torchaudio.functional.mvdr_weights_souden

torchaudio.functional.mvdr_weights_souden(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

Compute the Minimum Variance Distortionless Response (MVDR [Capon, 1969]) beamforming weights by the method proposed by Souden et, al. [Souden et al., 2009].

Given 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 method computes the MVDR beamforming weight martrix \(\textbf{w}_{\text{MVDR}}\). The formula is defined as:

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

Parameters:

• 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:

The complex-valued MVDR beamforming weight matrix with dimensions (…, freq, channel).

Return type:

torch.Tensor