add deconv fuction to pyfar/dsp/dsp

[al-de]

This code implements a function named 'deconv' in the DSP module of pyfar.
It returns the deconvolution of a measurement signal and an excitation signal and makes use of the regularized spectrum inversion.
It can be used to calculate an impulse response for example from two sweeps recorded before and after passing a device under test.

[f-brinkmann]

This already looks good to me. Most comments are regarding code style and documentation only.
After @mberz gave feedback we could think about testing.

[f-brinkmann]

• Can be shorter by directly using excitation.time = np.concatenate(...).
• Does this work for multichannel signals or do we need np.zeros(excitation.cshape + (exc.n_samples - meas.n_samples, )) for that?

[al-de]

1. That's a good point, I implemented the shorter version in my latest commit.
2. At the moment I think this code would only work for single channel signals, I will use your suggestion to make it work for multichannel signals, too. Thank you. :)

[f-brinkmann]

see above :)

[al-de]

check

[f-brinkmann]

This will reference the signal class in the Sphinx documentation :)

Suggested change

	pyfar.Signal
	signal : Signal

You should as well replace pyfar.Signal with Signal above...

[al-de]

check

[f-brinkmann]

I think this could also be omitted. In case the user needs frequency data, we save two FFTs without this line.

Suggested change

result.domain = 'time'

[al-de]

check

[f-brinkmann]

What would be the best name for this?

• devonv
• deconvolution
• spectral_deconvolution

[f-brinkmann]

This comment is a bit picky - I think the one line docstring guideline is to start with a verb :)

Suggested change

	"""Function to calculate the deconvolution of two signals.
	"""Calculate transfer functions by spectral deconvolution of two signals.

[al-de]

check. :)

[f-brinkmann]

We could add information to make things really obvious for novices:

The transfer function :math:`H(\\omega)` is calculated by spectral
deconvolution (spectral division)

.. math::
   \\H(\\omega) = \\frac{Y(\\omega)}{X(\\omega)}, 

where :math:`X(\\omega)` is the excitation signal and :math:`Y(\\omega)`
the measured signal. Regulated inversion is used to avoid numerical issues
in calculating :math:`\\hat{X(\\omega)} = 1/X(\\omega)` for small values of
:math:`X(\\omega)` (see :py:func:`pyfar.dsp.regulated_spectrum_inversion`).
The transfer function is thus calculated as

.. mat::
    \\H(\\omega) = Y(\\omega)\\hat{X(\\omega)}.

For more information, refer to [#]_

and add below

References
-----------
.. [#] S. Mueller and P. Masserani "Transfer function measurement with sweeps. Directors cut.
       J. Audio Eng. Soc. 49(6):443-471, (2001, June).

[al-de]

Thank you for that suggestion, I added this with my latest commit.

[f-brinkmann]

Mention that you set the fft_norm to 'none'

[al-de]

check

[f-brinkmann]

I like the idea with the comment, but would suggest the following to make it a bit more obvious:

result.comment = "Calculated with pyfar.dsp.deconv."
if measurement.comment != 'none':
    result.comment += f" Measured signal: {measurement.comment}."
if excitation.comment != 'none':
    result.comment += f" Excitation signal: {excitation.comment}."

[al-de]

Good idea, this looks much cleaner than in my draft.

[f-brinkmann]

You should add that measurement is zero padded if it is shorter than excitation. (And add the opposite below to excitation)

[al-de]

check