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import torch
from torch_complex import functional as FC
from torch_complex.tensor import ComplexTensor
def get_power_spectral_density_matrix(
xs: ComplexTensor, mask: torch.Tensor, normalization=True, eps: float = 1e-15
) -> ComplexTensor:
"""Return cross-channel power spectral density (PSD) matrix
Args:
xs (ComplexTensor): (..., F, C, T)
mask (torch.Tensor): (..., F, C, T)
normalization (bool):
eps (float):
Returns
psd (ComplexTensor): (..., F, C, C)
"""
# outer product: (..., C_1, T) x (..., C_2, T) -> (..., T, C, C_2)
psd_Y = FC.einsum("...ct,...et->...tce", [xs, xs.conj()])
# Averaging mask along C: (..., C, T) -> (..., T)
mask = mask.mean(dim=-2)
# Normalized mask along T: (..., T)
if normalization:
# If assuming the tensor is padded with zero, the summation along
# the time axis is same regardless of the padding length.
mask = mask / (mask.sum(dim=-1, keepdim=True) + eps)
# psd: (..., T, C, C)
psd = psd_Y * mask[..., None, None]
# (..., T, C, C) -> (..., C, C)
psd = psd.sum(dim=-3)
return psd
def get_mvdr_vector(
psd_s: ComplexTensor,
psd_n: ComplexTensor,
reference_vector: torch.Tensor,
eps: float = 1e-15,
) -> ComplexTensor:
"""Return the MVDR(Minimum Variance Distortionless Response) vector:
h = (Npsd^-1 @ Spsd) / (Tr(Npsd^-1 @ Spsd)) @ u
Reference:
On optimal frequency-domain multichannel linear filtering
for noise reduction; M. Souden et al., 2010;
https://ieeexplore.ieee.org/document/5089420
Args:
psd_s (ComplexTensor): (..., F, C, C)
psd_n (ComplexTensor): (..., F, C, C)
reference_vector (torch.Tensor): (..., C)
eps (float):
Returns:
beamform_vector (ComplexTensor)r: (..., F, C)
"""
# Add eps
C = psd_n.size(-1)
eye = torch.eye(C, dtype=psd_n.dtype, device=psd_n.device)
shape = [1 for _ in range(psd_n.dim() - 2)] + [C, C]
eye = eye.view(*shape)
psd_n += eps * eye
# numerator: (..., C_1, C_2) x (..., C_2, C_3) -> (..., C_1, C_3)
numerator = FC.einsum("...ec,...cd->...ed", [psd_n.inverse(), psd_s])
# ws: (..., C, C) / (...,) -> (..., C, C)
ws = numerator / (FC.trace(numerator)[..., None, None] + eps)
# h: (..., F, C_1, C_2) x (..., C_2) -> (..., F, C_1)
beamform_vector = FC.einsum("...fec,...c->...fe", [ws, reference_vector])
return beamform_vector
def apply_beamforming_vector(
beamform_vector: ComplexTensor, mix: ComplexTensor
) -> ComplexTensor:
# (..., C) x (..., C, T) -> (..., T)
es = FC.einsum("...c,...ct->...t", [beamform_vector.conj(), mix])
return es
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