Stft

## Usage

```
torch_stft(
input,
n_fft,
hop_length = NULL,
win_length = NULL,
window = NULL,
center = TRUE,
pad_mode = "reflect",
normalized = FALSE,
onesided = NULL,
return_complex = NULL
)
```

## Arguments

- input
(Tensor) the input tensor

- n_fft
(int) size of Fourier transform

- hop_length
(int, optional) the distance between neighboring sliding window frames. Default:

`NULL`

(treated as equal to`floor(n_fft / 4)`

)- win_length
(int, optional) the size of window frame and STFT filter. Default:

`NULL`

(treated as equal to`n_fft`

)- window
(Tensor, optional) the optional window function. Default:

`NULL`

(treated as window of all \(1\) s)- center
(bool, optional) whether to pad

`input`

on both sides so that the \(t\)-th frame is centered at time \(t \times \mbox{hop\_length}\). Default:`TRUE`

- pad_mode
(string, optional) controls the padding method used when

`center`

is`TRUE`

. Default:`"reflect"`

- normalized
(bool, optional) controls whether to return the normalized STFT results Default:

`FALSE`

- onesided
(bool, optional) controls whether to return half of results to avoid redundancy Default:

`TRUE`

- return_complex
(bool, optional) controls whether to return complex tensors or not.

## Short-time Fourier transform (STFT).

Short-time Fourier transform (STFT).

$$
X[m, \omega] = \sum_{k = 0}^{\mbox{win\_length-1}}%
\mbox{window}[k]\ \mbox{input}[m \times \mbox{hop\_length} + k]\ %
\exp\left(- j \frac{2 \pi \cdot \omega k}{\mbox{win\_length}}\right),
$$
where \(m\) is the index of the sliding window, and \(\omega\) is
the frequency that \(0 \leq \omega < \mbox{n\_fft}\). When
`onesided`

is the default value `TRUE`

,

```
* `input` must be either a 1-D time sequence or a 2-D batch of time
sequences.
* If `hop_length` is `NULL` (default), it is treated as equal to
`floor(n_fft / 4)`.
* If `win_length` is `NULL` (default), it is treated as equal to
`n_fft`.
* `window` can be a 1-D tensor of size `win_length`, e.g., from
`torch_hann_window`. If `window` is `NULL` (default), it is
treated as if having \eqn{1} everywhere in the window. If
\eqn{\mbox{win\_length} < \mbox{n\_fft}}, `window` will be padded on
both sides to length `n_fft` before being applied.
* If `center` is `TRUE` (default), `input` will be padded on
both sides so that the \eqn{t}-th frame is centered at time
\eqn{t \times \mbox{hop\_length}}. Otherwise, the \eqn{t}-th frame
begins at time \eqn{t \times \mbox{hop\_length}}.
* `pad_mode` determines the padding method used on `input` when
`center` is `TRUE`. See `torch_nn.functional.pad` for
all available options. Default is `"reflect"`.
* If `onesided` is `TRUE` (default), only values for \eqn{\omega}
in \eqn{\left[0, 1, 2, \dots, \left\lfloor \frac{\mbox{n\_fft}}{2} \right\rfloor + 1\right]}
are returned because the real-to-complex Fourier transform satisfies the
conjugate symmetry, i.e., \eqn{X[m, \omega] = X[m, \mbox{n\_fft} - \omega]^*}.
* If `normalized` is `TRUE` (default is `FALSE`), the function
returns the normalized STFT results, i.e., multiplied by \eqn{(\mbox{frame\_length})^{-0.5}}.
Returns the real and the imaginary parts together as one tensor of size
\eqn{(* \times N \times T \times 2)}, where \eqn{*} is the optional
batch size of `input`, \eqn{N} is the number of frequencies where
STFT is applied, \eqn{T} is the total number of frames used, and each pair
in the last dimension represents a complex number as the real part and the
imaginary part.
```