"""
The following documents the audio classes and arithmethic operations for
audio data. More details and background is given in the concepts (
:py:mod:`audio classes <pyfar._concepts.audio_classes>`,
:py:mod:`Fourier transform <pyfar._concepts.fft>`,
:py:mod:`arithmetic operations <pyfar._concepts.arithmetic_operations>`).
"""
from copy import deepcopy
import warnings
import deepdiff
import numpy as np
import pyfar.dsp.fft as fft
from typing import Callable
from .warnings import PyfarDeprecationWarning
class _Audio():
"""Abstract class for audio objects.
This class holds all the methods and properties that are common to its
three sub-classes :py:func:`TimeData`, :py:func:`FrequencyData`, and
:py:func:`Signal`.
"""
# indicate use of _Audio arithmetic operations for overloaded operators
# (e.g. __rmul__)
__array_priority__ = 1.0
def __init__(self, domain, comment=""):
# initialize valid parameter spaces
self._VALID_DOMAINS = ["time", "freq"]
# initialize global parameters
self.comment = comment
if domain in self._VALID_DOMAINS:
self._domain = domain
else:
raise ValueError("Incorrect domain, needs to be time/freq.")
def __eq__(self, other):
"""Check for equality of two objects."""
return not deepdiff.DeepDiff(self.__dict__, other.__dict__)
@property
def domain(self):
"""The domain the data is stored in."""
return self._domain
@property
def cshape(self):
"""
Return channel shape.
The channel shape gives the shape of the audio data excluding the last
dimension, which is `n_samples` for time domain objects and
`n_bins` for frequency domain objects.
"""
return self._data.shape[:-1]
def reshape(self, newshape):
"""
Return reshaped copy of the audio object.
Parameters
----------
newshape : int, tuple
new `cshape` of the audio object. One entry of newshape dimension
can be ``-1``. In this case, the value is inferred from the
remaining dimensions.
Returns
-------
reshaped : Signal, FrequencyData, TimeData
reshaped copy of the audio object.
Notes
-----
The number of samples and frequency bins always remains the same.
"""
# check input
if not isinstance(newshape, int) and not isinstance(newshape, tuple):
raise ValueError("newshape must be an integer or tuple")
if isinstance(newshape, int):
newshape = (newshape, )
# reshape
reshaped = deepcopy(self)
length_last_dimension = reshaped._data.shape[-1]
try:
reshaped._data = reshaped._data.reshape(
newshape + (length_last_dimension, ))
except ValueError:
if np.prod(newshape) != np.prod(self.cshape):
raise ValueError((f"Can not reshape audio object of cshape "
f"{self.cshape} to {newshape}"))
return reshaped
def flatten(self):
"""Return flattened copy of the audio object.
Returns
-------
flat : Signal, FrequencyData, TimeData
Flattened copy of audio object with
``flat.cshape = np.prod(audio.cshape)``
Notes
-----
The number of samples and frequency bins always remains the same, e.g.,
an audio object of ``cshape=(4,3)`` and ``n_samples=512`` will have
``cshape=(12, )`` and ``n_samples=512`` after flattening.
"""
newshape = int(np.prod(self.cshape))
return self.reshape(newshape)
@property
def comment(self):
"""Get comment."""
return self._comment
@comment.setter
def comment(self, value):
"""Set comment."""
if not isinstance(value, str):
raise TypeError("comment has to be of type string.")
else:
self._comment = value
def copy(self):
"""Return a copy of the audio object."""
return deepcopy(self)
def _return_item(self):
raise NotImplementedError("To be implemented by derived classes.")
def _assert_matching_meta_data(self):
raise NotImplementedError("To be implemented by derived classes.")
def _encode(self):
"""Return dictionary for the encoding."""
class_dict = self.copy().__dict__
return class_dict
def _decode(self):
"""Return dictionary for the encoding."""
raise NotImplementedError("To be implemented by derived classes.")
def __getitem__(self, key):
"""
Get copied slice of the audio object at key.
Examples
--------
Get the first channel of a multi channel audio object
>>> import pyfar as pf
>>> signal = pf.signals.noise(10, rms=[1, 1])
>>> first_channel = signal[0]
"""
data = self._data[key]
return self._return_item(data)
def __setitem__(self, key, value):
"""
Set channels of audio object at key.
Examples
--------
Set the first channel of a multi channel audio object
>>> import pyfar as pf
>>> signal = pf.signals.noise(10, rms=[1, 1])
>>> signal[0] = pf.signals.noise(10, rms=2)
"""
self._assert_matching_meta_data(value)
self._data[key] = value._data
[docs]
class TimeData(_Audio):
"""Class for time data.
Objects of this class contain time data which is not directly convertible
to frequency domain, i.e., non-equidistant samples.
"""
[docs]
def __init__(self, data, times, comment=""):
"""Create TimeData object with data, and times.
Parameters
----------
data : array, double
Raw data in the time domain. The memory layout of data is 'C'.
E.g. data of ``shape = (3, 2, 1024)`` has 3 x 2 channels with
1024 samples each. The data can be ``int`` or ``float`` and is
converted to ``float`` in any case.
times : array, double
Times in seconds at which the data is sampled. The number of times
must match the `size` of the last dimension of `data`.
comment : str
A comment related to `data`. The default is ``''``, which
initializes an empty string.
"""
_Audio.__init__(self, 'time', comment)
self.time = data
self._times = np.atleast_1d(np.asarray(times).flatten())
if self._times.size != self.n_samples:
raise ValueError(
"The length of times must be data.shape[-1]")
if np.any(np.diff(self._times) <= 0) and len(self._times) > 1:
raise ValueError("Times must be monotonously increasing.")
@property
def time(self):
"""Return the data in the time domain."""
return self._data
@time.setter
def time(self, value):
"""Set the time data."""
# check and set the data and meta data
data = np.atleast_2d(np.asarray(value))
if data.dtype.kind == "i":
data = data.astype("float")
elif data.dtype.kind != "f":
raise ValueError(
f"time data is {data.dtype} must be int or float")
data = np.atleast_2d(np.asarray(value, dtype=float))
self._data = data
self._n_samples = data.shape[-1]
# setting the domain is only required for Signal. Setting it here
# avoids the need for overloading the setter and does not harm TimeData
self._domain = 'time'
@property
def n_samples(self):
"""The number of samples."""
return self._n_samples
@property
def signal_length(self):
"""The length of the data in seconds."""
return self.times[-1]
@property
def times(self):
"""Time in seconds at which the signal is sampled."""
return self._times
[docs]
def find_nearest_time(self, value):
"""Return the index that is closest to the query time.
Parameters
----------
value : float, array-like
The times for which the indices are to be returned
Returns
-------
indices : int, array-like
The index for the given time instance. If the input was an array
like, a numpy array of indices is returned.
"""
times = np.atleast_1d(value)
indices = np.zeros_like(times).astype(int)
for idx, time in enumerate(times):
indices[idx] = np.argmin(np.abs(self.times - time))
return np.squeeze(indices)
def _assert_matching_meta_data(self, other):
"""
Check if the meta data matches across two :py:func:`TimeData` objects.
"""
if other.__class__ != TimeData:
raise ValueError("Comparison only valid against TimeData objects.")
if self.n_samples != other.n_samples:
raise ValueError("The number of samples does not match.")
def _return_item(self, data):
"""Return new :py:func:`TimeData` object with data."""
item = TimeData(
data, times=self.times, comment=self.comment)
return item
def __repr__(self):
"""String representation of TimeData class."""
repr_string = (
f"TimeData:\n"
f"{self.cshape} channels with {self.n_samples} samples")
return repr_string
@classmethod
def _decode(cls, obj_dict):
"""Decode object based on its respective `_encode` counterpart."""
obj = cls(
obj_dict['_data'],
obj_dict['_times'],
obj_dict['_comment'])
obj.__dict__.update(obj_dict)
return obj
def __add__(self, data):
return add((self, data), 'time')
def __radd__(self, data):
return add((data, self), 'time')
def __sub__(self, data):
return subtract((self, data), 'time')
def __rsub__(self, data):
return subtract((data, self), 'time')
def __mul__(self, data):
return multiply((self, data), 'time')
def __rmul__(self, data):
return multiply((data, self), 'time')
def __truediv__(self, data):
return divide((self, data), 'time')
def __rtruediv__(self, data):
return divide((data, self), 'time')
def __pow__(self, data):
return power((self, data), 'time')
def __rpow__(self, data):
return power((data, self), 'time')
def __matmul__(self, data):
return matrix_multiplication(
(self, data), 'time')
def __rmatmul__(self, data):
return matrix_multiplication(
(data, self), 'time')
[docs]
class FrequencyData(_Audio):
"""Class for frequency data.
Objects of this class contain frequency data which is not directly
convertible to the time domain, i.e., non-equidistantly spaced bins or
incomplete spectra.
"""
[docs]
def __init__(self, data, frequencies, comment=""):
"""Create FrequencyData with data, and frequencies.
Parameters
----------
data : array, double
Raw data in the frequency domain. The memory layout of Data is 'C'.
E.g. data of ``shape = (3, 2, 1024)`` has 3 x 2 channels with 1024
frequency bins each. Data can be ``int``, ``float`` or ``complex``.
Data of type ``int`` is converted to ``float``.
frequencies : array, double
Frequencies of the data in Hz. The number of frequencies must match
the size of the last dimension of data.
comment : str, optional
A comment related to the data. The default is ``""``, which
initializes an empty string.
Notes
-----
FrequencyData objects do not support an FFT norm, because this requires
knowledge about the sampling rate or the number of samples of the time
signal [#]_.
References
----------
.. [#] J. Ahrens, C. Andersson, P. Höstmad, and W. Kropp, “Tutorial on
Scaling of the Discrete Fourier Transform and the Implied
Physical Units of the Spectra of Time-Discrete Signals,” Vienna,
Austria, May 2020, p. e-Brief 600.
"""
_Audio.__init__(self, 'freq', comment)
# init
freqs = np.atleast_1d(np.asarray(frequencies).flatten())
self._frequencies = freqs
self.freq = data
# check frequencies
if np.any(np.diff(freqs) <= 0) and len(frequencies) > 1:
raise ValueError("Frequencies must be monotonously increasing.")
if len(freqs) != self.n_bins:
raise ValueError(
"Number of frequencies does not match number of data points")
@property
def freq(self):
"""Return the data in the frequency domain."""
return self._data
@freq.setter
def freq(self, value):
"""Set the frequency data."""
# check data type
data = np.atleast_2d(np.asarray(value))
if data.dtype.kind == "i":
data = data.astype("float")
elif data.dtype.kind not in ["f", "c"]:
raise ValueError((f"frequency data is {data.dtype} must be int, "
"float, or complex"))
# match shape of frequencies
if self.frequencies.size != data.shape[-1]:
raise ValueError(
"Number of frequency values does not match the number of"
"frequencies.")
self._data = data
@property
def frequencies(self):
"""Frequencies of the discrete signal spectrum."""
return self._frequencies
@property
def n_bins(self):
"""Number of frequency bins."""
return self._data.shape[-1]
[docs]
def find_nearest_frequency(self, value):
"""Return the index that is closest to the query frequency.
Parameters
----------
value : float, array-like
The frequencies for which the indices are to be returned
Returns
-------
indices : int, array-like
The index for the given frequency. If the input was an array like,
a numpy array of indices is returned.
"""
freqs = np.atleast_1d(value)
indices = np.zeros_like(freqs).astype(int)
for idx, freq in enumerate(freqs):
indices[idx] = np.argmin(np.abs(self.frequencies - freq))
return np.squeeze(indices)
def _assert_matching_meta_data(self, other):
"""Check if the meta data matches across two FrequencyData objects."""
if other.__class__ != FrequencyData:
raise ValueError(
"Comparison only valid against FrequencyData objects.")
if self.n_bins != other.n_bins:
raise ValueError(
"The number of frequency bins does not match.")
def _return_item(self, data):
"""Return new FrequencyData object with data."""
item = FrequencyData(
data, frequencies=self.frequencies,
comment=self.comment)
return item
def __repr__(self):
"""String representation of FrequencyData class."""
repr_string = (
f"FrequencyData:\n"
f"{self.cshape} channels with {self.n_bins} frequencies\n")
return repr_string
@classmethod
def _decode(cls, obj_dict):
"""Decode object based on its respective `_encode` counterpart."""
obj = cls(
obj_dict['_data'],
obj_dict['_frequencies'],
obj_dict['_comment'])
obj.__dict__.update(obj_dict)
return obj
def __add__(self, data):
return add((self, data), 'freq')
def __radd__(self, data):
return add((data, self), 'freq')
def __sub__(self, data):
return subtract((self, data), 'freq')
def __rsub__(self, data):
return subtract((data, self), 'freq')
def __mul__(self, data):
return multiply((self, data), 'freq')
def __rmul__(self, data):
return multiply((data, self), 'freq')
def __truediv__(self, data):
return divide((self, data), 'freq')
def __rtruediv__(self, data):
return divide((data, self), 'freq')
def __pow__(self, data):
return power((self, data), 'freq')
def __rpow__(self, data):
return power((data, self), 'freq')
def __matmul__(self, data):
return matrix_multiplication(
(self, data), 'freq')
def __rmatmul__(self, data):
return matrix_multiplication(
(data, self), 'freq')
[docs]
class Signal(FrequencyData, TimeData):
"""Class for audio signals.
Objects of this class contain data which is directly convertible between
time and frequency domain (equally spaced samples and frequency bins). The
data is always real valued in the time domain and complex valued in the
frequency domain.
"""
[docs]
def __init__(
self,
data,
sampling_rate,
n_samples=None,
domain='time',
fft_norm='none',
comment=""):
"""Create Signal with data, and sampling rate.
Parameters
----------
data : ndarray, double
Raw data of the signal in the time or frequency domain. The memory
layout of data is 'C'. E.g. data of ``shape = (3, 2, 1024)`` has
3 x 2 channels with 1024 samples or frequency bins each. Time data
is converted to ``float``. Frequency is converted to ``complex``
and must be provided as single sided spectra, i.e., for all
frequencies between 0 Hz and half the sampling rate.
sampling_rate : double
Sampling rate in Hz
n_samples : int, optional
Number of samples of the time signal. Required if domain is
``'freq'``. The default is ``None``, which assumes an even number
of samples if the data is provided in the frequency domain.
domain : ``'time'``, ``'freq'``, optional
Domain of data. The default is ``'time'``
fft_norm : str, optional
The normalization of the Discrete Fourier Transform (DFT). Can be
``'none'``, ``'unitary'``, ``'amplitude'``, ``'rms'``, ``'power'``,
or ``'psd'``. See :py:func:`~pyfar.dsp.fft.normalization` and [#]_
for more information. The default is ``'none'``, which is typically
used for energy signals, such as impulse responses.
comment : str
A comment related to `data`. The default is ``""``, which
initializes an empty string.
References
----------
.. [#] J. Ahrens, C. Andersson, P. Höstmad, and W. Kropp, “Tutorial on
Scaling of the Discrete Fourier Transform and the Implied
Physical Units of the Spectra of Time-Discrete Signals,” Vienna,
Austria, May 2020, p. e-Brief 600.
"""
# initialize signal specific parameters
self._sampling_rate = sampling_rate
self._VALID_FFT_NORMS = [
"none", "unitary", "amplitude", "rms", "power", "psd"]
# check fft norm
if fft_norm in self._VALID_FFT_NORMS:
self._fft_norm = fft_norm
else:
raise ValueError(("Invalid FFT normalization. Has to be "
f"{', '.join(self._VALID_FFT_NORMS)}, but "
f"found '{fft_norm}'"))
# time / normalized frequency data (depending on domain)
data = np.atleast_2d(data)
# initialize domain specific parameters
if domain == 'time':
self._n_samples = data.shape[-1]
times = np.atleast_1d(
np.arange(0, self._n_samples) / sampling_rate)
TimeData.__init__(self, data, times, comment)
elif domain == 'freq':
# check and set n_samples
if n_samples is None:
n_samples = max(1, (data.shape[-1] - 1)*2)
warnings.warn(
f"Number of samples not given, assuming {n_samples} "
f"samples from {data.shape[-1]} frequency bins.")
elif n_samples > 2 * data.shape[-1] - 1:
raise ValueError(("n_samples can not be larger than "
"2 * data.shape[-1] - 2"))
self._n_samples = n_samples
# Init remaining parameters
FrequencyData.__init__(self, data, self.frequencies, comment)
delattr(self, '_frequencies')
else:
raise ValueError("Invalid domain. Has to be 'time' or 'freq'.")
@TimeData.time.getter
def time(self):
"""Return the data in the time domain."""
# converts the data from 'freq' to 'time'
self.domain = 'time'
return super().time
@FrequencyData.freq.getter
def freq(self):
"""Return the normalized frequency domain data.
The normalized data is usually used for inspecting the data, e.g.,
using plots or when extracting information such as the amplitude of
harmonic components. Most processing operations, e.g., frequency
domain convolution, require the non-normalized data stored as
``freq_raw``.
"""
data = fft.normalization(
self.freq_raw, self.n_samples, self.sampling_rate,
self.fft_norm, inverse=False)
return data
@freq.setter
def freq(self, value):
"""Set the normalized frequency domain data."""
self._freq(value, raw=False)
@property
def freq_raw(self):
"""Return the frequency domain data without normalization.
Most processing operations, e.g., frequency
domain convolution, require the non-normalized data.
The normalized data stored as ``freq`` is usually used for inspecting
the data, e.g., using plots or when extracting information such as the
amplitude of harmonic components.
"""
self.domain = 'freq'
return self._data
@freq_raw.setter
def freq_raw(self, value):
"""Set the frequency domain data without normalization."""
self._freq(value, raw=True)
def _freq(self, value, raw):
"""Set the frequency domain data."""
# check data type
data = np.atleast_2d(np.asarray(value))
if data.dtype.kind not in ["i", "f", "c"]:
raise ValueError((f"frequency data is {data.dtype} must be int, "
"float, or complex"))
# Check n_samples
if data.shape[-1] != self.n_bins:
self._n_samples = max(1, (data.shape[-1] - 1)*2)
warnings.warn(
f"Number of samples not given, assuming {self.n_samples} "
f"samples from {data.shape[-1]} frequency bins.")
# set domain
self._domain = 'freq'
if not raw:
# remove normalization
data = fft.normalization(
data, self._n_samples, self._sampling_rate,
self._fft_norm, inverse=True)
self._data = data.astype(complex)
@_Audio.domain.setter
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 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
# (without normalization)
# and need to do an inverse Fourier Transform
self._data = fft.irfft(
self._data, self.n_samples, self._sampling_rate,
fft_norm='none')
elif new_domain == 'freq':
# If the new domain should be freq, we had sampled time data
# and need to do a Fourier Transform (without normalization)
self._data = fft.rfft(
self._data, self.n_samples, self._sampling_rate,
fft_norm='none')
self._domain = new_domain
@property
def sampling_rate(self):
"""The sampling rate of the signal."""
return self._sampling_rate
@sampling_rate.setter
def sampling_rate(self, value):
self._sampling_rate = value
@property
def times(self):
"""Time instances the signal is sampled at."""
return np.atleast_1d(np.arange(0, self.n_samples) / self.sampling_rate)
@property
def frequencies(self):
"""Frequencies of the discrete signal spectrum."""
return np.atleast_1d(fft.rfftfreq(self.n_samples, self.sampling_rate))
@property
def n_bins(self):
"""Number of frequency bins."""
return fft._n_bins(self.n_samples)
@property
def fft_norm(self):
"""
The normalization for the Discrete Fourier Transform (DFT).
See :py:func:`~pyfar.dsp.fft.normalization` and
:py:mod:`FFT concepts <pyfar._concepts.fft>` for more information.
"""
return self._fft_norm
@fft_norm.setter
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}'"))
self._fft_norm = value
def _assert_matching_meta_data(self, other):
"""Check if the meta data matches across two Signal objects."""
if not isinstance(other, Signal):
raise ValueError("Comparison only valid against Signal objects.")
if self.sampling_rate != other.sampling_rate:
raise ValueError("The sampling rates do not match.")
if self.n_samples != other.n_samples:
raise ValueError("The number of samples does not match.")
if self.fft_norm != other.fft_norm:
raise ValueError("The FFT norms do not match.")
def _return_item(self, data):
"""Return new Signal object with data."""
item = Signal(data, sampling_rate=self.sampling_rate,
n_samples=self.n_samples, domain=self.domain,
fft_norm=self.fft_norm, comment=self.comment)
return item
def _encode(self):
"""Return dictionary for the encoding."""
selfcopy = self.copy()
selfcopy.domain = "time"
class_dict = selfcopy.__dict__
return class_dict
@classmethod
def _decode(cls, obj_dict):
"""Decode object based on its respective `_encode` counterpart."""
obj = cls(
obj_dict['_data'],
obj_dict['_sampling_rate'],
obj_dict['_n_samples'])
obj.__dict__.update(obj_dict)
return obj
@property
def signal_type(self):
"""
The signal type is ``'energy'`` if the ``fft_norm = None`` and
``'power'`` otherwise.
"""
stype = 'energy' if self.fft_norm == 'none' else 'power'
return stype
def __repr__(self):
"""String representation of Signal class."""
repr_string = (
f"{self.domain} domain {self.signal_type} Signal:\n"
f"{self.cshape} channels with {self.n_samples} samples @ "
f"{self._sampling_rate} Hz sampling rate and {self.fft_norm} "
"FFT normalization\n")
return repr_string
def __len__(self):
"""Length of the object which is the number of samples stored.
"""
warnings.warn(
("len(Signal) will be deprecated in pyfar 0.8.0 "
"Use Signal.n_samples instead"), PyfarDeprecationWarning)
return self.n_samples
[docs]
def __iter__(self):
"""Iterator for :py:func:`Signal` objects.
Iterate across the first dimension of a :py:func:`Signal`. The actual
iteration is handled through numpy's array iteration.
Examples
--------
Iterate channels of a :py:func:`Signal`
>>> import pyfar as pf
>>> signal = pf.signals.impulse(2, amplitude=[1, 1, 1])
>>> for idx, channel in enumerate(signal):
>>> channel.time *= idx
>>> signal[idx] = channel
"""
return _SignalIterator(self._data.__iter__(), self)
class _SignalIterator(object):
"""Iterator for :py:func:`Signal`
"""
def __init__(self, array_iterator, signal):
self._array_iterator = array_iterator
self._signal = signal
self._iterated_sig = Signal(
signal._data[..., 0, :],
sampling_rate=signal.sampling_rate,
n_samples=signal.n_samples,
domain=signal.domain,
fft_norm=signal.fft_norm)
def __next__(self):
if self._signal.domain == self._iterated_sig.domain:
data = self._array_iterator.__next__()
self._iterated_sig._data = np.atleast_2d(data)
else:
raise RuntimeError("domain changes during iterations break stuff!")
return self._iterated_sig
[docs]
def add(data: tuple, domain='freq'):
"""Add pyfar audio objects, array likes, and scalars.
Pyfar audio objects are: :py:func:`Signal`, :py:func:`TimeData`, and
:py:func:`FrequencyData`.
Parameters
----------
data : tuple of the form ``(data_1, data_2, ..., data_N)``
Data to be added. Can contain pyfar audio objects, array likes, and
scalars. Pyfar audio objects can not be mixed, e.g.,
:py:func:`TimeData` and :py:func:`FrequencyData` objects do not work
together. See below or
:py:mod:`arithmetic operations <pyfar._concepts.arithmetic_operations>`
for possible combinations of Signal FFT normalizations.
domain : ``'time'``, ``'freq'``, optional
Flag to indicate if the operation should be performed in the time or
frequency domain. Frequency domain operations work on the raw
spectrum (see :py:func:`pyfar.dsp.fft.normalization`). The default is
``'freq'``.
Returns
-------
results : Signal, TimeData, FrequencyData, numpy array
Result of the operation as numpy array, if `data` contains only array
likes and numbers. Result as pyfar audio object if `data` contains an
audio object.
Notes
-----
The shape of arrays included in data need to match or be broadcastable
into the ``cshape`` of the resulting audio object.
The `fft_norm` of the result is as follows
* If one signal has the FFT normalization ``'none'``, the results gets
the normalization of the other signal.
* If both signals have the same FFT normalization, the results gets the
same normalization.
* Other combinations raise an error.
"""
return _arithmetic(data, domain, _add)
[docs]
def subtract(data: tuple, domain='freq'):
"""Subtract pyfar audio objects, array likes, and scalars.
Pyfar audio objects are: :py:func:`Signal`, :py:func:`TimeData`, and
:py:func:`FrequencyData`.
Parameters
----------
data : tuple of the form (data_1, data_2, ..., data_N)
Data to be subtracted. Can contain pyfar audio objects, array likes,
and scalars. Pyfar audio objects can not be mixed, e.g.,
:py:func:`TimeData` and :py:func:`FrequencyData` objects do not work
together. See below or
:py:mod:`arithmetic operations <pyfar._concepts.arithmetic_operations>`
for possible combinations of Signal FFT normalizations.
domain : ``'time'``, ``'freq'``, optional
Flag to indicate if the operation should be performed in the time or
frequency domain. Frequency domain operations work on the raw
spectrum (See :py:func:`pyfar.dsp.fft.normalization`). The default is
``'freq'``.
Returns
-------
results : Signal, TimeData, FrequencyData, numpy array
Result of the operation as numpy array, if `data` contains only array
likes and numbers. Result as pyfar audio object if `data` contains an
audio object.
Notes
-----
The shape of arrays included in data need to match or be broadcastable
into the ``cshape`` of the resulting audio object.
The `fft_norm` of the result is as follows
* If one signal has the FFT normalization ``'none'``, the results gets
the normalization of the other signal.
* If both signals have the same FFT normalization, the results gets the
same normalization.
* Other combinations raise an error.
"""
return _arithmetic(data, domain, _subtract)
[docs]
def multiply(data: tuple, domain='freq'):
"""Multiply pyfar audio objects, array likes, and scalars.
Pyfar audio objects are: :py:func:`Signal`, :py:func:`TimeData`, and
:py:func:`FrequencyData`.
Parameters
----------
data : tuple of the form (data_1, data_2, ..., data_N)
Data to be multiplied. Can contain pyfar audio objects, array likes,
and scalars. Pyfar audio objects can not be mixed, e.g.,
:py:func:`TimeData` and :py:func:`FrequencyData` objects do not work
together. See below or
:py:mod:`arithmetic operations <pyfar._concepts.arithmetic_operations>`
for possible combinations of Signal FFT normalizations.
domain : ``'time'``, ``'freq'``, optional
Flag to indicate if the operation should be performed in the time or
frequency domain. Frequency domain operations work on the raw
spectrum (See :py:func:`pyfar.dsp.fft.normalization`). The default is
``'freq'``.
Returns
-------
results : Signal, TimeData, FrequencyData, numpy array
Result of the operation as numpy array, if `data` contains only array
likes and numbers. Result as pyfar audio object if `data` contains an
audio object.
Notes
-----
The shape of arrays included in data need to match or be broadcastable
into the ``cshape`` of the resulting audio object.
The `fft_norm` of the result is as follows
* If one signal has the FFT normalization ``'none'``, the results gets
the normalization of the other signal.
* If both signals have the same FFT normalization, the results gets the
same normalization.
* Other combinations raise an error.
"""
return _arithmetic(data, domain, _multiply)
[docs]
def divide(data: tuple, domain='freq'):
"""Divide pyfar audio objects, array likes, and scalars.
Pyfar audio objects are: :py:func:`Signal`, :py:func:`TimeData`, and
:py:func:`FrequencyData`.
Parameters
----------
data : tuple of the form (data_1, data_2, ..., data_N)
Data to be divided. Can contain pyfar audio objects, array likes, and
scalars. Pyfar audio objects can not be mixed, e.g.,
:py:func:`TimeData` and :py:func:`FrequencyData` objects do not work
together. See below or
:py:mod:`arithmetic operations <pyfar._concepts.arithmetic_operations>`
for possible combinations of Signal FFT normalizations.
domain : ``'time'``, ``'freq'``, optional
Flag to indicate if the operation should be performed in the time or
frequency domain. Frequency domain operations work on the raw
spectrum (See :py:func:`pyfar.dsp.fft.normalization`). The default is
``'freq'``.
Returns
-------
results : Signal, TimeData, FrequencyData, numpy array
Result of the operation as numpy array, if `data` contains only array
likes and numbers. Result as pyfar audio object if `data` contains an
audio object.
Notes
-----
The shape of arrays included in data need to match or be broadcastable
into the ``cshape`` of the resulting audio object.
The `fft_norm` of the result is as follows
* If the denominator signal has the FFT normalization ``'none'``, the
result gets the normalization of the numerator signal.
* If both signals have the same FFT normalization, the results gets the
normalization ``'none'``.
* Other combinations raise an error.
"""
return _arithmetic(data, domain, _divide)
[docs]
def power(data: tuple, domain='freq'):
"""Power of pyfar audio objects, array likes, and scalars.
Pyfar audio objects are: :py:func:`Signal`, :py:func:`TimeData`, and
:py:func:`FrequencyData`.
Parameters
----------
data : tuple of the form (data_1, data_2, ..., data_N)
The base for which the power is calculated. Can contain pyfar audio
objects, array likes, and scalars. Pyfar audio objects can not be
mixed, e.g., :py:func:`TimeData` and :py:func:`FrequencyData` objects
do not work together. See below or
:py:mod:`arithmetic operations <pyfar._concepts.arithmetic_operations>`
for possible combinations of Signal FFT normalizations.
domain : ``'time'``, ``'freq'``, optional
Flag to indicate if the operation should be performed in the time or
frequency domain. Frequency domain operations work on the raw
spectrum (See :py:func:`pyfar.dsp.fft.normalization`). The default is
``'freq'``.
Returns
-------
results : Signal, TimeData, FrequencyData, numpy array
Result of the operation as numpy array, if `data` contains only array
likes and numbers. Result as pyfar audio object if `data` contains an
audio object.
Notes
-----
The shape of arrays included in data need to match or be broadcastable
into the ``cshape`` of the resulting audio object.
The `fft_norm` of the result is as follows
* If one signal has the FFT normalization ``'none'``, the results gets
the normalization of the other signal.
* If both signals have the same FFT normalization, the results gets the
same normalization.
* Other combinations raise an error.
"""
return _arithmetic(data, domain, _power)
[docs]
def matrix_multiplication(
data: tuple, domain='freq', axes=[(-2, -1), (-2, -1), (-2, -1)]):
"""Matrix multiplication of multidimensional pyfar audio objects and/or
array likes.
The multiplication is based on ``numpy.matmul`` and acts on the channels
of audio objects (:py:func:`Signal`, :py:func:`TimeData`, and
:py:func:`FrequencyData`). Alternatively, the ``@`` operator can be used
for frequency domain matrix multiplications with the default parameters.
Parameters
----------
data : tuple of the form (data_1, data_2, ..., data_N)
Data to be multiplied. Can contain pyfar audio objects and array likes.
If multiple audio objects are passed they must be of the same type and
their FFT normalizations must allow the multiplication (see
:py:mod:`arithmetic operations <pyfar._concepts.arithmetic_operations>`
and notes below).
If audio objects and arrays are included, the arrays' shape need
to match the audio objects' cshape (not the shape of the underlying
time or frequency data). More Information on the requirements regarding
the shapes and cshapes and their handling is given in the notes below.
domain : ``'time'``, ``'freq'``, optional
Flag to indicate if the operation should be performed in the time or
frequency domain. Frequency domain operations work on the raw
spectrum (see :py:func:`pyfar.dsp.fft.normalization`). The default is
``'freq'``.
axes : list of 3 tuples
Each tuple in the list specifies two axes to define the matrices for
multiplication. The default ``[(-2, -1), (-2, -1), (-2, -1)]`` uses the
last two axes of the input to define the matrices (first and
second tuple) and writes the result to the last two axes of the output
data (third tuple).
In case of pyfar audio objects, the indices refer to the channel
dimensions and ignore the last dimension of the underlying data that
contains the samples or frequency bins (see
:py:mod:`audio classes <pyfar._concepts.audio_classes>` for more
information). For example, a signal with 4 times 2 channels and 120
frequency bins has a cshape of ``(4, 2)``, while the shape of the
underlying frequency data is ``(4, 2, 120)``. The default tuple
``(-2, -1)`` would result in 120 matrices of shape ``(4, 2)`` used
for the multiplication and not 4 matrices of shape ``(2, 120)``.
If `data` contains more than two operands, the scheme given by `axes`
refers to all of the sequential multiplications.
See notes and examples for more details.
Returns
-------
results : Signal, TimeData, FrequencyData, numpy array
Result of the operation as numpy array, if `data` contains only array
likes and numbers. Result as pyfar audio object if `data` contains an
audio object.
Notes
-----
Matrix muliplitcation of arrays including a time of frequency dependent
dimension is possible by first converting these audio objects
(:py:func:`Signal`, :py:func:`TimeData`, :py:func:`FrequencyData`).
See example below.
Audio objects with a one dimensional cshape are expanded to allow matrix
multiplication:
* If the first signal is 1-D, it is expanded to 2-D by prepending a
dimension. For example a cshape of ``(10,)`` becomes ``(1, 10)``.
* If the second signal is 1-D, it is expanded to 2-D by appending a
dimension. For example a cshape of ``(10,)`` becomes ``(10, 1)``
The shapes of array likes and cshapes of audio objects must be
`broadcastable <https://numpy.org/doc/stable/user/basics.broadcasting.
html>`_ except for the axes specified by the `axes` parameter.
The `fft_norm` of the result is as follows
* If one signal has the FFT normalization ``'none'``, the results gets
the normalization of the other signal.
* If both signals have the same FFT normalization, the results gets the
same normalization.
* Other combinations raise an error.
Examples
--------
Matrix multiplication of two-dimensional signals.
>>> a = pf.signals.impulse(10, amplitude=np.ones((2, 3)))
>>> b = pf.signals.impulse(10, amplitude=np.ones((3, 4)))
>>> a.cshape
(2, 3)
>>> b.cshape
(3, 4)
>>> pf.matrix_multiplication((a, b)).cshape
(2, 4)
>>> (a @ b).cshape
(2, 4)
Matrix multiplication of signal with a frequency dependent matrix
requires to convert the matrix into a Signal object first.
>>> x = pf.signals.impulse(10, amplitude=np.ones((3, 1)))
>>> M = np.ones((2, 3, x.n_bins)) * x.frequencies
>>> # convert to Signal
>>> Ms = pf.Signal(M, x.sampling_rate, domain='freq')
>>> # pf.matrix_multiplication((M, x)) raises an error
>>> pf.matrix_multiplication((Ms, x)).cshape
(2, 1)
Matrix multiplication of three-dimensional signals. The third dimension
needs to match or it is broadcasted (per default this refers to axis 0).
>>> a_match = pf.signals.impulse(10, amplitude=np.ones((2, 3, 4)))
>>> b = pf.signals.impulse(10, amplitude=np.ones((2, 4, 5)))
>>> pf.matrix_multiplication((a_match, b)).cshape
(2, 3, 5)
>>> a_bcast1 = pf.signals.impulse(10, amplitude=np.ones((1, 3, 4)))
>>> pf.matrix_multiplication((a_bcast1, b)).cshape
(2, 3, 5)
>>> a_bcast2 = pf.signals.impulse(10, amplitude=np.ones((3, 4)))
>>> pf.matrix_multiplication((a_bcast2, b)).cshape
(2, 3, 5)
Use the `axes` parameter to multiply along first two channel dimensions.
>>> a = pf.signals.impulse(10, amplitude=np.ones((2, 3, 4)))
>>> b = pf.signals.impulse(10, amplitude=np.ones((3, 5, 4)))
>>> pf.matrix_multiplication((a, b), axes=[(0, 1), (0, 1), (0, 1)]).cshape
(2, 5, 4)
Matrix multiplications of numpy arrays and signals.
>>> B = np.ones((3, 4))
>>> s1 = pf.signals.impulse(10, amplitude=np.ones((4)))
>>> s2 = pf.signals.impulse(10, amplitude=np.ones((4, 2)))
>>> s3 = pf.signals.impulse(10, amplitude=np.ones((2, 4)))
>>> pf.matrix_multiplication((B, s1)).cshape
(3, 1)
>>> pf.matrix_multiplication((B, s2)).cshape
(3, 2)
>>> pf.matrix_multiplication(
>>> (B, s3), axes=[(-2, -1), (-1, -2), (-1, -2)]).cshape
(2, 3)
Fancy use of the `axes` parameter.
>>> a = pf.signals.impulse(10, amplitude=np.ones((2, 3, 4)))
>>> b = pf.signals.impulse(10, amplitude=np.ones((4, 3, 6)))
>>> pf.matrix_multiplication((a, b), axes=[(0, 1), (1, 2), (2, 1)]).cshape
(4, 6, 2)
Extension of a signal with a 1-D ``cshape``.
>>> a = pf.signals.impulse(10, amplitude=np.ones((2,)))
>>> a.cshape
(2,)
>>> b = pf.signals.impulse(10, amplitude=np.ones((3, 2, 4)))
>>> pf.matrix_multiplication((a, b)).cshape
(3, 1, 4)
>>> a = pf.signals.impulse(10, amplitude=np.ones((2, 3, 4)))
>>> b = pf.signals.impulse(10, amplitude=np.ones((4, )))
>>> pf.matrix_multiplication((a, b)).cshape
(2, 3, 1)
"""
return _arithmetic(data, domain, _matrix_multiplication, axes=axes)
def _arithmetic(data: tuple, domain: str, operation: Callable, **kwargs):
"""Apply arithmetic operations."""
# check input and obtain meta data of new signal
division = True if operation == _divide else False
matmul = True if operation == _matrix_multiplication else False
sampling_rate, n_samples, fft_norm, times, frequencies, audio_type, \
cshape = \
_assert_match_for_arithmetic(data, domain, division, matmul)
# apply arithmetic operation
result = _get_arithmetic_data(data[0], domain, cshape, matmul, audio_type)
for d in range(1, len(data)):
if matmul:
kwargs['audio_type'] = audio_type
result = operation(
result,
_get_arithmetic_data(data[d], domain, cshape, matmul, audio_type),
**kwargs)
# check if to return an audio object
if audio_type == Signal:
# Set unnormalized spectrum
result = Signal(
result, sampling_rate, n_samples, domain, fft_norm='none')
# Set fft norm
result.fft_norm = fft_norm
elif audio_type == TimeData:
result = TimeData(result, times)
elif audio_type == FrequencyData:
result = FrequencyData(result, frequencies)
return result
def _assert_match_for_arithmetic(data: tuple, domain: str, division: bool,
matmul: bool):
"""Check if type and meta data of input is fine for arithmetic operations.
Check if sampling rate and number of samples agree if multiple signals are
provided. Check if arrays are numeric. Check if a power signal is contained
in the input. Extract cshape of result.
Input:
data : tuple
Can contain Signal, TimeData, FrequencyData, and array like data
domain : str
Domain in which the arithmetic operation should be performed. 'time' or
'freq'.
division : bool
``True`` if a division is performed, ``False`` otherwise
matmul: bool
``True`` if a matrix multiplication is performed, ``False`` otherwise
Returns
-------
sampling_rate : number, None
Sampling rate of the signals. None, if no signal is contained in `data`
n_samples : number, None
Number of samples of the signals. None, if no signal is contained in
`data`
fft_norm : str, None
FFT norm of the first signal in `data`, if all FFT norms are None.
Otherwise the first FFT norm that is not None is taken.
times : numpy array, None
The times if a TimeData object was passed. None otherwise.
frequencies : numpy array, None
The frequencies if a FrequencyData object was passed. None otherwise.
audio_type : type, None
Type of the audio class if contained in data. Otherwise None.
cshape : tuple, None
Largest channel shape of the audio classes if contained in data.
Otherwise empty tuple.
"""
# we need at least two signals
if not isinstance(data, tuple):
raise ValueError("Input argument 'data' must be a tuple.")
# check validity of domain
if domain not in ['time', 'freq']:
raise ValueError(f"domain must be time or freq but is {domain}.")
# properties that must match
sampling_rate = None
n_samples = None
fft_norm = 'none'
times = None
frequencies = None
audio_type = type(None)
cshape = ()
# check input types and meta data
found_audio_data = False
for n, d in enumerate(data):
if isinstance(d, (Signal, TimeData, FrequencyData)):
# store meta data upon first appearance
if not found_audio_data:
if isinstance(d, Signal):
sampling_rate = d.sampling_rate
n_samples = d.n_samples
# if a signal comes first (n==0) its fft_norm is taken
# directly. If a signal does not come first, (n>0, e.g.
# 1/signal), the fft norm is matched
fft_norm = d.fft_norm if n == 0 else \
_match_fft_norm(fft_norm, d.fft_norm, division)
elif isinstance(d, TimeData):
if domain != "time":
raise ValueError("The domain must be 'time'.")
times = d.times
elif isinstance(d, FrequencyData):
if domain != "freq":
raise ValueError("The domain must be 'freq'.")
frequencies = d.frequencies
if not matmul:
cshape = d.cshape
found_audio_data = True
audio_type = type(d)
# check if type and meta data matches after first appearance
else:
if not isinstance(d, audio_type):
raise ValueError("The audio objects do not match.")
if isinstance(d, Signal):
if sampling_rate != d.sampling_rate:
raise ValueError("The sampling rates do not match.")
if n_samples != d.n_samples:
raise ValueError(
"The number of samples does not match.")
fft_norm = _match_fft_norm(fft_norm, d.fft_norm, division)
elif isinstance(d, TimeData):
if not np.allclose(times, d.times, atol=1e-15):
raise ValueError(
"The times does not match.")
elif isinstance(d, FrequencyData):
if not np.allclose(
frequencies, d.frequencies, atol=1e-15):
raise ValueError(
"The frequencies do not match.")
if not matmul:
try:
cshape = np.broadcast_shapes(cshape, d.cshape)
except ValueError:
raise ValueError(
"The cshapes do not match.")
# check type of non signal input
else:
if np.asarray(d).dtype.kind not in ["i", "f", "c"]:
raise ValueError(
"Input must be of type Signal, int, float, or complex")
if np.asarray(d).dtype.kind == "c" and domain == 'time':
raise ValueError(
"Complex input can not be applied in the time domain.")
return (sampling_rate, n_samples, fft_norm, times, frequencies, audio_type,
cshape)
def _get_arithmetic_data(data, domain, cshape, matmul, audio_type):
"""
Return data in desired domain without any fft normalization.
Parameters
----------
data : Signal, array like, number
Input data
domain : 'time', 'freq'
Domain in which the data is returned
cshape : tuple
Desired channel shape of output (required for operations including
array likes and Audio objects).
matmul: bool
``True`` if a matrix multiplication is performed, ``False`` otherwise
audio_type : type, None
Type of the audio class of the operation's result.
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":
if isinstance(data, Signal):
data_out = data.freq_raw.copy()
else:
data_out = data.freq.copy()
else:
raise ValueError(
f"domain must be 'time' or 'freq' but found {domain}")
else:
data_out = np.asarray(data)
if data_out.ndim <= len(cshape) or\
(matmul and not isinstance(None, audio_type)):
# extend by time/frequency axis, scalars are extended to shape (1,)
data_out = data_out[..., None]
elif cshape != ():
# operation includes arrays and audio objects
raise ValueError(
"array dimension is larger than the channel dimensions")
return data_out
def _add(a, b):
return a + b
def _subtract(a, b):
return a - b
def _multiply(a, b):
return a * b
def _divide(a, b):
return a / b
def _power(a, b):
return a**b
def _matrix_multiplication(a, b, axes, audio_type):
if not isinstance(None, audio_type):
# adjust data and axes if output is a pyfar audio object
# add dimension if operand is only 2d
a = np.expand_dims(a, 0) if a.ndim == 2 else a
b = np.expand_dims(b, 1) if b.ndim == 2 else b
# note: axes is implicitly copied
axes = [tuple([ax-1 if ax < 0 else ax for ax in t]) for t in axes]
return np.matmul(a, b, axes=axes)
def _match_fft_norm(fft_norm_1, fft_norm_2, division=False):
"""
Helper function to determine the fft_norm resulting from an
arithmetic operation of two audio objects.
For addition, subtraction and multiplication:
Either: one signal has fft_norm ``'none'`` , the results gets the other
norm.
Or: both have the same fft_norm, the results gets the same norm.
Other combinations raise an error.
For division:
Either: the denominator (fft_norm_2) is ``'none'``, the result gets the
fft_norm of the numerator (fft_norm_1).
Or: both have the same fft_norm, the results gets the fft_norm ``'none'``.
Other combinations raise an error.
Parameters
----------
fft_norm_1 : str, ``'none'``, ``'unitary'``, ``'amplitude'``, ``'rms'``,
``'power'`` or ``'psd'``
First fft_norm for matching.
fft_norm_2 : str, ``'none'``, ``'unitary'``, ``'amplitude'``, ``'rms'``,
``'power'`` or ``'psd'``
Second fft_norm for matching.
division : bool
``False`` if arithmetic operation is addition, subtraction or
multiplication;
``True`` if arithmetic operation is division.
Returns
-------
fft_norm_result : str, ``'none'``, ``'unitary'``, ``'amplitude'``,
``'rms'``, ``'power'`` or ``'psd'``
The fft_norm resulting from arithmetic operation.
"""
# check if fft_norms are valid
valid_fft_norms = ['none', 'unitary', 'amplitude', 'rms', 'power', 'psd']
if fft_norm_1 not in valid_fft_norms:
raise ValueError((f"fft_norm_1 is {fft_norm_1} but must be in "
f"{', '.join(valid_fft_norms)}"))
if fft_norm_2 not in valid_fft_norms:
raise ValueError((f"fft_norm_2 is {fft_norm_2} but must be in "
f"{', '.join(valid_fft_norms)}"))
# check if parameter division is type bool
if not isinstance(division, bool):
raise TypeError("Parameter division must be type bool.")
if not division:
if fft_norm_1 == fft_norm_2:
fft_norm_result = fft_norm_1
elif fft_norm_1 == 'none':
fft_norm_result = fft_norm_2
elif fft_norm_2 == 'none':
fft_norm_result = fft_norm_1
else:
raise ValueError(("Either one fft_norm has to be 'none' or both "
"fft_norms must be the same, but they are ",
f"{fft_norm_1} and {fft_norm_2}."))
else:
if fft_norm_2 == 'none':
fft_norm_result = fft_norm_1
elif fft_norm_1 == fft_norm_2:
fft_norm_result = 'none'
else:
raise ValueError(("Either fft_norm_2 (denominator) has to be "
"'none' or both fft_norms must be the same, but "
f"they are {fft_norm_1} and {fft_norm_2}."))
return fft_norm_result
