Audio (Signal, TimeData, FrequencyData)

The following documents the audio classes and arithmethic operations for audio data. More details and background is given in the concepts ( audio classes, Fourier transform, arithmetic operations).

Classes:

FrequencyData(data, frequencies[, comment])	Class for frequency data.
Signal(data, sampling_rate[, n_samples, ...])	Class for audio signals.
TimeData(data, times[, comment])	Class for time data.

Functions:

add(data[, domain])	Add pyfar audio objects, array likes, and scalars.
divide(data[, domain])	Divide pyfar audio objects, array likes, and scalars.
matrix_multiplication(data[, domain, axes])	Matrix multiplication of multidimensional pyfar audio objects and/or array likes.
multiply(data[, domain])	Multiply pyfar audio objects, array likes, and scalars.
power(data[, domain])	Power of pyfar audio objects, array likes, and scalars.
subtract(data[, domain])	Subtract pyfar audio objects, array likes, and scalars.

class pyfar.classes.audio.FrequencyData(data, frequencies, comment='')

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.

Methods:

__getitem__(key)	Get copied slice of the audio object at key.
__init__(data, frequencies[, comment])	Create FrequencyData with data, and frequencies.
__setitem__(key, value)	Set channels of audio object at key.
copy()	Return a copy of the audio object.
find_nearest_frequency(value)	Return the index that is closest to the query frequency.
flatten()	Return flattened copy of the audio object.
reshape(newshape)	Return reshaped copy of the audio object.

Attributes:

comment	Get comment.
cshape	Return channel shape.
domain	The domain the data is stored in.
freq	Return the data in the frequency domain.
frequencies	Frequencies of the discrete signal spectrum.
n_bins	Number of frequency bins.

__getitem__(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]

__init__(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 [1].

References

[1]

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.

__setitem__(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)

property comment

Get comment.

copy()

Return a copy of the audio object.

property cshape

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.

property domain

The domain the data is stored in.

find_nearest_frequency(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 – The index for the given frequency. If the input was an array like, a numpy array of indices is returned.

Return type:

int, array-like

flatten()

Return flattened copy of the audio object.

Returns:

flat – Flattened copy of audio object with flat.cshape = np.prod(audio.cshape)

Return type:

Signal, FrequencyData, TimeData

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.

property freq

Return the data in the frequency domain.

property frequencies

Frequencies of the discrete signal spectrum.

property n_bins

Number of frequency bins.

reshape(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 – reshaped copy of the audio object.

Return type:

Signal, FrequencyData, TimeData

Notes

The number of samples and frequency bins always remains the same.

class pyfar.classes.audio.Signal(data, sampling_rate, n_samples=None, domain='time', fft_norm='none', comment='')

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.

Methods:

__getitem__(key)	Get copied slice of the audio object at key.
__init__(data, sampling_rate[, n_samples, ...])	Create Signal with data, and sampling rate.
__iter__()	Iterator for Signal objects.
__setitem__(key, value)	Set channels of audio object at key.
copy()	Return a copy of the audio object.
find_nearest_frequency(value)	Return the index that is closest to the query frequency.
find_nearest_time(value)	Return the index that is closest to the query time.
flatten()	Return flattened copy of the audio object.
reshape(newshape)	Return reshaped copy of the audio object.

Attributes:

comment	Get comment.
cshape	Return channel shape.
domain	The domain the data is stored in.
fft_norm	The normalization for the Discrete Fourier Transform (DFT).
freq	Return the normalized frequency domain data.
freq_raw	Return the frequency domain data without normalization.
frequencies	Frequencies of the discrete signal spectrum.
n_bins	Number of frequency bins.
n_samples	The number of samples.
sampling_rate	The sampling rate of the signal.
signal_length	The length of the data in seconds.
signal_type	The signal type is 'energy' if the fft_norm = None and 'power' otherwise.
time	Return the data in the time domain.
times	Time instances the signal is sampled at.

__getitem__(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]

__init__(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 normalization and [2] 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

[2]

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.

__iter__()

Iterator for Signal objects.

Iterate across the first dimension of a Signal. The actual iteration is handled through numpy’s array iteration.

Examples

Iterate channels of a 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

__setitem__(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)

property comment

Get comment.

copy()

Return a copy of the audio object.

property cshape

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.

property domain

The domain the data is stored in.

property fft_norm

The normalization for the Discrete Fourier Transform (DFT).

See normalization and FFT concepts for more information.

find_nearest_frequency(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 – The index for the given frequency. If the input was an array like, a numpy array of indices is returned.

Return type:

int, array-like

find_nearest_time(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 – The index for the given time instance. If the input was an array like, a numpy array of indices is returned.

Return type:

int, array-like

flatten()

Return flattened copy of the audio object.

Returns:

flat – Flattened copy of audio object with flat.cshape = np.prod(audio.cshape)

Return type:

Signal, FrequencyData, TimeData

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.

property freq

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.

property freq_raw

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.

property frequencies

Frequencies of the discrete signal spectrum.

property n_bins

Number of frequency bins.

property n_samples

The number of samples.

reshape(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 – reshaped copy of the audio object.

Return type:

Signal, FrequencyData, TimeData

Notes

The number of samples and frequency bins always remains the same.

property sampling_rate

The sampling rate of the signal.

property signal_length

The length of the data in seconds.

property signal_type

The signal type is 'energy' if the fft_norm = None and 'power' otherwise.

property time

Return the data in the time domain.

property times

Time instances the signal is sampled at.

class pyfar.classes.audio.TimeData(data, times, comment='')

Class for time data.

Objects of this class contain time data which is not directly convertible to frequency domain, i.e., non-equidistant samples.

Methods:

__getitem__(key)	Get copied slice of the audio object at key.
__init__(data, times[, comment])	Create TimeData object with data, and times.
__setitem__(key, value)	Set channels of audio object at key.
copy()	Return a copy of the audio object.
find_nearest_time(value)	Return the index that is closest to the query time.
flatten()	Return flattened copy of the audio object.
reshape(newshape)	Return reshaped copy of the audio object.

Attributes:

comment	Get comment.
cshape	Return channel shape.
domain	The domain the data is stored in.
n_samples	The number of samples.
signal_length	The length of the data in seconds.
time	Return the data in the time domain.
times	Time in seconds at which the signal is sampled.

__getitem__(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]

__init__(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.

__setitem__(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)

property comment

Get comment.

copy()

Return a copy of the audio object.

property cshape

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.

property domain

The domain the data is stored in.

find_nearest_time(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 – The index for the given time instance. If the input was an array like, a numpy array of indices is returned.

Return type:

int, array-like

flatten()

Return flattened copy of the audio object.

Returns:

flat – Flattened copy of audio object with flat.cshape = np.prod(audio.cshape)

Return type:

Signal, FrequencyData, TimeData

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.

property n_samples

The number of samples.

reshape(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 – reshaped copy of the audio object.

Return type:

Signal, FrequencyData, TimeData

Notes

The number of samples and frequency bins always remains the same.

property signal_length

The length of the data in seconds.

property time

Return the data in the time domain.

property times

Time in seconds at which the signal is sampled.

pyfar.classes.audio.add(data: tuple, domain='freq')

Add pyfar audio objects, array likes, and scalars.

Pyfar audio objects are: Signal, TimeData, and 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., TimeData and FrequencyData objects do not work together. See below or 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 pyfar.dsp.fft.normalization). The default is 'freq'.

Returns:

results – 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.

Return type:

Signal, TimeData, FrequencyData, numpy array

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.

pyfar.classes.audio.divide(data: tuple, domain='freq')

Divide pyfar audio objects, array likes, and scalars.

Pyfar audio objects are: Signal, TimeData, and 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., TimeData and FrequencyData objects do not work together. See below or 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 pyfar.dsp.fft.normalization). The default is 'freq'.

Returns:

results – 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.

Return type:

Signal, TimeData, FrequencyData, numpy array

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.

pyfar.classes.audio.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 (Signal, TimeData, and 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 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 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 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 – 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.

Return type:

Signal, TimeData, FrequencyData, numpy array

Notes

Matrix muliplitcation of arrays including a time of frequency dependent dimension is possible by first converting these audio objects (Signal, TimeData, 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 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)

pyfar.classes.audio.multiply(data: tuple, domain='freq')

Multiply pyfar audio objects, array likes, and scalars.

Pyfar audio objects are: Signal, TimeData, and 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., TimeData and FrequencyData objects do not work together. See below or 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 pyfar.dsp.fft.normalization). The default is 'freq'.

Returns:

results – 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.

Return type:

Signal, TimeData, FrequencyData, numpy array

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.

pyfar.classes.audio.power(data: tuple, domain='freq')

Power of pyfar audio objects, array likes, and scalars.

Pyfar audio objects are: Signal, TimeData, and 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., TimeData and FrequencyData objects do not work together. See below or 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 pyfar.dsp.fft.normalization). The default is 'freq'.

Returns:

results – 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.

Return type:

Signal, TimeData, FrequencyData, numpy array

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.

pyfar.classes.audio.subtract(data: tuple, domain='freq')

Subtract pyfar audio objects, array likes, and scalars.

Pyfar audio objects are: Signal, TimeData, and 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., TimeData and FrequencyData objects do not work together. See below or 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 pyfar.dsp.fft.normalization). The default is 'freq'.

Returns:

results – 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.

Return type:

Signal, TimeData, FrequencyData, numpy array

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.