#!/usr/bin/env python
# -*- coding: utf-8 -*-
"""
Effects
=======
Harmonic-percussive source separation
-------------------------------------
.. autosummary::
:toctree: generated/
hpss
harmonic
percussive
Time and frequency
------------------
.. autosummary::
:toctree: generated/
time_stretch
pitch_shift
Miscellaneous
-------------
.. autosummary::
:toctree: generated/
remix
trim
split
preemphasis
deemphasis
"""
import numpy as np
import scipy.signal
from . import core
from . import decompose
from . import feature
from . import util
from .util.exceptions import ParameterError
from typing import Any, Callable, Iterable, Optional, Tuple, List, Union, overload
from typing_extensions import Literal
from numpy.typing import ArrayLike
from ._typing import (
_WindowSpec,
_PadMode,
_PadModeSTFT,
_SequenceLike,
_ScalarOrSequence,
_ComplexLike_co,
_IntLike_co,
_FloatLike_co,
)
__all__ = [
"hpss",
"harmonic",
"percussive",
"time_stretch",
"pitch_shift",
"remix",
"trim",
"split",
]
[docs]def hpss(
y: np.ndarray,
*,
kernel_size: Union[
_IntLike_co, Tuple[_IntLike_co, _IntLike_co], List[_IntLike_co]
] = 31,
power: float = 2.0,
mask: bool = False,
margin: Union[
_FloatLike_co, Tuple[_FloatLike_co, _FloatLike_co], List[_FloatLike_co]
] = 1.0,
n_fft: int = 2048,
hop_length: Optional[int] = None,
win_length: Optional[int] = None,
window: _WindowSpec = "hann",
center: bool = True,
pad_mode: _PadModeSTFT = "constant",
) -> Tuple[np.ndarray, np.ndarray]:
"""Decompose an audio time series into harmonic and percussive components.
This function automates the STFT->HPSS->ISTFT pipeline, and ensures that
the output waveforms have equal length to the input waveform ``y``.
Parameters
----------
y : np.ndarray [shape=(..., n)]
audio time series. Multi-channel is supported.
kernel_size
power
mask
margin
See `librosa.deocmpose.hpss`
n_fft
hop_length
win_length
window
center
pad_mode
See `librosa.stft`
Returns
-------
y_harmonic : np.ndarray [shape=(..., n)]
audio time series of the harmonic elements
y_percussive : np.ndarray [shape=(..., n)]
audio time series of the percussive elements
See Also
--------
harmonic : Extract only the harmonic component
percussive : Extract only the percussive component
librosa.decompose.hpss : HPSS on spectrograms
Examples
--------
>>> # Extract harmonic and percussive components
>>> y, sr = librosa.load(librosa.ex('choice'))
>>> y_harmonic, y_percussive = librosa.effects.hpss(y)
>>> # Get a more isolated percussive component by widening its margin
>>> y_harmonic, y_percussive = librosa.effects.hpss(y, margin=(1.0,5.0))
"""
# Compute the STFT matrix
stft = core.stft(
y,
n_fft=n_fft,
hop_length=hop_length,
win_length=win_length,
center=center,
pad_mode=pad_mode,
)
# Decompose into harmonic and percussives
stft_harm, stft_perc = decompose.hpss(
stft, kernel_size=kernel_size, power=power, mask=mask, margin=margin
)
# Invert the STFTs. Adjust length to match the input.
y_harm = core.istft(
stft_harm,
dtype=y.dtype,
n_fft=n_fft,
hop_length=hop_length,
win_length=win_length,
center=center,
length=y.shape[-1],
)
y_perc = core.istft(
stft_perc,
dtype=y.dtype,
n_fft=n_fft,
hop_length=hop_length,
win_length=win_length,
center=center,
length=y.shape[-1],
)
return y_harm, y_perc
[docs]def harmonic(
y: np.ndarray,
*,
kernel_size: Union[
_IntLike_co, Tuple[_IntLike_co, _IntLike_co], List[_IntLike_co]
] = 31,
power: float = 2.0,
mask: bool = False,
margin: Union[
_FloatLike_co, Tuple[_FloatLike_co, _FloatLike_co], List[_FloatLike_co]
] = 1.0,
n_fft: int = 2048,
hop_length: Optional[int] = None,
win_length: Optional[int] = None,
window: _WindowSpec = "hann",
center: bool = True,
pad_mode: _PadModeSTFT = "constant",
) -> np.ndarray:
"""Extract harmonic elements from an audio time-series.
Parameters
----------
y : np.ndarray [shape=(..., n)]
audio time series. Multi-channel is supported.
kernel_size
power
mask
margin
See `librosa.deocmpose.hpss`
n_fft
hop_length
win_length
window
center
pad_mode
See `librosa.stft`
Returns
-------
y_harmonic : np.ndarray [shape=(..., n)]
audio time series of just the harmonic portion
See Also
--------
hpss : Separate harmonic and percussive components
percussive : Extract only the percussive component
librosa.decompose.hpss : HPSS for spectrograms
Examples
--------
>>> # Extract harmonic component
>>> y, sr = librosa.load(librosa.ex('choice'))
>>> y_harmonic = librosa.effects.harmonic(y)
>>> # Use a margin > 1.0 for greater harmonic separation
>>> y_harmonic = librosa.effects.harmonic(y, margin=3.0)
"""
# Compute the STFT matrix
stft = core.stft(
y,
n_fft=n_fft,
hop_length=hop_length,
win_length=win_length,
center=center,
pad_mode=pad_mode,
)
# Remove percussives
stft_harm = decompose.hpss(
stft, kernel_size=kernel_size, power=power, mask=mask, margin=margin
)[0]
# Invert the STFTs
y_harm = core.istft(
stft_harm,
dtype=y.dtype,
n_fft=n_fft,
hop_length=hop_length,
win_length=win_length,
center=center,
length=y.shape[-1],
)
return y_harm
[docs]def percussive(
y: np.ndarray,
*,
kernel_size: Union[
_IntLike_co, Tuple[_IntLike_co, _IntLike_co], List[_IntLike_co]
] = 31,
power: float = 2.0,
mask: bool = False,
margin: Union[
_FloatLike_co, Tuple[_FloatLike_co, _FloatLike_co], List[_FloatLike_co]
] = 1.0,
n_fft: int = 2048,
hop_length: Optional[int] = None,
win_length: Optional[int] = None,
window: _WindowSpec = "hann",
center: bool = True,
pad_mode: _PadModeSTFT = "constant",
) -> np.ndarray:
"""Extract percussive elements from an audio time-series.
Parameters
----------
y : np.ndarray [shape=(..., n)]
audio time series. Multi-channel is supported.
kernel_size
power
mask
margin
See `librosa.deocmpose.hpss`
n_fft
hop_length
win_length
window
center
pad_mode
See `librosa.stft`
Returns
-------
y_percussive : np.ndarray [shape=(..., n)]
audio time series of just the percussive portion
See Also
--------
hpss : Separate harmonic and percussive components
harmonic : Extract only the harmonic component
librosa.decompose.hpss : HPSS for spectrograms
Examples
--------
>>> # Extract percussive component
>>> y, sr = librosa.load(librosa.ex('choice'))
>>> y_percussive = librosa.effects.percussive(y)
>>> # Use a margin > 1.0 for greater percussive separation
>>> y_percussive = librosa.effects.percussive(y, margin=3.0)
"""
# Compute the STFT matrix
stft = core.stft(
y,
n_fft=n_fft,
hop_length=hop_length,
win_length=win_length,
center=center,
pad_mode=pad_mode,
)
# Remove harmonics
stft_perc = decompose.hpss(
stft, kernel_size=kernel_size, power=power, mask=mask, margin=margin
)[1]
# Invert the STFT
y_perc = core.istft(
stft_perc,
dtype=y.dtype,
n_fft=n_fft,
hop_length=hop_length,
win_length=win_length,
center=center,
length=y.shape[-1],
)
return y_perc
[docs]def time_stretch(y: np.ndarray, *, rate: float, **kwargs: Any) -> np.ndarray:
"""Time-stretch an audio series by a fixed rate.
Parameters
----------
y : np.ndarray [shape=(..., n)]
audio time series. Multi-channel is supported.
rate : float > 0 [scalar]
Stretch factor. If ``rate > 1``, then the signal is sped up.
If ``rate < 1``, then the signal is slowed down.
**kwargs : additional keyword arguments.
See `librosa.decompose.stft` for details.
Returns
-------
y_stretch : np.ndarray [shape=(..., round(n/rate))]
audio time series stretched by the specified rate
See Also
--------
pitch_shift :
pitch shifting
librosa.phase_vocoder :
spectrogram phase vocoder
pyrubberband.pyrb.time_stretch :
high-quality time stretching using RubberBand
Examples
--------
Compress to be twice as fast
>>> y, sr = librosa.load(librosa.ex('choice'))
>>> y_fast = librosa.effects.time_stretch(y, rate=2.0)
Or half the original speed
>>> y_slow = librosa.effects.time_stretch(y, rate=0.5)
"""
if rate <= 0:
raise ParameterError("rate must be a positive number")
# Construct the short-term Fourier transform (STFT)
stft = core.stft(y, **kwargs)
# Stretch by phase vocoding
stft_stretch = core.phase_vocoder(
stft,
rate=rate,
hop_length=kwargs.get("hop_length", None),
n_fft=kwargs.get("n_fft", None),
)
# Predict the length of y_stretch
len_stretch = int(round(y.shape[-1] / rate))
# Invert the STFT
y_stretch = core.istft(stft_stretch, dtype=y.dtype, length=len_stretch, **kwargs)
return y_stretch
[docs]def pitch_shift(
y: np.ndarray,
*,
sr: float,
n_steps: float,
bins_per_octave: int = 12,
res_type: str = "soxr_hq",
scale: bool = False,
**kwargs: Any,
) -> np.ndarray:
"""Shift the pitch of a waveform by ``n_steps`` steps.
A step is equal to a semitone if ``bins_per_octave`` is set to 12.
Parameters
----------
y : np.ndarray [shape=(..., n)]
audio time series. Multi-channel is supported.
sr : number > 0 [scalar]
audio sampling rate of ``y``
n_steps : float [scalar]
how many (fractional) steps to shift ``y``
bins_per_octave : int > 0 [scalar]
how many steps per octave
res_type : string
Resample type. By default, 'soxr_hq' is used.
See `librosa.resample` for more information.
scale : bool
Scale the resampled signal so that ``y`` and ``y_hat`` have approximately
equal total energy.
**kwargs : additional keyword arguments.
See `librosa.decompose.stft` for details.
Returns
-------
y_shift : np.ndarray [shape=(..., n)]
The pitch-shifted audio time-series
See Also
--------
time_stretch :
time stretching
librosa.phase_vocoder :
spectrogram phase vocoder
pyrubberband.pyrb.pitch_shift :
high-quality pitch shifting using RubberBand
Examples
--------
Shift up by a major third (four steps if ``bins_per_octave`` is 12)
>>> y, sr = librosa.load(librosa.ex('choice'))
>>> y_third = librosa.effects.pitch_shift(y, sr=sr, n_steps=4)
Shift down by a tritone (six steps if ``bins_per_octave`` is 12)
>>> y_tritone = librosa.effects.pitch_shift(y, sr=sr, n_steps=-6)
Shift up by 3 quarter-tones
>>> y_three_qt = librosa.effects.pitch_shift(y, sr=sr, n_steps=3,
... bins_per_octave=24)
"""
if not util.is_positive_int(bins_per_octave):
raise ParameterError(
f"bins_per_octave={bins_per_octave} must be a positive integer."
)
rate = 2.0 ** (-float(n_steps) / bins_per_octave)
# Stretch in time, then resample
y_shift = core.resample(
time_stretch(y, rate=rate, **kwargs),
orig_sr=float(sr) / rate,
target_sr=sr,
res_type=res_type,
scale=scale,
)
# Crop to the same dimension as the input
return util.fix_length(y_shift, size=y.shape[-1])
[docs]def remix(
y: np.ndarray, intervals: Iterable[Tuple[int, int]], *, align_zeros: bool = True
) -> np.ndarray:
"""Remix an audio signal by re-ordering time intervals.
Parameters
----------
y : np.ndarray [shape=(..., t)]
Audio time series. Multi-channel is supported.
intervals : iterable of tuples (start, end)
An iterable (list-like or generator) where the ``i``th item
``intervals[i]`` indicates the start and end (in samples)
of a slice of ``y``.
align_zeros : boolean
If ``True``, interval boundaries are mapped to the closest
zero-crossing in ``y``. If ``y`` is stereo, zero-crossings
are computed after converting to mono.
Returns
-------
y_remix : np.ndarray [shape=(..., d)]
``y`` remixed in the order specified by ``intervals``
Examples
--------
Load in the example track and reverse the beats
>>> y, sr = librosa.load(librosa.ex('choice'))
Compute beats
>>> _, beat_frames = librosa.beat.beat_track(y=y, sr=sr,
... hop_length=512)
Convert from frames to sample indices
>>> beat_samples = librosa.frames_to_samples(beat_frames)
Generate intervals from consecutive events
>>> intervals = librosa.util.frame(beat_samples, frame_length=2,
... hop_length=1).T
Reverse the beat intervals
>>> y_out = librosa.effects.remix(y, intervals[::-1])
"""
y_out = []
if align_zeros:
y_mono = core.to_mono(y)
zeros = np.nonzero(core.zero_crossings(y_mono))[-1]
# Force end-of-signal onto zeros
zeros = np.append(zeros, [len(y_mono)])
for interval in intervals:
if align_zeros:
interval = zeros[util.match_events(interval, zeros)]
y_out.append(y[..., interval[0] : interval[1]])
return np.concatenate(y_out, axis=-1)
def _signal_to_frame_nonsilent(
y: np.ndarray,
frame_length: int = 2048,
hop_length: int = 512,
top_db: float = 60,
ref: Union[Callable, float] = np.max,
aggregate: Callable = np.max,
) -> np.ndarray:
"""Frame-wise non-silent indicator for audio input.
This is a helper function for `trim` and `split`.
Parameters
----------
y : np.ndarray
Audio signal, mono or stereo
frame_length : int > 0
The number of samples per frame
hop_length : int > 0
The number of samples between frames
top_db : number > 0
The threshold (in decibels) below reference to consider as
silence
ref : callable or float
The reference amplitude
aggregate : callable [default: np.max]
Function to aggregate dB measurements across channels (if y.ndim > 1)
Note: for multiple leading axes, this is performed using ``np.apply_over_axes``.
Returns
-------
non_silent : np.ndarray, shape=(m,), dtype=bool
Indicator of non-silent frames
"""
# Compute the MSE for the signal
mse = feature.rms(y=y, frame_length=frame_length, hop_length=hop_length)
# Convert to decibels and slice out the mse channel
db: np.ndarray = core.amplitude_to_db(mse[..., 0, :], ref=ref, top_db=None)
# Aggregate everything but the time dimension
if db.ndim > 1:
db = np.apply_over_axes(aggregate, db, range(db.ndim - 1))
# Squeeze out leading singleton dimensions here
# We always want to keep the trailing dimension though
db = np.squeeze(db, axis=tuple(range(db.ndim - 1)))
return db > -top_db
[docs]def trim(
y: np.ndarray,
*,
top_db: float = 60,
ref: Union[float, Callable] = np.max,
frame_length: int = 2048,
hop_length: int = 512,
aggregate: Callable = np.max,
) -> Tuple[np.ndarray, np.ndarray]:
"""Trim leading and trailing silence from an audio signal.
Silence is defined as segments of the audio signal that are `top_db`
decibels (or more) quieter than a reference level, `ref`.
By default, `ref` is set to the signal's maximum RMS value.
It's important to note that if the entire signal maintains a uniform
RMS value, there will be no segments considered quieter than the maximum,
leading to no trimming.
This implies that a completely silent signal will remain untrimmed with the default `ref` setting.
In these situations, an explicit value for `ref` (in decibels) should be used instead.
Parameters
----------
y : np.ndarray, shape=(..., n)
Audio signal. Multi-channel is supported.
top_db : number > 0
The threshold (in decibels) below reference to consider as
silence
ref : number or callable
The reference amplitude. By default, it uses `np.max` and compares
to the peak amplitude in the signal.
frame_length : int > 0
The number of samples per analysis frame
hop_length : int > 0
The number of samples between analysis frames
aggregate : callable [default: np.max]
Function to aggregate across channels (if y.ndim > 1)
Returns
-------
y_trimmed : np.ndarray, shape=(..., m)
The trimmed signal
index : np.ndarray, shape=(2,)
the interval of ``y`` corresponding to the non-silent region:
``y_trimmed = y[index[0]:index[1]]`` (for mono) or
``y_trimmed = y[:, index[0]:index[1]]`` (for stereo).
Examples
--------
>>> # Load some audio
>>> y, sr = librosa.load(librosa.ex('choice'))
>>> # Trim the beginning and ending silence
>>> yt, index = librosa.effects.trim(y)
>>> # Print the durations
>>> print(librosa.get_duration(y, sr=sr), librosa.get_duration(yt, sr=sr))
25.025986394557822 25.007891156462584
"""
non_silent = _signal_to_frame_nonsilent(
y,
frame_length=frame_length,
hop_length=hop_length,
ref=ref,
top_db=top_db,
aggregate=aggregate,
)
nonzero = np.flatnonzero(non_silent)
if nonzero.size > 0:
# Compute the start and end positions
# End position goes one frame past the last non-zero
start = int(core.frames_to_samples(nonzero[0], hop_length=hop_length))
end = min(
y.shape[-1],
int(core.frames_to_samples(nonzero[-1] + 1, hop_length=hop_length)),
)
else:
# The entire signal is trimmed here: nothing is above the threshold
start, end = 0, 0
# Build the mono/stereo index
full_index = [slice(None)] * y.ndim
full_index[-1] = slice(start, end)
return y[tuple(full_index)], np.asarray([start, end])
[docs]def split(
y: np.ndarray,
*,
top_db: float = 60,
ref: Union[float, Callable] = np.max,
frame_length: int = 2048,
hop_length: int = 512,
aggregate: Callable = np.max,
) -> np.ndarray:
"""Split an audio signal into non-silent intervals.
Parameters
----------
y : np.ndarray, shape=(..., n)
An audio signal. Multi-channel is supported.
top_db : number > 0
The threshold (in decibels) below reference to consider as
silence
ref : number or callable
The reference amplitude. By default, it uses `np.max` and compares
to the peak amplitude in the signal.
frame_length : int > 0
The number of samples per analysis frame
hop_length : int > 0
The number of samples between analysis frames
aggregate : callable [default: np.max]
Function to aggregate across channels (if y.ndim > 1)
Returns
-------
intervals : np.ndarray, shape=(m, 2)
``intervals[i] == (start_i, end_i)`` are the start and end time
(in samples) of non-silent interval ``i``.
"""
non_silent = _signal_to_frame_nonsilent(
y,
frame_length=frame_length,
hop_length=hop_length,
ref=ref,
top_db=top_db,
aggregate=aggregate,
)
# Interval slicing, adapted from
# https://stackoverflow.com/questions/2619413/efficiently-finding-the-interval-with-non-zeros-in-scipy-numpy-in-python
# Find points where the sign flips
edges = np.flatnonzero(np.diff(non_silent.astype(int)))
# Pad back the sample lost in the diff
edges = [edges + 1]
# If the first frame had high energy, count it
if non_silent[0]:
edges.insert(0, np.array([0]))
# Likewise for the last frame
if non_silent[-1]:
edges.append(np.array([len(non_silent)]))
# Convert from frames to samples
edges = core.frames_to_samples(np.concatenate(edges), hop_length=hop_length)
# Clip to the signal duration
edges = np.minimum(edges, y.shape[-1])
# Stack the results back as an ndarray
edges = edges.reshape((-1, 2)) # type: np.ndarray
return edges
@overload
def preemphasis(
y: np.ndarray,
*,
coef: float = ...,
zi: Optional[ArrayLike] = ...,
return_zf: Literal[False] = ...,
) -> np.ndarray: ...
@overload
def preemphasis(
y: np.ndarray,
*,
coef: float = ...,
zi: Optional[ArrayLike] = ...,
return_zf: Literal[True],
) -> Tuple[np.ndarray, np.ndarray]: ...
@overload
def preemphasis(
y: np.ndarray,
*,
coef: float = ...,
zi: Optional[ArrayLike] = ...,
return_zf: bool,
) -> Union[np.ndarray, Tuple[np.ndarray, np.ndarray]]: ...
[docs]def preemphasis(
y: np.ndarray,
*,
coef: float = 0.97,
zi: Optional[ArrayLike] = None,
return_zf: bool = False,
) -> Union[np.ndarray, Tuple[np.ndarray, np.ndarray]]:
"""Pre-emphasize an audio signal with a first-order differencing filter:
y[n] -> y[n] - coef * y[n-1]
Parameters
----------
y : np.ndarray [shape=(..., n)]
Audio signal. Multi-channel is supported.
coef : positive number
Pre-emphasis coefficient. Typical values of ``coef`` are between 0 and 1.
At the limit ``coef=0``, the signal is unchanged.
At ``coef=1``, the result is the first-order difference of the signal.
The default (0.97) matches the pre-emphasis filter used in the HTK
implementation of MFCCs [#]_.
.. [#] https://htk.eng.cam.ac.uk/
zi : number
Initial filter state. When making successive calls to non-overlapping
frames, this can be set to the ``zf`` returned from the previous call.
(See example below.)
By default ``zi`` is initialized as ``2*y[0] - y[1]``.
return_zf : boolean
If ``True``, return the final filter state.
If ``False``, only return the pre-emphasized signal.
Returns
-------
y_out : np.ndarray
pre-emphasized signal
zf : number
if ``return_zf=True``, the final filter state is also returned
Examples
--------
Apply a standard pre-emphasis filter
>>> import matplotlib.pyplot as plt
>>> y, sr = librosa.load(librosa.ex('trumpet'))
>>> y_filt = librosa.effects.preemphasis(y)
>>> # and plot the results for comparison
>>> S_orig = librosa.amplitude_to_db(np.abs(librosa.stft(y)), ref=np.max, top_db=None)
>>> S_preemph = librosa.amplitude_to_db(np.abs(librosa.stft(y_filt)), ref=np.max, top_db=None)
>>> fig, ax = plt.subplots(nrows=2, sharex=True, sharey=True)
>>> librosa.display.specshow(S_orig, y_axis='log', x_axis='time', ax=ax[0])
>>> ax[0].set(title='Original signal')
>>> ax[0].label_outer()
>>> img = librosa.display.specshow(S_preemph, y_axis='log', x_axis='time', ax=ax[1])
>>> ax[1].set(title='Pre-emphasized signal')
>>> fig.colorbar(img, ax=ax, format="%+2.f dB")
Apply pre-emphasis in pieces for block streaming. Note that the second block
initializes ``zi`` with the final state ``zf`` returned by the first call.
>>> y_filt_1, zf = librosa.effects.preemphasis(y[:1000], return_zf=True)
>>> y_filt_2, zf = librosa.effects.preemphasis(y[1000:], zi=zf, return_zf=True)
>>> np.allclose(y_filt, np.concatenate([y_filt_1, y_filt_2]))
True
See Also
--------
deemphasis
"""
b = np.asarray([1.0, -coef], dtype=y.dtype)
a = np.asarray([1.0], dtype=y.dtype)
if zi is None:
# Initialize the filter to implement linear extrapolation
zi = 2 * y[..., 0:1] - y[..., 1:2]
zi = np.atleast_1d(zi)
y_out: np.ndarray
z_f: np.ndarray
y_out, z_f = scipy.signal.lfilter(b, a, y, zi=np.asarray(zi, dtype=y.dtype))
if return_zf:
return y_out, z_f
return y_out
@overload
def deemphasis(
y: np.ndarray,
*,
coef: float = ...,
zi: Optional[ArrayLike] = ...,
return_zf: Literal[False] = ...,
) -> np.ndarray: ...
@overload
def deemphasis(
y: np.ndarray,
*,
coef: float = ...,
zi: Optional[ArrayLike] = ...,
return_zf: Literal[True],
) -> Tuple[np.ndarray, np.ndarray]: ...
[docs]def deemphasis(
y: np.ndarray,
*,
coef: float = 0.97,
zi: Optional[ArrayLike] = None,
return_zf: bool = False,
) -> Union[np.ndarray, Tuple[np.ndarray, np.ndarray]]:
"""De-emphasize an audio signal with the inverse operation of preemphasis():
If y = preemphasis(x, coef=coef, zi=zi), the deemphasis is:
>>> x[i] = y[i] + coef * x[i-1]
>>> x = deemphasis(y, coef=coef, zi=zi)
Parameters
----------
y : np.ndarray [shape=(..., n)]
Audio signal. Multi-channel is supported.
coef : positive number
Pre-emphasis coefficient. Typical values of ``coef`` are between 0 and 1.
At the limit ``coef=0``, the signal is unchanged.
At ``coef=1``, the result is the first-order difference of the signal.
The default (0.97) matches the pre-emphasis filter used in the HTK
implementation of MFCCs [#]_.
.. [#] https://htk.eng.cam.ac.uk/
zi : number
Initial filter state. If inverting a previous preemphasis(), the same value should be used.
By default ``zi`` is initialized as
``((2 - coef) * y[0] - y[1]) / (3 - coef)``. This
value corresponds to the transformation of the default initialization of ``zi`` in ``preemphasis()``,
``2*x[0] - x[1]``.
return_zf : boolean
If ``True``, return the final filter state.
If ``False``, only return the pre-emphasized signal.
Returns
-------
y_out : np.ndarray
de-emphasized signal
zf : number
if ``return_zf=True``, the final filter state is also returned
Examples
--------
Apply a standard pre-emphasis filter and invert it with de-emphasis
>>> y, sr = librosa.load(librosa.ex('trumpet'))
>>> y_filt = librosa.effects.preemphasis(y)
>>> y_deemph = librosa.effects.deemphasis(y_filt)
>>> np.allclose(y, y_deemph)
True
See Also
--------
preemphasis
"""
b = np.array([1.0, -coef], dtype=y.dtype)
a = np.array([1.0], dtype=y.dtype)
y_out: np.ndarray
zf: np.ndarray
if zi is None:
# initialize with all zeros
zi = np.zeros(list(y.shape[:-1]) + [1], dtype=y.dtype)
y_out, zf = scipy.signal.lfilter(a, b, y, zi=zi)
# factor in the linear extrapolation
y_out -= (
((2 - coef) * y[..., 0:1] - y[..., 1:2])
/ (3 - coef)
* (coef ** np.arange(y.shape[-1]))
)
else:
zi = np.atleast_1d(zi)
y_out, zf = scipy.signal.lfilter(a, b, y, zi=zi.astype(y.dtype))
if return_zf:
return y_out, zf
else:
return y_out