Fix one-bin frequency shift in get_response (fixes #3)

[jankoslavic]

Summary

Fixes #3 — get_response(domain="f") synthesised responses using an FRF shifted by one frequency bin relative to get_FRF_matrix.

Root cause

get_response built its frequency vector as

len_freq = exc.shape[1] // 2 + 1
freq = np.arange(1, len_freq+1, 1) * (sampling_rate / exc.shape[1])  # avoid zero frequency

i.e. [1·df, 2·df, …], starting at df. But EXC = np.fft.rfft(exc) has its bins at [0, df, 2·df, …]. The response loop then multiplies matrix[..., i] (the FRF at (i+1)·df) by EXC[:, i] (the spectrum at i·df), so the synthesised transfer function is shifted up by one bin: H_used[k] == get_FRF_matrix[k+1].

Fix

Use the aligned rfft grid, which includes the 0 Hz (rigid-body / static) term, and compute the FRF at every bin — this is the previously commented-out # old line:

freq = np.fft.rfftfreq(exc.shape[1], 1/sampling_rate)

get_response now reproduces get_FRF_matrix bin-for-bin, DC included.

Verification

before:  get_FRF_matrix vs get_response FRF, full band  max|Δ| = 2.6e-3   (one-bin shift)
after :  get_FRF_matrix vs get_response FRF, full band  max|Δ| = 0.0      (0 Hz included)

• get_response(return_matrix=True) now equals get_FRF_matrix at every bin, including DC.
• domain="f" and domain="t" responses agree.
• pyLump test suite: 4 passed (test_response updated — it previously encoded the shifted grid, minus 0 Hz, in its reference).

Note on unconstrained ("free") systems at 0 Hz

Because 0 Hz is now included, get_response/get_FRF_matrix behave identically at DC — which for a free system means the impedance-inverse method (frf_method="f") raises LinAlgError there (the stiffness matrix is singular for the rigid-body mode; H(0) is theoretically infinite). The state-space method (frf_method="s") computes it fine. This matches get_FRF_matrix's existing behaviour, so the two are consistent. If you'd like the "f" method to also return something usable at 0 Hz for unconstrained systems (e.g. via a pseudo-inverse), that would be a separate change to get_FRF_matrix — happy to follow up.

Found while adding pyLump-based cross-validation tests to pyFRF.

[jankoslavic]

Superseded by #5, which contains the same reviewed fix (aligned rfftfreq grid including 0 Hz) from a clean branch.

[jankoslavic]

This does not make sense.