def test_fft_orthogonality_noise_even_fftw(noise, fft_lib_pyfftw):
signal_spec = fft.rfft(
noise.time, noise.n_samples, noise.sampling_rate, noise.fft_norm)
transformed_signal_time = fft.irfft(
signal_spec, noise.n_samples, noise.sampling_rate, noise.fft_norm)
npt.assert_allclose(
transformed_signal_time, noise.time,
rtol=1e-10, atol=10*np.finfo(float).eps)
def test_fft_orthogonality_sine_odd_fftw(sine_odd, fft_lib_pyfftw):
signal_spec = fft.rfft(
sine_odd.time, sine_odd.n_samples, sine_odd.sampling_rate,
sine_odd.fft_norm)
transformed_signal_time = fft.irfft(
signal_spec, sine_odd.n_samples, sine_odd.sampling_rate,
sine_odd.fft_norm)
npt.assert_allclose(
transformed_signal_time, sine_odd.time,
rtol=1e-10, atol=10*np.finfo(float).eps)
def domain(self, new_domain):
"""Set the domain of the signal."""
if new_domain not in self._VALID_DOMAINS:
raise ValueError("Incorrect domain, needs to be time/freq.")
if not (self._domain == new_domain):
# Only process if we change domain
if new_domain == 'time':
# If the new domain should be time, we had a saved spectrum
# and need to do an inverse Fourier Transform
self.time = fft.irfft(self._data, self.n_samples,
self._sampling_rate, self._fft_norm)
elif new_domain == 'freq':
# If the new domain should be freq, we had sampled time data
# and need to do a Fourier Transform
self.freq = fft.rfft(self._data, self.n_samples,
self._sampling_rate, self._fft_norm)
def noise(n_samples, spectrum="white", rms=1, sampling_rate=44100, seed=None):
"""
Generate single or multi channel normally distributed white or pink noise.
The pink noise is generated by applying a sqrt(1/f) filter to the spectrum.
Parameters
----------
n_samples : int
The length of the signal in samples
spectrum : str, optional
'white' to generate noise with constant energy across frequency.
'pink' to generate noise with constant energy across filters with
constant relative bandwith.
rms : double, array like, optional
The route mean square (RMS) value of the noise signal. A multi channel
noise signal is generated if an array of RMS values is passed.
The default is 1.
sampling_rate : int, optional
The sampling rate in Hz. The default is 44100.
seed : int, None
The seed for the random generator. Pass a seed to obtain identical
results for multiple calls of white noise. The default is None, which
will yield different results with every call.
Returns
-------
signal : Signal
The noise as a Signal object. The Signal is in the time domain and
has the 'rms' FFT normalization (see pyfar.fft.normalization).
"""
# generate the noise
rms = np.atleast_1d(rms)
n_samples = int(n_samples)
cshape = np.atleast_1d(rms).shape
rng = np.random.default_rng(seed)
noise = rng.standard_normal(np.prod(cshape + (n_samples, )))
noise = noise.reshape(cshape + (n_samples, ))
if spectrum == "pink":
# apply 1/f filter in the frequency domain
noise = fft.rfft(noise, n_samples, sampling_rate, 'none')
noise /= np.sqrt(np.arange(1, noise.shape[-1] + 1))
noise = fft.irfft(noise, n_samples, sampling_rate, 'none')
elif spectrum != "white":
raise ValueError(
f"spectrum is '{spectrum}' but must be 'white' or 'pink'")
# level the noise
rms_current = np.atleast_1d(np.sqrt(np.mean(noise**2, axis=-1)))
for idx in np.ndindex(rms.shape):
noise[idx] = noise[idx] / rms_current[idx] * rms[idx]
# save to Signal
nl = "\n" # required as variable because f-strings cannot contain "\"
comment = f"{spectrum} noise signal (rms = {str(rms).replace(nl, ',')})"
signal = Signal(noise, sampling_rate, fft_norm="rms", comment=comment)
return signal
