dft#

ivy.dft(x, /, *, axis=1, inverse=False, onesided=False, dft_length=None, norm='backward', out=None)[source]#

Compute the discrete Fourier transform of input.

Parameters:

  • x (Union[Array, NativeArray]) – Input volume […,d_in,…], where d_in indicates the dimension that needs FFT.

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

  • inverse (bool) – Whether to perform the inverse discrete fourier transform. (default: False) By default this value is set to False.

  • onesided (bool) – If onesided is True, only values for w in [0, 1, 2, …, floor(n_fft/2) + 1] (default: False) 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 False. Values can be True or False.

  • dft_length (Optional[Union[int, Tuple[int]]]) – The length of the signal.If greater than the axis dimension, (default: None) 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.

  • norm (str) – Optional argument, “backward”, “ortho” or “forward”. Defaults to be (default: 'backward') “backward”. “backward” indicates no normalization. “ortho” indicates normalization by 1/sqrt(n). “forward” indicates normalization by 1/n.

  • out (Optional[Array]) – Optional output array, for writing the result to. It must (default: None) have a shape that the inputs broadcast to.

Return type:

Array

Returns:

ret – The Fourier Transform of the input vector.If onesided is False, the following shape is expected: [batch_idx][signal_dim1][signal_dim2] …[signal_dimN][2]. If axis=0 and onesided is True, the following shape is expected: [batch_idx][floor(signal_dim1/2)+1][signal_dim2]…[signal_dimN][2]. If axis=1 and onesided is True, the following shape is expected: [batch_idx][signal_dim1][floor(signal_dim2/2)+1]…[signal_dimN][2]. If axis=N-1 and onesided is True, 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.

Array.dft(self, /, *, axis=1, inverse=False, onesided=False, dft_length=None, norm='backward', out=None)#

Compute the discrete Fourier transform of input.

Parameters:

  • self – Input volume […,d_in,…], where d_in indicates the dimension that needs FFT.

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

  • inverse (bool) – Whether to perform the inverse discrete fourier transform. (default: False) By default this value is set to False.

  • onesided (bool) – If onesided is True, only values for w in [0, 1, 2, …, floor(n_fft/2) + 1] (default: False) 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 False. Values can be True or False.

  • dft_length (Optional[Union[int, Tuple[int]]]) – The length of the signal.If greater than the axis dimension, (default: None) 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.

  • norm (str) – Optional argument, “backward”, “ortho” or “forward”. Defaults to be (default: 'backward') “backward”. “backward” indicates no normalization. “ortho” indicates normalization by 1/sqrt(n). “forward” indicates normalization by 1/n.

  • out (Optional[Array]) – Optional output array, for writing the result to. It must (default: None) have a shape that the inputs broadcast to.

Return type:

Array

Returns:

ret – The Fourier Transform of the input vector.If onesided is False, the following shape is expected: [batch_idx][signal_dim1][signal_dim2] …[signal_dimN][2]. If axis=0 and onesided is True, the following shape is expected: [batch_idx][floor(signal_dim1/2)+1][signal_dim2] …[signal_dimN][2]. If axis=1 and onesided is True, the following shape is expected: [batch_idx][signal_dim1] [floor(signal_dim2/2)+1] …[signal_dimN][2]. If axis=N-1 and onesided is True, 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.

Container.dft(self, /, *, axis=1, inverse=False, onesided=False, dft_length=None, norm='backward', key_chains=None, to_apply=True, prune_unapplied=False, map_sequences=False, out=None)#
Parameters:

  • axis (int) – (default: 1)

  • inverse (bool) – (default: False)

  • onesided (bool) – (default: False)

  • dft_length (Optional[Union[int, Tuple[int]]]) – (default: None)

  • norm (str) – (default: 'backward')

  • key_chains (Optional[Union[List[str], Dict[str, str]]]) – (default: None)

  • to_apply (bool) – (default: True)

  • prune_unapplied (bool) – (default: False)

  • map_sequences (bool) – (default: False)

  • out (Optional[Array]) – (default: None)

Return type:

Container