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Op semantics for FFT.

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Brian Patton 2019-04-13 06:51:06 -07:00 committed by TensorFlower Gardener
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tensorflow/compiler/xla/g3doc/operation_semantics.md
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@ -1258,6 +1258,59 @@ Arguments | Type | Semantics
The function is applied to each element in the `operand` array, resulting in an The function is applied to each element in the `operand` array, resulting in an
array with the same shape. It is allowed for `operand` to be a scalar (rank 0). array with the same shape. It is allowed for `operand` to be a scalar (rank 0).
## Fft
The XLA FFT operation implements the forward and inverse Fourier Transforms for
real and complex inputs/outputs. Multidimensional FFTs on up to 3 axes are
supported, except on TPU, where only a single axis is supported (please file a
github issue if you require higher order).
See also
[`XlaBuilder::Fft`](https://www.tensorflow.org/code/tensorflow/compiler/xla/client/xla_builder.h).
| Arguments | Type | Semantics |
| ------------ | ------------------- | ------------------------ |
| `operand` | `XlaOp` | The array we are Fourier |
: : : transforming. :
| `fft_type` | `FftType` | See the table below. |
| `fft_length` | `ArraySlice<int64>` | The time-domain lengths |
: : : of the axes being :
: : : transformed. This is :
: : : needed in particular for :
: : : IRFFT to right-size the :
: : : innermost axis, since :
: : : `RFFT(fft_length=[16])` :
: : : has the same output :
: : : shape as :
: : : `RFFT(fft_length=[17])`. :
| `FftType` | Semantics |
| --------- | --------------------------------------------------------------- |
| `FFT` | Forward complex-to-complex FFT. Shape is unchanged. |
| `IFFT` | Inverse complex-to-complex FFT. Shape is unchanged. |
| `RFFT` | Forward real-to-complex FFT. Shape of the innermost axis is |
: : reduced to `fft_length[-1] // 2 + 1`, omitting the reversed :
: : conjugate part of the transformed signal beyond the Nyquist :
: : frequency. :
| `IRFFT` | Inverse real-to-complex FFT (i.e. takes complex, returns real). |
: : Shape of the innermost axis is expanded to `fft_length[-1]`, :
: : inferring the part of the transformed signal beyond the Nyquist :
: : frequency from the reverse conjugate of the `1` to :
: : `fft_length[-1] // 2 + 1` entries. :
#### Multidimensional FFT
When more than 1 `fft_length` is provided, this is equivalent to applying a
cascade of FFT operations to each of the innermost axes. Note that for the
real->complex and complex->real cases, the innermost axis transform is
(effectively) performed first (RFFT; last for IRFFT), which is why the innermost
axis is the one which changes size. Other axis transforms will then be
complex->complex.
#### Implementation details
CPU FFT is backed by Eigen's TensorFFT. GPU FFT uses cuFFT.
## Gather ## Gather
The XLA gather operation stitches together several slices (each slice at a The XLA gather operation stitches together several slices (each slice at a