diff --git a/torchaudio/functional/functional.py b/torchaudio/functional/functional.py
index f7109c6531..2f08a4fd48 100644
--- a/torchaudio/functional/functional.py
+++ b/torchaudio/functional/functional.py
@@ -1831,34 +1831,37 @@ def mvdr_weights_souden(
 
     .. properties:: Autograd TorchScript
 
+    Given the power spectral density (PSD) matrix of target speech :math:`\bf{\Phi}_{\textbf{SS}}`,
+    the PSD matrix of noise :math:`\bf{\Phi}_{\textbf{NN}}`, and a one-hot vector that represents the
+    reference channel :math:`\bf{u}`, the method computes the MVDR beamforming weight martrix
+    :math:`\textbf{w}_{\text{MVDR}}`. The formula is defined as:
+
     .. math::
         \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}
-    where :math:`\bf{\Phi}_{\textbf{SS}}` and :math:`\bf{\Phi}_{\textbf{NN}}`
-    are the power spectral density (PSD) matrices of speech and noise, respectively.
-    :math:`\bf{u}` is a one-hot vector that represents the reference channel.
 
     Args:
-        psd_s (Tensor): The complex-valued power spectral density (PSD) matrix of target speech.
-            Tensor of dimension `(..., freq, channel, channel)`
-        psd_n (Tensor): The complex-valued power spectral density (PSD) matrix of noise.
-            Tensor of dimension `(..., freq, channel, channel)`
-        reference_channel (int or Tensor): Indicate the reference channel.
-            If the dtype is ``int``, it represent the reference channel index.
-            If the dtype is ``Tensor``, the dimension is `(..., channel)`, where the ``channel`` dimension
+        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): whether to apply diagonal loading to psd_n
+        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
-            (Default: ``1e-7``)
-        eps (float, optional): a value added to the denominator in mask normalization. (Default: ``1e-8``)
+        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:
-        Tensor: The complex-valued MVDR beamforming weight matrix of dimension (..., freq, channel).
+        torch.Tensor: The complex-valued MVDR beamforming weight matrix with dimensions `(..., freq, channel)`.
     """
     if diagonal_loading:
-        psd_n = _tik_reg(psd_n, reg=diag_eps, eps=eps)
+        psd_n = _tik_reg(psd_n, reg=diag_eps)
     numerator = torch.linalg.solve(psd_n, psd_s)  # psd_n.inv() @ psd_s
     # ws: (..., C, C) / (...,) -> (..., C, C)
     ws = numerator / (_compute_mat_trace(numerator)[..., None, None] + eps)
diff --git a/torchaudio/transforms/_transforms.py b/torchaudio/transforms/_transforms.py
index 7b91bac2d5..dbb66f93cb 100644
--- a/torchaudio/transforms/_transforms.py
+++ b/torchaudio/transforms/_transforms.py
@@ -2099,14 +2099,22 @@ class SoudenMVDR(torch.nn.Module):
 
     .. properties:: Autograd TorchScript
 
+    Given the multi-channel complex-valued spectrum :math:`\textbf{Y}`, the power spectral density (PSD) matrix
+    of target speech :math:`\bf{\Phi}_{\textbf{SS}}`, the PSD matrix of noise :math:`\bf{\Phi}_{\textbf{NN}}`, and
+    a one-hot vector that represents the reference channel :math:`\bf{u}`, the module computes the single-channel
+    complex-valued spectrum of the enhaned speech :math:`\hat{\textbf{S}}`. The formula is defined as:
+
+    .. math::
+        \hat{\textbf{S}}(f) = \textbf{w}_{\text{bf}}(f)^{\mathsf{H}} \textbf{Y}(f)
+
+    where :math:`\textbf{w}_{\text{bf}}(f)` is the MVDR beamforming weight for the :math:`f`-th frequency bin.
+
+    The beamforming weight is computed by:
+
     .. math::
         \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}
-
-    where :math:`\bf{\Phi}_{\textbf{SS}}` and :math:`\bf{\Phi}_{\textbf{NN}}`
-    are the power spectral density (PSD) matrices of speech and noise, respectively.
-    :math:`\bf{u}` is a one-hot vector that represents the reference channel.
     """
 
     def forward(
@@ -2118,28 +2126,28 @@ def forward(
         diagonal_loading: bool = True,
         diag_eps: float = 1e-7,
         eps: float = 1e-8,
-    ) -> Tensor:
+    ) -> torch.Tensor:
         """
         Args:
-            specgram (Tensor): Multi-channel complex-valued spectrum.
-                Tensor of dimension `(..., channel, freq, time)`
-            psd_s (Tensor): The complex-valued power spectral density (PSD) matrix of target speech.
-                Tensor of dimension `(..., freq, channel, channel)`
-            psd_n (Tensor): The complex-valued power spectral density (PSD) matrix of noise.
-                Tensor of dimension `(..., freq, channel, channel)`
-            reference_channel (int or Tensor): Indicate the reference channel.
-                If the dtype is ``int``, it represent the reference channel index.
-                If the dtype is ``Tensor``, the dimension is `(..., channel)`, where the ``channel`` dimension
+            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): whether to apply diagonal loading to psd_n
+            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
-                (Default: ``1e-7``)
-            eps (float, optional): a value added to the denominator in the beamforming weight computation.
+            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:
-            Tensor: Single-channel complex-valued enhanced spectrum of dimension (..., freq, time).
+            torch.Tensor: Single-channel complex-valued enhanced spectrum with dimensions `(..., freq, time)`.
         """
         w_mvdr = F.mvdr_weights_souden(psd_s, psd_n, reference_channel, diagonal_loading, diag_eps, eps)
         spectrum_enhanced = F.apply_beamforming(w_mvdr, specgram)