def test_normalization_exceptions():
# Call without numpy array
with raises(ValueError):
fft.normalization(1, 1, 44100, 'rms')
# Invalid normalization
with raises(ValueError):
fft.normalization(np.array([1]), 1, 44100, 'goofy')
def test_normalization_with_window():
"""
Test if the window cancels out if applying the normalization and
inverse normalization.
"""
# test with window as list and numpy array
windows = [[1, 1, 1, 1], np.array([1, 1, 1, 1])]
fft_norms = ['unitary', 'amplitude', 'rms', 'power', 'psd']
for window in windows:
for fft_norm in fft_norms:
print(f"testing: {window}, {fft_norm}")
spec = fft.normalization(np.array([.5, 1, .5]),
4,
44100,
fft_norm,
window=window)
spec = fft.normalization(spec,
4,
44100,
fft_norm,
inverse=True,
window=window)
npt.assert_allclose(spec, np.array([.5, 1, .5]), atol=1e-15)
def test_normalization_with_window_value_error():
"""
Test if normalization throws a ValueError if the window has the
wrong length.
"""
with raises(ValueError):
# n_samples=5, and len(window)=5
fft.normalization(np.array([.5, 1, .5]),
4,
44100,
'amplitude',
window=[1, 1, 1, 1, 1])
def _arithmetic(data: tuple, domain: str, operation: Callable):
"""Apply arithmetic operations."""
# check input and obtain meta data of new signal
sampling_rate, n_samples, fft_norm, times, frequencies, audio_type = \
_assert_match_for_arithmetic(data, domain)
# apply arithmetic operation
result = _get_arithmetic_data(data[0], n_samples, domain)
for d in range(1, len(data)):
result = operation(
result, _get_arithmetic_data(data[d], n_samples, domain))
# check if to return an audio object
if audio_type == Signal:
# apply desired fft normalization
if domain == 'freq':
result = fft.normalization(result, n_samples, sampling_rate,
fft_norm)
result = Signal(
result, sampling_rate, n_samples, domain, fft_norm=fft_norm)
elif audio_type == TimeData:
result = TimeData(result, times)
elif audio_type == FrequencyData:
result = FrequencyData(result, frequencies, fft_norm)
return result
def test_normalization_none(impulse_stub):
spec_out = fft.normalization(impulse_stub.freq.copy(),
impulse_stub.n_samples,
impulse_stub.sampling_rate,
impulse_stub.fft_norm,
inverse=False)
npt.assert_allclose(spec_out,
impulse_stub.freq,
atol=10 * np.finfo(float).eps)
spec_out = fft.normalization(impulse_stub.freq.copy(),
impulse_stub.n_samples,
impulse_stub.sampling_rate,
impulse_stub.fft_norm,
inverse=True)
npt.assert_allclose(spec_out,
impulse_stub.freq,
atol=10 * np.finfo(float).eps)
def test_normalization_single_sided_multi_channel_even_samples():
# single sided test spectrum
v = 1 / 3 + 1 / 3j
vsq = v * np.abs(v)
tile = (4, 2, 1)
spec_single = np.tile(np.array([v, v, v]), tile)
# valid number of samples of time signal corresponding to spec_single
N = 4 # time signal with even number of samples
Nsq = N**2 # factor for power and psd normalization
fs = 40 # arbitrary sampling frequency for psd normalization
# expected results for even number of samples
sqrt2 = np.sqrt(2)
truth = {
'unitary': np.array([v, v * 2, v]),
'amplitude': np.array([v / N, v / N * 2, v / N]),
'rms': np.array([v / N, v / N / sqrt2 * 2, v / N]),
'power': np.array([vsq / Nsq, vsq / Nsq * 2, vsq / Nsq]),
'psd': np.array([vsq / N / fs, vsq / N / fs * 2, vsq / N / fs])
}
for normalization in truth:
print(f"Assesing normalization: '{normalization}'")
spec_out = fft.normalization(spec_single.copy(),
N,
fs,
normalization,
inverse=False)
npt.assert_allclose(spec_out,
np.tile(truth[normalization], tile),
atol=1e-15)
print(f"Assesing normalization: '{normalization}' (inverse)")
spec_out_inv = fft.normalization(spec_out,
N,
fs,
normalization,
inverse=True)
npt.assert_allclose(spec_out_inv, spec_single, atol=1e-15)
def fft_norm(self, value):
"""
The normalization for the Discrete Fourier Transform (DFT).
See :py:func:`~pyfar.dsp.fft.normalization` for more information.
"""
# check input
if value not in self._VALID_FFT_NORMS:
raise ValueError(("Invalid FFT normalization. Has to be "
f"{', '.join(self._VALID_FFT_NORMS)}, but found "
f"'{value}'"))
# apply new normalization if Signal is in frequency domain
if self._fft_norm != value and self._domain == 'freq':
# de-normalize
self._data = fft.normalization(
self._data, self._n_samples, self._sampling_rate,
self._fft_norm, inverse=True)
# normalize
self._data = fft.normalization(
self._data, self._n_samples, self._sampling_rate,
value, inverse=False)
self._fft_norm = value
def test_normalization_both_sided_single_channel():
# single sided test spectrum
v = 1 / 3 + 1 / 3j
vsq = v * np.abs(v)
spec_single = np.array([v, v, v])
# valid number of samples of time signal corresponding to spec_single
N = 3 # time signal with even number of samples
Nsq = N**2 # factor for power and psd normalization
fs = 30 # arbitrary sampling frequency for psd normalization
# expected results for even number of samples
truth = {
'unitary': np.array([v, v, v]),
'amplitude': np.array([v / N, v / N, v / N]),
'power': np.array([vsq / Nsq, vsq / Nsq, vsq / Nsq]),
'psd': np.array([vsq / N / fs, vsq / N / fs, vsq / N / fs])
}
for normalization in truth:
print(f"Assesing normalization: '{normalization}'")
spec_out = fft.normalization(spec_single.copy(),
N,
fs,
normalization,
inverse=False,
single_sided=False)
npt.assert_allclose(spec_out, truth[normalization], atol=1e-15)
print(f"Assesing normalization: '{normalization}' (inverse)")
spec_out_inv = fft.normalization(spec_out,
N,
fs,
normalization,
inverse=True,
single_sided=False)
npt.assert_allclose(spec_out_inv, spec_single, atol=1e-15)
def _get_arithmetic_data(data, n_samples, domain):
"""
Return data in desired domain without any fft normalization.
Parameters
----------
data : Signal, array like, number
Input data
n_samples :
Number of samples of data if data is a Signal (required for fft
normalization).
domain : 'time', 'freq'
Domain in which the data is returned
Returns
-------
data_out : numpy array
Data in desired domain without any fft normalization if data is a
Signal. `np.asarray(data)` otherwise.
"""
if isinstance(data, (Signal, TimeData, FrequencyData)):
# get signal in correct domain
if domain == "time":
data_out = data.time.copy()
elif domain == "freq":
data_out = data.freq.copy()
if isinstance(data, Signal):
if data.fft_norm != 'none':
# remove current fft normalization
data_out = fft.normalization(
data_out, n_samples, data.sampling_rate,
data.fft_norm, inverse=True)
else:
raise ValueError(
f"domain must be 'time' or 'freq' but found {domain}")
else:
data_out = np.asarray(data)
return data_out