Potential Discrepancy in DOLfYN `fft_frequency` for Half Frequencies

[ssolson]

@jmcvey3 can you let me know if I am approaching this incorrectly?

Description:

Issue with Half Frequencies in fft_frequency Function I think there is potential issue in the fft_frequency function, specifically related to how the half frequencies (positive frequencies) are returned. The current implementation might be including an extra frequency bin which should not be present.

https://github.com/MHKiT-Software/MHKiT-Python/blob/2ccc286a65685e5e2f5ab68a467209917f0161d9/mhkit/dolfyn/tools/fft.py#L6-L31

Current Behavior:

The function, when called with full=False, returns np.abs(f[1:int(nfft / 2. + 1)]). This slice appears to include one frequency bin more than expected for the positive frequency range.

Expected Behavior:

I believe the correct implementation for returning half frequencies should be np.abs(f[1:int(nfft / 2.0)]), excluding the additional bin at the end.

Test Case Issue:

In my test case for this function, I encountered a size mismatch error when comparing the returned half frequencies to the expected positive frequencies. This issue arises in the line assert_allclose(freq_half, positive_freqs), where freq_half is expected to match the size and values of positive_freqs.

If the current returned value is correct could you let me know if I am slicing the positive and negative values from the full frequencies incorrectly?

def test_fft_frequency(self):
    fs = 1000  # Sampling frequency
    nfft = 512  # Number of samples in a window

    # Test for full frequency range
    freq_full = tools.fft.fft_frequency(nfft, fs, full=True)
    assert_equal(len(freq_full), nfft)

    # Check symmetry of positive and negative frequencies, ignoring the zero frequency
    positive_freqs = freq_full[1:int(nfft / 2)]
    negative_freqs = freq_full[int(nfft / 2) + 1:]
    assert_allclose(positive_freqs, -negative_freqs[::-1])

    # Test for half frequency range
    freq_half = tools.fft.fft_frequency(nfft, fs, full=False)
    assert_equal(len(freq_half), int(nfft / 2) - 1)
    assert_allclose(freq_half, positive_freqs)  # Ignore the zero frequency