aspcore.fouriertransform.real_vec_to_dft_domain

aspcore.fouriertransform.real_vec_to_dft_domain(vec_real, scale=True, num_freqs_removed_low=0)

Isomorphism between a real-valued vector and a complex DFT domain vector

Note that this is not a Fourier transform, but merely a way to treat frequency domain vectors as real-valued vectors.

Parameters:

  • vec (ndarray of shape (num_freqs, ...)) – Real-valued vector, where num_freqs is the number of time-domain samples used in the DFT Should be oriented such that the first half of the first axis corresponds to the real part, and the second half corresponds to the imaginary part.

  • scale (bool, optional) – If true, it is scaled such that the inner product of the real vector and the dft vector are equal. According to the definitions in [brunnstromTimedomain2025], where the real DFT is unitary.

  • num_freqs_removed_low (int, optional) – The number of frequencies that were removed from the low end of the spectrum. Default option is 0, which corresponds to the full real DFT.

Returns:

dft_vec – Complex DFT domain vector, where num_real_freqs is the number of positive frequency bins.

Return type:

ndarray of shape (num_real_freqs, …)