Inverting signal with division operator throws error when using fft normalization

[tjueterb]

General

• pyfar version: 0.6.5
• Python version: 3.11.2
• Operating System: macOS
• Did you install pyfar via pip: yes

Description

Hi,

When using an fft normalization other than none, inverting the signal with the division operator 1 / signal throws the error:

ValueError: Either fft_norm_2 (denominator) has to be 'none' or both fft_norms must be the same, but they are none and rms.

Inverting with signal**-1 works fine.

What I Did

import pyfar as pf
signal = pf.signals.exponential_sweep_time(44100, (50, 2e4))
signal.fft_norm = 'rms'
1 / signal

{
	"name": "ValueError",
	"message": "Either fft_norm_2 (denominator) has to be 'none' or both fft_norms must be the same, but they are none and rms.",
	"stack": "---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In[4], line 4
      2 signal = pf.signals.exponential_sweep_time(44100, (50, 2e4))
      3 signal.fft_norm = 'rms'
----> 4 1 / signal

File ~/anaconda3/envs/electroacoustics/lib/python3.11/site-packages/pyfar/classes/audio.py:519, in FrequencyData.__rtruediv__(self, data)
    518 def __rtruediv__(self, data):
--> 519     return divide((data, self), 'freq')

File ~/anaconda3/envs/electroacoustics/lib/python3.11/site-packages/pyfar/classes/audio.py:1049, in divide(data, domain)
   1008 def divide(data: tuple, domain='freq'):
   1009     \"\"\"Divide pyfar audio objects, array likes, and scalars.
   1010 
   1011     Pyfar audio objects are: :py:func:`Signal`, :py:func:`TimeData`, and
   (...)
   1047     * Other combinations raise an error.
   1048    \"\"\"
-> 1049     return _arithmetic(data, domain, _divide)

File ~/anaconda3/envs/electroacoustics/lib/python3.11/site-packages/pyfar/classes/audio.py:1271, in _arithmetic(data, domain, operation, **kwargs)
   1267 division = True if operation == _divide else False
   1268 matmul = True if operation == _matrix_multiplication else False
   1269 sampling_rate, n_samples, fft_norm, times, frequencies, audio_type, \\
   1270     cshape = \\
-> 1271     _assert_match_for_arithmetic(data, domain, division, matmul)
   1273 # apply arithmetic operation
   1274 result = _get_arithmetic_data(data[0], domain, cshape, matmul, audio_type)

File ~/anaconda3/envs/electroacoustics/lib/python3.11/site-packages/pyfar/classes/audio.py:1370, in _assert_match_for_arithmetic(data, domain, division, matmul)
   1365     n_samples = d.n_samples
   1366     # if a signal comes first (n==0) its fft_norm is taken
   1367     # directly. If a signal does not come first, (n>0, e.g.
   1368     # 1/signal), the fft norm is matched
   1369     fft_norm = d.fft_norm if n == 0 else \\
-> 1370         _match_fft_norm(fft_norm, d.fft_norm, division)
   1371 elif isinstance(d, TimeData):
   1372     if domain != \"time\":

File ~/anaconda3/envs/electroacoustics/lib/python3.11/site-packages/pyfar/classes/audio.py:1579, in _match_fft_norm(fft_norm_1, fft_norm_2, division)
   1576         fft_norm_result = 'none'
   1578     else:
-> 1579         raise ValueError((\"Either fft_norm_2 (denominator) has to be \"
   1580                           \"'none' or both fft_norms must be the same, but \"
   1581                           f\"they are {fft_norm_1} and {fft_norm_2}.\"))
   1583 return fft_norm_result

ValueError: Either fft_norm_2 (denominator) has to be 'none' or both fft_norms must be the same, but they are none and rms."
}

[mberz]

That's an interesting issue. Seems like it is due to the fact that internally 1 is "cast" to a Signal with "none" normalisation.

In any case I'd recommend using the regularised spectrum inversion for the example you provided (if the example you provided is not an irrelevant toy example)

[tjueterb]

The example was just for demonstration purposes, of course I always use regularized inversion 😇