spectral density (PSD) matrix of target speech \(\bf{\Phi}_{\textbf{SS}}\), the PSD matrix of noise \(\bf{\Phi}_{\textbf{NN}}\), and a one-hot vector that represents the reference channel \(\bf{u}\), the module computes the single-channel complex-valued spectrum of the enhanced speech \(\hat{\textbf{S}}\). The formula is defined as:

\[\hat{\textbf{S}}(f) = \textbf{w}_{\text{bf}}(f)^{\mathsf{H}} \textbf{Y}(f) \]

where \(\textbf{w}_{\text{bf}}(f)\) is the MVDR beamforming weight for the \(f\)-th frequency bin.

The beamforming weight is computed by:

\[\textbf{w}_{\text{MVDR}}(f) = \frac{{{\bf{\Phi}_{\textbf{NN}}^{-1}}(f){\bf{\Phi}_{\textbf{SS}}}}(f)} {\text{Trace}({{{\bf{\Phi}_{\textbf{NN}}^{-1}}(f) \bf{\Phi}_{\textbf{SS}}}(f))}}\bm{u} \]

Tutorials using SoudenMVDR:

Speech Enhancement with MVDR Beamforming

Speech Enhancement with MVDR Beamforming

forward(specgram: Tensor, psd_s: Tensor, psd_n: Tensor, reference_channel: Union[int, Tensor], diagonal_loading: bool = True, diag_eps: float = 1e-07, eps: float = 1e-08) → Tensor

Parameters:

• specgram (torch.Tensor) – Multi-channel complex-valued spectrum. Tensor with dimensions (…, channel, freq, time).

• psd_s (torch.Tensor) – The complex-valued power spectral density (PSD) matrix of target speech. Tensor with dimensions (…, freq, channel, channel).

• psd_n (torch.Tensor) – The complex-valued power spectral density (PSD) matrix of noise. Tensor with dimensions (…, freq, channel, channel).

• reference_channel (int or torch.Tensor) – Specifies the reference channel. If the dtype is int, it represents the reference channel index. If the dtype is torch.Tensor, its shape is (…, channel), where the channel dimension is one-hot.

• diagonal_loading (bool, optional) – If True, enables applying diagonal loading to psd_n. (Default: True)

• diag_eps (float, optional) – The coefficient multiplied to the identity matrix for diagonal loading. It is only effective when diagonal_loading is set to True. (Default: 1e-7)

• eps (float, optional) – Value to add to the denominator in the beamforming weight formula. (Default: 1e-8)

Returns:

Single-channel complex-valued enhanced spectrum with dimensions (…, freq, time).

Return type:

torch.Tensor