The formula of DaS in paper is

```
y(k) = \sum\limits_{i=1}^M x_i(k-\Delta_i)
```

But in speechbrain the code is different

```
# Get useful dimensions
n_mics = Xs.shape[4]
# Generate unmixing coefficients
Ws_re = As[..., 0, :] / n_mics
Ws_im = -1 * As[..., 1, :] / n_mics
# Get input signal
Xs_re = Xs[..., 0, :]
Xs_im = Xs[..., 1, :]
# Applying delay and sum
Ys_re = torch.sum((Ws_re * Xs_re - Ws_im * Xs_im), dim=3, keepdim=True)
Ys_im = torch.sum((Ws_re * Xs_im + Ws_im * Xs_re), dim=3, keepdim=True)
# Assembling the result
Ys = torch.stack((Ys_re, Ys_im), 3)
```

Do you have a source of that formulas, because I donâ€™t understand how do they relate with origin?