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Source code for librosa.core.time_frequency
#!/usr/bin/env python
# -*- coding: utf-8 -*-
'''Time and frequency utilities'''
import re
import warnings
import numpy as np
import six
from ..util.exceptions import ParameterError
from ..util.deprecation import Deprecated
__all__ = ['frames_to_samples', 'frames_to_time',
'samples_to_frames', 'samples_to_time',
'time_to_samples', 'time_to_frames',
'blocks_to_samples', 'blocks_to_frames',
'blocks_to_time',
'note_to_hz', 'note_to_midi',
'midi_to_hz', 'midi_to_note',
'hz_to_note', 'hz_to_midi',
'hz_to_mel', 'hz_to_octs',
'mel_to_hz',
'octs_to_hz',
'fft_frequencies',
'cqt_frequencies',
'mel_frequencies',
'tempo_frequencies',
'fourier_tempo_frequencies',
'A_weighting',
'samples_like',
'times_like']
[docs]def frames_to_samples(frames, hop_length=512, n_fft=None):
"""Converts frame indices to audio sample indices.
Parameters
----------
frames : number or np.ndarray [shape=(n,)]
frame index or vector of frame indices
hop_length : int > 0 [scalar]
number of samples between successive frames
n_fft : None or int > 0 [scalar]
Optional: length of the FFT window.
If given, time conversion will include an offset of `n_fft / 2`
to counteract windowing effects when using a non-centered STFT.
Returns
-------
times : number or np.ndarray
time (in samples) of each given frame number:
`times[i] = frames[i] * hop_length`
See Also
--------
frames_to_time : convert frame indices to time values
samples_to_frames : convert sample indices to frame indices
Examples
--------
>>> y, sr = librosa.load(librosa.util.example_audio_file())
>>> tempo, beats = librosa.beat.beat_track(y, sr=sr)
>>> beat_samples = librosa.frames_to_samples(beats)
"""
offset = 0
if n_fft is not None:
offset = int(n_fft // 2)
return (np.asanyarray(frames) * hop_length + offset).astype(int)
[docs]def samples_to_frames(samples, hop_length=512, n_fft=None):
"""Converts sample indices into STFT frames.
Examples
--------
>>> # Get the frame numbers for every 256 samples
>>> librosa.samples_to_frames(np.arange(0, 22050, 256))
array([ 0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6,
7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13,
14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20,
21, 21, 22, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27,
28, 28, 29, 29, 30, 30, 31, 31, 32, 32, 33, 33, 34, 34,
35, 35, 36, 36, 37, 37, 38, 38, 39, 39, 40, 40, 41, 41,
42, 42, 43])
Parameters
----------
samples : int or np.ndarray [shape=(n,)]
sample index or vector of sample indices
hop_length : int > 0 [scalar]
number of samples between successive frames
n_fft : None or int > 0 [scalar]
Optional: length of the FFT window.
If given, time conversion will include an offset of `- n_fft / 2`
to counteract windowing effects in STFT.
.. note:: This may result in negative frame indices.
Returns
-------
frames : int or np.ndarray [shape=(n,), dtype=int]
Frame numbers corresponding to the given times:
`frames[i] = floor( samples[i] / hop_length )`
See Also
--------
samples_to_time : convert sample indices to time values
frames_to_samples : convert frame indices to sample indices
"""
offset = 0
if n_fft is not None:
offset = int(n_fft // 2)
samples = np.asanyarray(samples)
return np.floor((samples - offset) // hop_length).astype(int)
[docs]def frames_to_time(frames, sr=22050, hop_length=512, n_fft=None):
"""Converts frame counts to time (seconds).
Parameters
----------
frames : np.ndarray [shape=(n,)]
frame index or vector of frame indices
sr : number > 0 [scalar]
audio sampling rate
hop_length : int > 0 [scalar]
number of samples between successive frames
n_fft : None or int > 0 [scalar]
Optional: length of the FFT window.
If given, time conversion will include an offset of `n_fft / 2`
to counteract windowing effects when using a non-centered STFT.
Returns
-------
times : np.ndarray [shape=(n,)]
time (in seconds) of each given frame number:
`times[i] = frames[i] * hop_length / sr`
See Also
--------
time_to_frames : convert time values to frame indices
frames_to_samples : convert frame indices to sample indices
Examples
--------
>>> y, sr = librosa.load(librosa.util.example_audio_file())
>>> tempo, beats = librosa.beat.beat_track(y, sr=sr)
>>> beat_times = librosa.frames_to_time(beats, sr=sr)
"""
samples = frames_to_samples(frames,
hop_length=hop_length,
n_fft=n_fft)
return samples_to_time(samples, sr=sr)
[docs]def time_to_frames(times, sr=22050, hop_length=512, n_fft=None):
"""Converts time stamps into STFT frames.
Parameters
----------
times : np.ndarray [shape=(n,)]
time (in seconds) or vector of time values
sr : number > 0 [scalar]
audio sampling rate
hop_length : int > 0 [scalar]
number of samples between successive frames
n_fft : None or int > 0 [scalar]
Optional: length of the FFT window.
If given, time conversion will include an offset of `- n_fft / 2`
to counteract windowing effects in STFT.
.. note:: This may result in negative frame indices.
Returns
-------
frames : np.ndarray [shape=(n,), dtype=int]
Frame numbers corresponding to the given times:
`frames[i] = floor( times[i] * sr / hop_length )`
See Also
--------
frames_to_time : convert frame indices to time values
time_to_samples : convert time values to sample indices
Examples
--------
Get the frame numbers for every 100ms
>>> librosa.time_to_frames(np.arange(0, 1, 0.1),
... sr=22050, hop_length=512)
array([ 0, 4, 8, 12, 17, 21, 25, 30, 34, 38])
"""
samples = time_to_samples(times, sr=sr)
return samples_to_frames(samples, hop_length=hop_length, n_fft=n_fft)
[docs]def time_to_samples(times, sr=22050):
'''Convert timestamps (in seconds) to sample indices.
Parameters
----------
times : number or np.ndarray
Time value or array of time values (in seconds)
sr : number > 0
Sampling rate
Returns
-------
samples : int or np.ndarray [shape=times.shape, dtype=int]
Sample indices corresponding to values in `times`
See Also
--------
time_to_frames : convert time values to frame indices
samples_to_time : convert sample indices to time values
Examples
--------
>>> librosa.time_to_samples(np.arange(0, 1, 0.1), sr=22050)
array([ 0, 2205, 4410, 6615, 8820, 11025, 13230, 15435,
17640, 19845])
'''
return (np.asanyarray(times) * sr).astype(int)
[docs]def samples_to_time(samples, sr=22050):
'''Convert sample indices to time (in seconds).
Parameters
----------
samples : np.ndarray
Sample index or array of sample indices
sr : number > 0
Sampling rate
Returns
-------
times : np.ndarray [shape=samples.shape]
Time values corresponding to `samples` (in seconds)
See Also
--------
samples_to_frames : convert sample indices to frame indices
time_to_samples : convert time values to sample indices
Examples
--------
Get timestamps corresponding to every 512 samples
>>> librosa.samples_to_time(np.arange(0, 22050, 512))
array([ 0. , 0.023, 0.046, 0.07 , 0.093, 0.116, 0.139,
0.163, 0.186, 0.209, 0.232, 0.255, 0.279, 0.302,
0.325, 0.348, 0.372, 0.395, 0.418, 0.441, 0.464,
0.488, 0.511, 0.534, 0.557, 0.58 , 0.604, 0.627,
0.65 , 0.673, 0.697, 0.72 , 0.743, 0.766, 0.789,
0.813, 0.836, 0.859, 0.882, 0.906, 0.929, 0.952,
0.975, 0.998])
'''
return np.asanyarray(samples) / float(sr)
[docs]def blocks_to_frames(blocks, block_length):
'''Convert block indices to frame indices
Parameters
----------
blocks : np.ndarray
Block index or array of block indices
block_length : int > 0
The number of frames per block
Returns
-------
frames : np.ndarray [shape=samples.shape, dtype=int]
The index or indices of frames corresponding to the beginning
of each provided block.
See Also
--------
blocks_to_samples
blocks_to_time
Examples
--------
Get frame indices for each block in a stream
>>> filename = librosa.util.example_audio_file()
>>> sr = librosa.get_samplerate(filename)
>>> stream = librosa.stream(filename, block_length=16,
... frame_length=2048, hop_length=512)
>>> for n, y in enumerate(stream):
... n_frame = librosa.blocks_to_frames(n, block_length=16)
'''
return block_length * np.asanyarray(blocks)
[docs]def blocks_to_samples(blocks, block_length, hop_length):
'''Convert block indices to sample indices
Parameters
----------
blocks : np.ndarray
Block index or array of block indices
block_length : int > 0
The number of frames per block
hop_length : int > 0
The number of samples to advance between frames
Returns
-------
samples : np.ndarray [shape=samples.shape, dtype=int]
The index or indices of samples corresponding to the beginning
of each provided block.
Note that these correspond to the *first* sample index in
each block, and are not frame-centered.
See Also
--------
blocks_to_frames
blocks_to_time
Examples
--------
Get sample indices for each block in a stream
>>> filename = librosa.util.example_audio_file()
>>> sr = librosa.get_samplerate(filename)
>>> stream = librosa.stream(filename, block_length=16,
... frame_length=2048, hop_length=512)
>>> for n, y in enumerate(stream):
... n_sample = librosa.blocks_to_samples(n, block_length=16,
... hop_length=512)
'''
frames = blocks_to_frames(blocks, block_length)
return frames_to_samples(frames, hop_length=hop_length)
[docs]def blocks_to_time(blocks, block_length, hop_length, sr):
'''Convert block indices to time (in seconds)
Parameters
----------
blocks : np.ndarray
Block index or array of block indices
block_length : int > 0
The number of frames per block
hop_length : int > 0
The number of samples to advance between frames
sr : int > 0
The sampling rate (samples per second)
Returns
-------
times : np.ndarray [shape=samples.shape]
The time index or indices (in seconds) corresponding to the
beginning of each provided block.
Note that these correspond to the time of the *first* sample
in each block, and are not frame-centered.
See Also
--------
blocks_to_frames
blocks_to_samples
Examples
--------
Get time indices for each block in a stream
>>> filename = librosa.util.example_audio_file()
>>> sr = librosa.get_samplerate(filename)
>>> stream = librosa.stream(filename, block_length=16,
... frame_length=2048, hop_length=512)
>>> for n, y in enumerate(stream):
... n_time = librosa.blocks_to_time(n, block_length=16,
... hop_length=512, sr=sr)
'''
samples = blocks_to_samples(blocks, block_length, hop_length)
return samples_to_time(samples, sr=sr)
[docs]def note_to_hz(note, **kwargs):
'''Convert one or more note names to frequency (Hz)
Examples
--------
>>> # Get the frequency of a note
>>> librosa.note_to_hz('C')
array([ 16.352])
>>> # Or multiple notes
>>> librosa.note_to_hz(['A3', 'A4', 'A5'])
array([ 220., 440., 880.])
>>> # Or notes with tuning deviations
>>> librosa.note_to_hz('C2-32', round_midi=False)
array([ 64.209])
Parameters
----------
note : str or iterable of str
One or more note names to convert
kwargs : additional keyword arguments
Additional parameters to `note_to_midi`
Returns
-------
frequencies : number or np.ndarray [shape=(len(note),)]
Array of frequencies (in Hz) corresponding to `note`
See Also
--------
midi_to_hz
note_to_midi
hz_to_note
'''
return midi_to_hz(note_to_midi(note, **kwargs))
[docs]def note_to_midi(note, round_midi=True):
'''Convert one or more spelled notes to MIDI number(s).
Notes may be spelled out with optional accidentals or octave numbers.
The leading note name is case-insensitive.
Sharps are indicated with ``#``, flats may be indicated with ``!`` or ``b``.
Parameters
----------
note : str or iterable of str
One or more note names.
round_midi : bool
- If `True`, allow for fractional midi notes
- Otherwise, round cent deviations to the nearest note
Returns
-------
midi : float or np.array
Midi note numbers corresponding to inputs.
Raises
------
ParameterError
If the input is not in valid note format
See Also
--------
midi_to_note
note_to_hz
Examples
--------
>>> librosa.note_to_midi('C')
12
>>> librosa.note_to_midi('C#3')
49
>>> librosa.note_to_midi('f4')
65
>>> librosa.note_to_midi('Bb-1')
10
>>> librosa.note_to_midi('A!8')
116
>>> # Lists of notes also work
>>> librosa.note_to_midi(['C', 'E', 'G'])
array([12, 16, 19])
'''
if not isinstance(note, six.string_types):
return np.array([note_to_midi(n, round_midi=round_midi) for n in note])
pitch_map = {'C': 0, 'D': 2, 'E': 4, 'F': 5, 'G': 7, 'A': 9, 'B': 11}
acc_map = {'#': 1, '': 0, 'b': -1, '!': -1}
match = re.match(r'^(?P<note>[A-Ga-g])'
r'(?P<accidental>[#b!]*)'
r'(?P<octave>[+-]?\d+)?'
r'(?P<cents>[+-]\d+)?$',
note)
if not match:
raise ParameterError('Improper note format: {:s}'.format(note))
pitch = match.group('note').upper()
offset = np.sum([acc_map[o] for o in match.group('accidental')])
octave = match.group('octave')
cents = match.group('cents')
if not octave:
octave = 0
else:
octave = int(octave)
if not cents:
cents = 0
else:
cents = int(cents) * 1e-2
note_value = 12 * (octave + 1) + pitch_map[pitch] + offset + cents
if round_midi:
note_value = int(np.round(note_value))
return note_value
[docs]def midi_to_note(midi, octave=True, cents=False):
'''Convert one or more MIDI numbers to note strings.
MIDI numbers will be rounded to the nearest integer.
Notes will be of the format 'C0', 'C#0', 'D0', ...
Examples
--------
>>> librosa.midi_to_note(0)
'C-1'
>>> librosa.midi_to_note(37)
'C#2'
>>> librosa.midi_to_note(-2)
'A#-2'
>>> librosa.midi_to_note(104.7)
'A7'
>>> librosa.midi_to_note(104.7, cents=True)
'A7-30'
>>> librosa.midi_to_note(list(range(12, 24)))
['C0', 'C#0', 'D0', 'D#0', 'E0', 'F0', 'F#0', 'G0', 'G#0', 'A0', 'A#0', 'B0']
Parameters
----------
midi : int or iterable of int
Midi numbers to convert.
octave: bool
If True, include the octave number
cents: bool
If true, cent markers will be appended for fractional notes.
Eg, `midi_to_note(69.3, cents=True)` == `A4+03`
Returns
-------
notes : str or iterable of str
Strings describing each midi note.
Raises
------
ParameterError
if `cents` is True and `octave` is False
See Also
--------
midi_to_hz
note_to_midi
hz_to_note
'''
if cents and not octave:
raise ParameterError('Cannot encode cents without octave information.')
if not np.isscalar(midi):
return [midi_to_note(x, octave=octave, cents=cents) for x in midi]
note_map = ['C', 'C#', 'D', 'D#',
'E', 'F', 'F#', 'G',
'G#', 'A', 'A#', 'B']
note_num = int(np.round(midi))
note_cents = int(100 * np.around(midi - note_num, 2))
note = note_map[note_num % 12]
if octave:
note = '{:s}{:0d}'.format(note, int(note_num / 12) - 1)
if cents:
note = '{:s}{:+02d}'.format(note, note_cents)
return note
[docs]def midi_to_hz(notes):
"""Get the frequency (Hz) of MIDI note(s)
Examples
--------
>>> librosa.midi_to_hz(36)
65.406
>>> librosa.midi_to_hz(np.arange(36, 48))
array([ 65.406, 69.296, 73.416, 77.782, 82.407,
87.307, 92.499, 97.999, 103.826, 110. ,
116.541, 123.471])
Parameters
----------
notes : int or np.ndarray [shape=(n,), dtype=int]
midi number(s) of the note(s)
Returns
-------
frequency : number or np.ndarray [shape=(n,), dtype=float]
frequency (frequencies) of `notes` in Hz
See Also
--------
hz_to_midi
note_to_hz
"""
return 440.0 * (2.0 ** ((np.asanyarray(notes) - 69.0)/12.0))
[docs]def hz_to_midi(frequencies):
"""Get MIDI note number(s) for given frequencies
Examples
--------
>>> librosa.hz_to_midi(60)
34.506
>>> librosa.hz_to_midi([110, 220, 440])
array([ 45., 57., 69.])
Parameters
----------
frequencies : float or np.ndarray [shape=(n,), dtype=float]
frequencies to convert
Returns
-------
note_nums : number or np.ndarray [shape=(n,), dtype=float]
MIDI notes to `frequencies`
See Also
--------
midi_to_hz
note_to_midi
hz_to_note
"""
return 12 * (np.log2(np.asanyarray(frequencies)) - np.log2(440.0)) + 69
[docs]def hz_to_note(frequencies, **kwargs):
'''Convert one or more frequencies (in Hz) to the nearest note names.
Parameters
----------
frequencies : float or iterable of float
Input frequencies, specified in Hz
kwargs : additional keyword arguments
Arguments passed through to `midi_to_note`
Returns
-------
notes : list of str
`notes[i]` is the closest note name to `frequency[i]`
(or `frequency` if the input is scalar)
See Also
--------
hz_to_midi
midi_to_note
note_to_hz
Examples
--------
Get a single note name for a frequency
>>> librosa.hz_to_note(440.0)
['A5']
Get multiple notes with cent deviation
>>> librosa.hz_to_note([32, 64], cents=True)
['C1-38', 'C2-38']
Get multiple notes, but suppress octave labels
>>> librosa.hz_to_note(440.0 * (2.0 ** np.linspace(0, 1, 12)),
... octave=False)
['A', 'A#', 'B', 'C', 'C#', 'D', 'E', 'F', 'F#', 'G', 'G#', 'A']
'''
return midi_to_note(hz_to_midi(frequencies), **kwargs)
[docs]def hz_to_mel(frequencies, htk=False):
"""Convert Hz to Mels
Examples
--------
>>> librosa.hz_to_mel(60)
0.9
>>> librosa.hz_to_mel([110, 220, 440])
array([ 1.65, 3.3 , 6.6 ])
Parameters
----------
frequencies : number or np.ndarray [shape=(n,)] , float
scalar or array of frequencies
htk : bool
use HTK formula instead of Slaney
Returns
-------
mels : number or np.ndarray [shape=(n,)]
input frequencies in Mels
See Also
--------
mel_to_hz
"""
frequencies = np.asanyarray(frequencies)
if htk:
return 2595.0 * np.log10(1.0 + frequencies / 700.0)
# Fill in the linear part
f_min = 0.0
f_sp = 200.0 / 3
mels = (frequencies - f_min) / f_sp
# Fill in the log-scale part
min_log_hz = 1000.0 # beginning of log region (Hz)
min_log_mel = (min_log_hz - f_min) / f_sp # same (Mels)
logstep = np.log(6.4) / 27.0 # step size for log region
if frequencies.ndim:
# If we have array data, vectorize
log_t = (frequencies >= min_log_hz)
mels[log_t] = min_log_mel + np.log(frequencies[log_t]/min_log_hz) / logstep
elif frequencies >= min_log_hz:
# If we have scalar data, heck directly
mels = min_log_mel + np.log(frequencies / min_log_hz) / logstep
return mels
[docs]def mel_to_hz(mels, htk=False):
"""Convert mel bin numbers to frequencies
Examples
--------
>>> librosa.mel_to_hz(3)
200.
>>> librosa.mel_to_hz([1,2,3,4,5])
array([ 66.667, 133.333, 200. , 266.667, 333.333])
Parameters
----------
mels : np.ndarray [shape=(n,)], float
mel bins to convert
htk : bool
use HTK formula instead of Slaney
Returns
-------
frequencies : np.ndarray [shape=(n,)]
input mels in Hz
See Also
--------
hz_to_mel
"""
mels = np.asanyarray(mels)
if htk:
return 700.0 * (10.0**(mels / 2595.0) - 1.0)
# Fill in the linear scale
f_min = 0.0
f_sp = 200.0 / 3
freqs = f_min + f_sp * mels
# And now the nonlinear scale
min_log_hz = 1000.0 # beginning of log region (Hz)
min_log_mel = (min_log_hz - f_min) / f_sp # same (Mels)
logstep = np.log(6.4) / 27.0 # step size for log region
if mels.ndim:
# If we have vector data, vectorize
log_t = (mels >= min_log_mel)
freqs[log_t] = min_log_hz * np.exp(logstep * (mels[log_t] - min_log_mel))
elif mels >= min_log_mel:
# If we have scalar data, check directly
freqs = min_log_hz * np.exp(logstep * (mels - min_log_mel))
return freqs
[docs]def hz_to_octs(frequencies, tuning=0.0, bins_per_octave=12, A440=Deprecated()):
"""Convert frequencies (Hz) to (fractional) octave numbers.
Examples
--------
>>> librosa.hz_to_octs(440.0)
4.
>>> librosa.hz_to_octs([32, 64, 128, 256])
array([ 0.219, 1.219, 2.219, 3.219])
Parameters
----------
frequencies : number >0 or np.ndarray [shape=(n,)] or float
scalar or vector of frequencies
tuning : float
Tuning deviation from A440 in (fractional) bins per octave.
bins_per_octave : int > 0
Number of bins per octave.
A440 : float <DEPRECATED>
frequency of A440 (in Hz)
.. note:: This parameter is deprecated in 0.7.1 and will be removed
in version 0.8.0. Use `tuning=` instead.
Returns
-------
octaves : number or np.ndarray [shape=(n,)]
octave number for each frequency
See Also
--------
octs_to_hz
"""
if isinstance(A440, Deprecated):
A440 = 440.0 * 2.0**(tuning / bins_per_octave)
else:
warnings.warn('Parameter A440={} in hz_to_octs is deprecated in 0.7.1. '
'It will be removed in 0.8.0. '
'Use tuning= instead.'.format(A440), DeprecationWarning)
return np.log2(np.asanyarray(frequencies) / (float(A440) / 16))
[docs]def octs_to_hz(octs, tuning=0.0, bins_per_octave=12, A440=Deprecated()):
"""Convert octaves numbers to frequencies.
Octaves are counted relative to A.
Examples
--------
>>> librosa.octs_to_hz(1)
55.
>>> librosa.octs_to_hz([-2, -1, 0, 1, 2])
array([ 6.875, 13.75 , 27.5 , 55. , 110. ])
Parameters
----------
octaves : np.ndarray [shape=(n,)] or float
octave number for each frequency
tuning : float
Tuning deviation from A440 in (fractional) bins per octave.
bins_per_octave : int > 0
Number of bins per octave.
A440 : float <DEPRECATED>
frequency of A440
Returns
-------
frequencies : number or np.ndarray [shape=(n,)]
scalar or vector of frequencies
See Also
--------
hz_to_octs
"""
if isinstance(A440, Deprecated):
A440 = 440.0 * 2.0**(tuning / bins_per_octave)
else:
warnings.warn('Parameter A440={} in octs_to_hz is deprecated in 0.7.1. '
'It will be removed in 0.8.0. '
'Use tuning= instead.'.format(A440), DeprecationWarning)
return (float(A440) / 16)*(2.0**np.asanyarray(octs))
[docs]def fft_frequencies(sr=22050, n_fft=2048):
'''Alternative implementation of `np.fft.fftfreq`
Parameters
----------
sr : number > 0 [scalar]
Audio sampling rate
n_fft : int > 0 [scalar]
FFT window size
Returns
-------
freqs : np.ndarray [shape=(1 + n_fft/2,)]
Frequencies `(0, sr/n_fft, 2*sr/n_fft, ..., sr/2)`
Examples
--------
>>> librosa.fft_frequencies(sr=22050, n_fft=16)
array([ 0. , 1378.125, 2756.25 , 4134.375,
5512.5 , 6890.625, 8268.75 , 9646.875, 11025. ])
'''
return np.linspace(0,
float(sr) / 2,
int(1 + n_fft//2),
endpoint=True)
[docs]def cqt_frequencies(n_bins, fmin, bins_per_octave=12, tuning=0.0):
"""Compute the center frequencies of Constant-Q bins.
Examples
--------
>>> # Get the CQT frequencies for 24 notes, starting at C2
>>> librosa.cqt_frequencies(24, fmin=librosa.note_to_hz('C2'))
array([ 65.406, 69.296, 73.416, 77.782, 82.407, 87.307,
92.499, 97.999, 103.826, 110. , 116.541, 123.471,
130.813, 138.591, 146.832, 155.563, 164.814, 174.614,
184.997, 195.998, 207.652, 220. , 233.082, 246.942])
Parameters
----------
n_bins : int > 0 [scalar]
Number of constant-Q bins
fmin : float > 0 [scalar]
Minimum frequency
bins_per_octave : int > 0 [scalar]
Number of bins per octave
tuning : float
Deviation from A440 tuning in fractional bins
Returns
-------
frequencies : np.ndarray [shape=(n_bins,)]
Center frequency for each CQT bin
"""
correction = 2.0**(float(tuning) / bins_per_octave)
frequencies = 2.0**(np.arange(0, n_bins, dtype=float) / bins_per_octave)
return correction * fmin * frequencies
[docs]def mel_frequencies(n_mels=128, fmin=0.0, fmax=11025.0, htk=False):
"""Compute an array of acoustic frequencies tuned to the mel scale.
The mel scale is a quasi-logarithmic function of acoustic frequency
designed such that perceptually similar pitch intervals (e.g. octaves)
appear equal in width over the full hearing range.
Because the definition of the mel scale is conditioned by a finite number
of subjective psychoaoustical experiments, several implementations coexist
in the audio signal processing literature [1]_. By default, librosa replicates
the behavior of the well-established MATLAB Auditory Toolbox of Slaney [2]_.
According to this default implementation, the conversion from Hertz to mel is
linear below 1 kHz and logarithmic above 1 kHz. Another available implementation
replicates the Hidden Markov Toolkit [3]_ (HTK) according to the following formula:
`mel = 2595.0 * np.log10(1.0 + f / 700.0).`
The choice of implementation is determined by the `htk` keyword argument: setting
`htk=False` leads to the Auditory toolbox implementation, whereas setting it `htk=True`
leads to the HTK implementation.
.. [1] Umesh, S., Cohen, L., & Nelson, D. Fitting the mel scale.
In Proc. International Conference on Acoustics, Speech, and Signal Processing
(ICASSP), vol. 1, pp. 217-220, 1998.
.. [2] Slaney, M. Auditory Toolbox: A MATLAB Toolbox for Auditory
Modeling Work. Technical Report, version 2, Interval Research Corporation, 1998.
.. [3] Young, S., Evermann, G., Gales, M., Hain, T., Kershaw, D., Liu, X.,
Moore, G., Odell, J., Ollason, D., Povey, D., Valtchev, V., & Woodland, P.
The HTK book, version 3.4. Cambridge University, March 2009.
See Also
--------
hz_to_mel
mel_to_hz
librosa.feature.melspectrogram
librosa.feature.mfcc
Parameters
----------
n_mels : int > 0 [scalar]
Number of mel bins.
fmin : float >= 0 [scalar]
Minimum frequency (Hz).
fmax : float >= 0 [scalar]
Maximum frequency (Hz).
htk : bool
If True, use HTK formula to convert Hz to mel.
Otherwise (False), use Slaney's Auditory Toolbox.
Returns
-------
bin_frequencies : ndarray [shape=(n_mels,)]
Vector of n_mels frequencies in Hz which are uniformly spaced on the Mel
axis.
Examples
--------
>>> librosa.mel_frequencies(n_mels=40)
array([ 0. , 85.317, 170.635, 255.952,
341.269, 426.586, 511.904, 597.221,
682.538, 767.855, 853.173, 938.49 ,
1024.856, 1119.114, 1222.042, 1334.436,
1457.167, 1591.187, 1737.532, 1897.337,
2071.84 , 2262.393, 2470.47 , 2697.686,
2945.799, 3216.731, 3512.582, 3835.643,
4188.417, 4573.636, 4994.285, 5453.621,
5955.205, 6502.92 , 7101.009, 7754.107,
8467.272, 9246.028, 10096.408, 11025. ])
"""
# 'Center freqs' of mel bands - uniformly spaced between limits
min_mel = hz_to_mel(fmin, htk=htk)
max_mel = hz_to_mel(fmax, htk=htk)
mels = np.linspace(min_mel, max_mel, n_mels)
return mel_to_hz(mels, htk=htk)
[docs]def tempo_frequencies(n_bins, hop_length=512, sr=22050):
'''Compute the frequencies (in beats per minute) corresponding
to an onset auto-correlation or tempogram matrix.
Parameters
----------
n_bins : int > 0
The number of lag bins
hop_length : int > 0
The number of samples between each bin
sr : number > 0
The audio sampling rate
Returns
-------
bin_frequencies : ndarray [shape=(n_bins,)]
vector of bin frequencies measured in BPM.
.. note:: `bin_frequencies[0] = +np.inf` corresponds to 0-lag
Examples
--------
Get the tempo frequencies corresponding to a 384-bin (8-second) tempogram
>>> librosa.tempo_frequencies(384)
array([ inf, 2583.984, 1291.992, ..., 6.782,
6.764, 6.747])
'''
bin_frequencies = np.zeros(int(n_bins), dtype=np.float)
bin_frequencies[0] = np.inf
bin_frequencies[1:] = 60.0 * sr / (hop_length * np.arange(1.0, n_bins))
return bin_frequencies
[docs]def fourier_tempo_frequencies(sr=22050, win_length=384, hop_length=512):
'''Compute the frequencies (in beats per minute) corresponding
to a Fourier tempogram matrix.
Parameters
----------
sr : number > 0
The audio sampling rate
win_length : int > 0
The number of frames per analysis window
hop_length : int > 0
The number of samples between each bin
Returns
-------
bin_frequencies : ndarray [shape=(win_length // 2 + 1 ,)]
vector of bin frequencies measured in BPM.
Examples
--------
Get the tempo frequencies corresponding to a 384-bin (8-second) tempogram
>>> librosa.fourier_tempo_frequencies(384)
array([ 0. , 0.117, 0.234, ..., 22.266, 22.383, 22.5 ])
'''
# sr / hop_length gets the frame rate
# multiplying by 60 turns frames / sec into frames / minute
return fft_frequencies(sr=sr * 60 / float(hop_length), n_fft=win_length)
# A-weighting should be capitalized: suppress the naming warning
[docs]def A_weighting(frequencies, min_db=-80.0): # pylint: disable=invalid-name
'''Compute the A-weighting of a set of frequencies.
Parameters
----------
frequencies : scalar or np.ndarray [shape=(n,)]
One or more frequencies (in Hz)
min_db : float [scalar] or None
Clip weights below this threshold.
If `None`, no clipping is performed.
Returns
-------
A_weighting : scalar or np.ndarray [shape=(n,)]
`A_weighting[i]` is the A-weighting of `frequencies[i]`
See Also
--------
perceptual_weighting
Examples
--------
Get the A-weighting for CQT frequencies
>>> import matplotlib.pyplot as plt
>>> freqs = librosa.cqt_frequencies(108, librosa.note_to_hz('C1'))
>>> aw = librosa.A_weighting(freqs)
>>> plt.plot(freqs, aw)
>>> plt.xlabel('Frequency (Hz)')
>>> plt.ylabel('Weighting (log10)')
>>> plt.title('A-Weighting of CQT frequencies')
>>> plt.show()
'''
# Vectorize to make our lives easier
frequencies = np.asanyarray(frequencies)
# Pre-compute squared frequency
f_sq = frequencies**2.0
const = np.array([12200, 20.6, 107.7, 737.9])**2.0
weights = 2.0 + 20.0 * (np.log10(const[0]) + 4 * np.log10(frequencies)
- np.log10(f_sq + const[0])
- np.log10(f_sq + const[1])
- 0.5 * np.log10(f_sq + const[2])
- 0.5 * np.log10(f_sq + const[3]))
if min_db is not None:
weights = np.maximum(min_db, weights)
return weights
[docs]def times_like(X, sr=22050, hop_length=512, n_fft=None, axis=-1):
"""Return an array of time values to match the time axis from a feature matrix.
Parameters
----------
X : np.ndarray or scalar
- If ndarray, X is a feature matrix, e.g. STFT, chromagram, or mel spectrogram.
- If scalar, X represents the number of frames.
sr : number > 0 [scalar]
audio sampling rate
hop_length : int > 0 [scalar]
number of samples between successive frames
n_fft : None or int > 0 [scalar]
Optional: length of the FFT window.
If given, time conversion will include an offset of `n_fft / 2`
to counteract windowing effects when using a non-centered STFT.
axis : int [scalar]
The axis representing the time axis of X.
By default, the last axis (-1) is taken.
Returns
-------
times : np.ndarray [shape=(n,)]
ndarray of times (in seconds) corresponding to each frame of X.
See Also
--------
samples_like : Return an array of sample indices to match the time axis from a feature matrix.
Examples
--------
Provide a feature matrix input:
>>> y, sr = librosa.load(librosa.util.example_audio_file())
>>> X = librosa.stft(y)
>>> times = librosa.times_like(X)
>>> times
array([ 0.00000000e+00, 2.32199546e-02, 4.64399093e-02, ...,
6.13935601e+01, 6.14167800e+01, 6.14400000e+01])
Provide a scalar input:
>>> n_frames = 2647
>>> times = librosa.times_like(n_frames)
>>> times
array([ 0.00000000e+00, 2.32199546e-02, 4.64399093e-02, ...,
6.13935601e+01, 6.14167800e+01, 6.14400000e+01])
"""
samples = samples_like(X, hop_length=hop_length, n_fft=n_fft, axis=axis)
return samples_to_time(samples, sr=sr)
[docs]def samples_like(X, hop_length=512, n_fft=None, axis=-1):
"""Return an array of sample indices to match the time axis from a feature matrix.
Parameters
----------
X : np.ndarray or scalar
- If ndarray, X is a feature matrix, e.g. STFT, chromagram, or mel spectrogram.
- If scalar, X represents the number of frames.
hop_length : int > 0 [scalar]
number of samples between successive frames
n_fft : None or int > 0 [scalar]
Optional: length of the FFT window.
If given, time conversion will include an offset of `n_fft / 2`
to counteract windowing effects when using a non-centered STFT.
axis : int [scalar]
The axis representing the time axis of X.
By default, the last axis (-1) is taken.
Returns
-------
samples : np.ndarray [shape=(n,)]
ndarray of sample indices corresponding to each frame of X.
See Also
--------
times_like : Return an array of time values to match the time axis from a feature matrix.
Examples
--------
Provide a feature matrix input:
>>> y, sr = librosa.load(librosa.util.example_audio_file())
>>> X = librosa.stft(y)
>>> samples = librosa.samples_like(X)
>>> samples
array([ 0, 512, 1024, ..., 1353728, 1354240, 1354752])
Provide a scalar input:
>>> n_frames = 2647
>>> samples = librosa.samples_like(n_frames)
>>> samples
array([ 0, 512, 1024, ..., 1353728, 1354240, 1354752])
"""
if np.isscalar(X):
frames = np.arange(X)
else:
frames = np.arange(X.shape[axis])
return frames_to_samples(frames, hop_length=hop_length, n_fft=n_fft)