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Summary:
When computing the MVDR beamforming weights using the power iteration method, the PSD matrix of noise can be applied with diagonal loading to improve the robustness. This is also applicable to computing the RTF matrix (See https://github.com/espnet/espnet/blob/master/espnet2/enh/layers/beamformer.py#L614 as an example). This also aligns with current `torchaudio.transforms.MVDR` module to keep the consistency.

This PR adds the `diagonal_loading` argument with `True` as default value to `torchaudio.functional.rtf_power`.

Pull Request resolved: https://github.com/pytorch/audio/pull/2369

Reviewed By: carolineechen

Differential Revision: D36204130

Pulled By: nateanl

fbshipit-source-id: 93a58d5c2107841a16c4e32f0c16ab0d6b2d9420

Summary:
Add badges of supported properties and devices to functionals and transforms.

This commit adds `.. devices::` and `.. properties::` directives to sphinx.

APIs with these directives will have badges (based off of shields.io) which link to the
page with description of these features.

Continuation of https://github.com/pytorch/audio/issues/2316
Excluded dtypes for further improvement, and actually added badges to most of functional/transforms.

Pull Request resolved: https://github.com/pytorch/audio/pull/2321

Reviewed By: hwangjeff

Differential Revision: D35489063

Pulled By: mthrok

fbshipit-source-id: f68a70ebb22df29d5e9bd171273bd19007a81762

Summary:
This PR adds ``apply_beamforming`` method to ``torchaudio.functional``.
The method employs the beamforming weight to the multi-channel noisy spectrum to obtain the single-channel enhanced spectrum.
The input arguments are the complex-valued beamforming weight Tensor and the multi-channel noisy spectrum.

Pull Request resolved: https://github.com/pytorch/audio/pull/2232

Reviewed By: mthrok

Differential Revision: D34474561

Pulled By: nateanl

fbshipit-source-id: 2910251a8f111e65375dfb50495b6a415113f06d

Summary:
This PR adds ``rtf_power`` method to ``torchaudio.functional``.
The method computes the relative transfer function (RTF) or the steering vector by [the power iteration method](https://onlinelibrary.wiley.com/doi/abs/10.1002/zamm.19290090206).
[This paper](https://arxiv.org/pdf/2011.15003.pdf) describes the power iteration method in English.
The input arguments are the complex-valued power spectral density (PSD) matrix of the target speech, PSD matrix of noise, int or one-hot Tensor to indicate the reference channel, number of iterations, respectively.

Pull Request resolved: https://github.com/pytorch/audio/pull/2231

Reviewed By: mthrok

Differential Revision: D34474503

Pulled By: nateanl

fbshipit-source-id: 47011427ec4373f808755f0e8eff1efca57655eb

Summary:
This PR adds ``mvdr_weights_rtf`` method to ``torchaudio.functional``.
It computes the MVDR weight matrix based on the solution that applies relative transfer function (RTF). See [the paper](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.725.673&rep=rep1&type=pdf) for the reference.
The input arguments are the complex-valued RTF Tensor of the target speech, power spectral density (PSD) matrix of noise, int or one-hot Tensor to indicate the reference channel, respectively.

Pull Request resolved: https://github.com/pytorch/audio/pull/2229

Reviewed By: mthrok

Differential Revision: D34474119

Pulled By: nateanl

fbshipit-source-id: 2d6f62cd0858f29ed6e4e03c23dcc11c816204e2

Summary:
This PR adds ``mvdr_weights_souden`` method to ``torchaudio.functional``.
It computes the MVDR weight matrix based on the solution proposed by [``Souden et, al.``](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.725.673&rep=rep1&type=pdf).
The input arguments are the complex-valued power spectral density (PSD) matrix of the target speech, PSD matrix of noise, int or one-hot Tensor to indicate the reference channel, respectively.

Pull Request resolved: https://github.com/pytorch/audio/pull/2228

Reviewed By: mthrok

Differential Revision: D34474018

Pulled By: nateanl

fbshipit-source-id: 725df812f8f6e6cc81cc37e8c3cb0da2ab3b74fb

Summary:
This PR adds ``psd`` method to ``torchaudio.functional``.
It computes the power spectral density (PSD) matrix of the complex-valued spectrum.
The method also supports normalization of Time-Frequency mask.

Pull Request resolved: https://github.com/pytorch/audio/pull/2227

Reviewed By: mthrok

Differential Revision: D34473908

Pulled By: nateanl

fbshipit-source-id: c1cfc584085d77881b35d41d76d39b26fca1dda9

Summary:
In autograd tests, to guarantee the precision, the dtype of Tensors are converted to `torch.float64` if they are real. However, the complex dtype is not considered. This PR adds `self.complex_dtype` support to the inputs.

Pull Request resolved: https://github.com/pytorch/audio/pull/2244

Reviewed By: mthrok

Differential Revision: D34272998

Pulled By: nateanl

fbshipit-source-id: e8698a74d7b8d99ee0fcb5f5cb5f2ffc8c80b9b5

Summary:
Pull Request resolved: https://github.com/pytorch/audio/pull/2096

run: `arc lint --apply-patches --paths-cmd 'hg files -I "./**/*.py"'`

Reviewed By: mthrok

Differential Revision: D33297351

fbshipit-source-id: 7bf5956edf0717c5ca90219f72414ff4eeaf5aa8

* Add basic filtfilt implementation

* Add filtfilt to functional package; add tests
Co-authored-by: V G <vladislav.goncharenko@phystech.edu>

Use shorter input sequences to avoid time out error on CI