DFT - version 17#

This page documents version 17 of operator DFT. See DFT for the latest version (since version 20).

  • Domain: ai.onnx

  • Since version: 17

Computes the discrete Fourier transform of input.

Inputs

  • input (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 dimensions correspond to the signal’s dimensions. The final dimension represents the real and imaginary parts of the value in that order.

  • dft_length (T2): The length of the signal as a scalar. 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. If not provided, the default dft_length = signal_dim_axis, except for the IRFFT case (onesided=1, inverse=1), in which case the default dft_length is 2 * (signal_dim_axis - 1). It’s an optional value.

Outputs

  • output (T1): The Fourier Transform of the input vector. For standard DFT (onesided=0), the output shape is: [batch_idx][signal_dim1][signal_dim2]…[signal_dimN][2] (complex), with signal_dim_axis = dft_length. For RFFT (onesided=1, inverse=0), the output shape is: [batch_idx][signal_dim1][signal_dim2]…[signal_dimN][2] (one-sided complex), with signal_dim_axis = floor(dft_length/2) + 1. For IRFFT (onesided=1, inverse=1), the output shape is: [batch_idx][signal_dim1][signal_dim2]…[signal_dimN][1] (real), where signal_dim_axis = dft_length.

Attributes

  • axis (int): 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. Negative value means counting dimensions from the back. Accepted range is $[-r, -2] cup [0, r-2]$ where r = rank(input). The last dimension is for representing complex numbers and thus is an invalid axis.

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

  • onesided (int): If onesided is 1, only values for w in [0, 1, 2, …, floor(n_fft/2) + 1] are used or returned because the real-to-complex Fourier transform satisfies the conjugate symmetry, i.e., X[m, w] = X[m, n_fft-w]*. When onesided=1 and inverse=0 (forward DFT), only real input is supported and a one-sided complex spectrum is returned (RFFT). When onesided=1 and inverse=1 (inverse DFT), only complex input is supported and a full real signal is returned (IRFFT). When invoked with real or complex valued input, the default value is 0. Values can be 0 or 1.

Type Constraints

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

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

Examples#

test_cc_dft_inverse_opset17

Node:
  DFT(x) -> (y)
  Attributes:
    axis = 1
    inverse = 1

Inputs:
  x: shape=(1, 4, 2), dtype=float32
    [[[1., 0.],
      [2., 0.],
      [3., 0.],
      [4., 0.]]]

Outputs:
  y: shape=(1, 4, 2), dtype=float32
    [[[ 2.5000000e+00,  0.0000000e+00],
      [-5.0000000e-01, -5.0000000e-01],
      [-5.0000000e-01,  2.4492937e-16],
      [-5.0000000e-01,  5.0000000e-01]]]

test_cc_dft_opset17

Node:
  DFT(x) -> (y)
  Attributes:
    axis = 1

Inputs:
  x: shape=(1, 4, 1), dtype=float32
    [[[1.],
      [2.],
      [3.],
      [4.]]]

Outputs:
  y: shape=(1, 4, 2), dtype=float32
    [[[ 1.000000e+01,  0.000000e+00],
      [-2.000000e+00,  2.000000e+00],
      [-2.000000e+00, -9.797175e-16],
      [-2.000000e+00, -2.000000e+00]]]
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