DFT#

DFT - 17#

Version

• name: DFT (GitHub)

• domain: main

• since_version: 17

• function: False

• support_level: SupportType.COMMON

• shape inference: True

This version of the operator has been available since version 17.

Summary

Computes the discrete Fourier transform of input.

Attributes

• axis: The axis on which to perform the DFT. By default this value is set to 1, which corresponds to the first dimension after the batch index. Default value is `1`.

• inverse: Whether to perform the inverse discrete fourier transform. By default this value is set to 0, which corresponds to false. Default value is `0`.

• onesided: If onesided is 1, only values for w in [0, 1, 2, …, floor(n_fft/2) + 1] are returned because the real-to-complex Fourier transform satisfies the conjugate symmetry, i.e., X[m, w] = X[m,w]=X[m,n_fft-w]*. Note if the input or window tensors are complex, then onesided output is not possible. Enabling onesided with real inputs performs a Real-valued fast Fourier transform (RFFT). When invoked with real or complex valued input, the default value is 0. Values can be 0 or 1. Default value is `0`.

Inputs

Between 1 and 2 inputs.

• input (heterogeneous) - T1: For real input, the following shape is expected: [batch_idx][signal_dim1][signal_dim2]…[signal_dimN][1]. For complex input, the following shape is expected: [batch_idx][signal_dim1][signal_dim2]…[signal_dimN][2]. The first dimension is the batch dimension. The following N dimentions correspond to the signal’s dimensions. The final dimension represents the real and imaginary parts of the value in that order.

• dft_length (optional, heterogeneous) - T2: The length of the signal.If greater than the axis dimension, the signal will be zero-padded up to dft_length. If less than the axis dimension, only the first dft_length values will be used as the signal. It’s an optional value.

Outputs

• output (heterogeneous) - T1: The Fourier Transform of the input vector.If onesided is 0, the following shape is expected: [batch_idx][signal_dim1][signal_dim2]…[signal_dimN][2]. If axis=0 and onesided is 1, the following shape is expected: [batch_idx][floor(signal_dim1/2)+1][signal_dim2]…[signal_dimN][2]. If axis=1 and onesided is 1, the following shape is expected: [batch_idx][signal_dim1][floor(signal_dim2/2)+1]…[signal_dimN][2]. If axis=N-1 and onesided is 1, the following shape is expected: [batch_idx][signal_dim1][signal_dim2]…[floor(signal_dimN/2)+1][2]. The signal_dim at the specified axis is equal to the dft_length.

Type Constraints

• T1 in ( tensor(bfloat16), tensor(double), tensor(float), tensor(float16) ): Constrain input and output types to float tensors.

• T2 in ( tensor(int32), tensor(int64) ): Constrain scalar length types to int64_t.

Examples

default

```node = onnx.helper.make_node("DFT", inputs=["x"], outputs=["y"], axis=1)
x = np.arange(0, 100).reshape(10, 10).astype(np.float32)
y = np.fft.fft(x, axis=0)

x = x.reshape(1, 10, 10, 1)
y = np.stack((y.real, y.imag), axis=2).astype(np.float32).reshape(1, 10, 10, 2)
expect(node, inputs=[x], outputs=[y], name="test_dft")

node = onnx.helper.make_node("DFT", inputs=["x"], outputs=["y"], axis=2)
x = np.arange(0, 100).reshape(10, 10).astype(np.float32)
y = np.fft.fft(x, axis=1)

x = x.reshape(1, 10, 10, 1)
y = np.stack((y.real, y.imag), axis=2).astype(np.float32).reshape(1, 10, 10, 2)
expect(node, inputs=[x], outputs=[y], name="test_dft_axis")

node = onnx.helper.make_node(
"DFT", inputs=["x"], outputs=["y"], inverse=1, axis=1
)
x = np.arange(0, 100, dtype=np.complex64).reshape(
10,
10,
)
y = np.fft.ifft(x, axis=0)

x = np.stack((x.real, x.imag), axis=2).astype(np.float32).reshape(1, 10, 10, 2)
y = np.stack((y.real, y.imag), axis=2).astype(np.float32).reshape(1, 10, 10, 2)
expect(node, inputs=[x], outputs=[y], name="test_dft_inverse")
```