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"""
Methods which sonify annotations for "evaluation by ear".
All functions return a raw signal at the specified sampling rate.
"""
import numpy as np
import scipy.signal
from numpy.lib.stride_tricks import as_strided
from scipy.interpolate import interp1d
from . import util
from . import chord
def clicks(times, fs, click=None, length=None):
"""Return a signal with the signal 'click' placed at each specified time
Parameters
----------
times : np.ndarray
times to place clicks, in seconds
fs : int
desired sampling rate of the output signal
click : np.ndarray
click signal, defaults to a 1 kHz blip
length : int
desired number of samples in the output signal,
defaults to ``times.max()*fs + click.shape[0] + 1``
Returns
-------
click_signal : np.ndarray
Synthesized click signal
"""
# Create default click signal
if click is None:
# 1 kHz tone, 100ms
click = np.sin(2 * np.pi * np.arange(fs * 0.1) * 1000 / (1.0 * fs))
# Exponential decay
click *= np.exp(-np.arange(fs * 0.1) / (fs * 0.01))
# Set default length
if length is None:
length = int(times.max() * fs + click.shape[0] + 1)
# Pre-allocate click signal
click_signal = np.zeros(length)
# Place clicks
for time in times:
# Compute the boundaries of the click
start = int(time * fs)
end = start + click.shape[0]
# Make sure we don't try to output past the end of the signal
if start >= length:
break
if end >= length:
click_signal[start:] = click[: length - start]
break
# Normally, just add a click here
click_signal[start:end] = click
return click_signal
def time_frequency(
gram, frequencies, times, fs, function=np.sin, length=None, n_dec=1, threshold=0.01
):
r"""Reverse synthesis of a time-frequency representation of a signal
Parameters
----------
gram : np.ndarray
``gram[n, m]`` is the magnitude of ``frequencies[n]``
from ``times[m]`` to ``times[m + 1]``
Non-positive magnitudes are interpreted as silence.
frequencies : np.ndarray
array of size ``gram.shape[0]`` denoting the frequency (in Hz) of
each row of gram
times : np.ndarray, shape= ``(gram.shape[1],)`` or ``(gram.shape[1], 2)``
Either the start time (in seconds) of each column in the gram,
or the time interval (in seconds) corresponding to each column.
fs : int
desired sampling rate of the output signal
function : function
function to use to synthesize notes, should be :math:`2\pi`-periodic
length : int
desired number of samples in the output signal,
defaults to ``times[-1]*fs``
n_dec : int
the number of decimals used to approximate each sonfied frequency.
Defaults to 1 decimal place. Higher precision will be slower.
threshold : float
optimizes synthesis to only occur for frequencies that have a
linear magnitude of at least one element in gram above the given threshold.
Returns
-------
output : np.ndarray
synthesized version of the piano roll
"""
# Convert times to intervals if necessary
time_converted = False
if times.ndim == 1:
# Convert to intervals
times = np.hstack((times[:-1, np.newaxis], times[1:, np.newaxis]))
# We'll need this to keep track of whether we should pad an interval on
time_converted = True
# Default value for length
if length is None:
length = int(np.max(times) * fs)
last_time_in_secs = float(length) / fs
if time_converted and times.shape[0] != gram.shape[1]:
times = np.vstack((times, [np.max(times), last_time_in_secs]))
if times.shape[0] != gram.shape[1]:
raise ValueError(
f"times.shape={times.shape} is incompatible with gram.shape={gram.shape}"
)
if frequencies.shape[0] != gram.shape[0]:
raise ValueError(
f"frequencies.shape={frequencies.shape} is incompatible with gram.shape={gram.shape}"
)
padding = [0, 0]
stacking = []
if times.min() > 0:
# We need to pad a silence column on to gram at the beginning
padding[0] = 1
stacking.append([0, times.min()])
stacking.append(times)
if times.max() < last_time_in_secs:
# We need to pad a silence column onto gram at the end
padding[1] = 1
stacking.append([times.max(), last_time_in_secs])
gram = np.pad(gram, ((0, 0), padding), mode="constant")
times = np.vstack(stacking)
# Identify the time intervals that have some overlap with the duration
idx = np.logical_and(times[:, 1] >= 0, times[:, 0] <= last_time_in_secs)
gram = gram[:, idx]
times = np.clip(times[idx], 0, last_time_in_secs)
n_times = times.shape[0]
# Threshold the tfgram to remove negative values
gram = np.maximum(gram, 0)
# Pre-allocate output signal
output = np.zeros(length)
if gram.shape[1] == 0:
# There are no time intervals to process, so return
# the empty signal.
return output
# Discard frequencies below threshold
freq_keep = np.max(gram, axis=1) >= threshold
gram = gram[freq_keep, :]
frequencies = frequencies[freq_keep]
# Interpolate the values in gram over the time grid.
if n_times > 1:
interpolator = interp1d(
times[:, 0] * fs,
gram[:, :n_times],
kind="previous",
bounds_error=False,
fill_value=(gram[:, 0], gram[:, -1]),
)
signal = interpolator(np.arange(length))
else:
# NOTE: This is a special case where there is only one time interval.
# scipy 1.10 and above handle this case directly with the interp1d above,
# but older scipy's do not. This is a workaround for that.
#
# In the 0.9 release, we can bump the minimum scipy to 1.10 and remove this
signal = np.tile(gram[:, 0], (1, length))
for n, frequency in enumerate(frequencies):
# Get a waveform of length samples at this frequency
wave = _fast_synthesize(frequency, n_dec, fs, function, length)
# Use a two-cycle ramp to smooth over transients
period = 2 * int(fs / frequency)
filter = np.ones(period) / period
signal_n = scipy.signal.convolve(signal[n], filter, mode="same")
# Mix the signal into the output
output[:] += wave[: len(signal_n)] * signal_n
# Normalize, but only if there's non-zero values
norm = np.abs(output).max()
if norm >= np.finfo(output.dtype).tiny:
output /= norm
return output
def _fast_synthesize(frequency, n_dec, fs, function, length):
"""Efficiently synthesize a signal.
Generate one cycle, and simulate arbitrary repetitions
using array indexing tricks.
"""
# hack so that we can ensure an integer number of periods and samples
# rounds frequency to 1st decimal, s.t. 10 * frequency will be an int
frequency = np.round(frequency, n_dec)
# Generate 10*frequency periods at this frequency
# Equivalent to n_samples = int(n_periods * fs / frequency)
# n_periods = 10*frequency is the smallest integer that guarantees
# that n_samples will be an integer, since assuming 10*frequency
# is an integer
n_samples = int(10.0**n_dec * fs)
short_signal = function(2.0 * np.pi * np.arange(n_samples) * frequency / fs)
# Calculate the number of loops we need to fill the duration
n_repeats = int(np.ceil(length / float(short_signal.shape[0])))
# Simulate tiling the short buffer by using stride tricks
long_signal = as_strided(
short_signal,
shape=(n_repeats, len(short_signal)),
strides=(0, short_signal.itemsize),
)
# Use a flatiter to simulate a long 1D buffer
return long_signal.flat
def pitch_contour(
times, frequencies, fs, amplitudes=None, function=np.sin, length=None, kind="linear"
):
r"""Sonify a pitch contour.
Parameters
----------
times : np.ndarray
time indices for each frequency measurement, in seconds
frequencies : np.ndarray
frequency measurements, in Hz.
Non-positive measurements or NaNs will be interpreted as un-voiced samples.
fs : int
desired sampling rate of the output signal
amplitudes : np.ndarray
amplitude measurements, nonnegative
defaults to ``np.ones((length,))``
function : function
function to use to synthesize notes, should be :math:`2\pi`-periodic
length : int
desired number of samples in the output signal,
defaults to ``max(times)*fs``
kind : str
Interpolation mode for the frequency and amplitude values.
See: ``scipy.interpolate.interp1d`` for valid settings.
Returns
-------
output : np.ndarray
synthesized version of the pitch contour
"""
fs = float(fs)
if length is None:
length = int(times.max() * fs)
# Squash the negative frequencies.
# wave(0) = 0, so clipping here will un-voice the corresponding instants
frequencies = np.maximum(frequencies, 0.0)
# Convert nans to zeros to unvoice
frequencies = np.nan_to_num(frequencies, copy=False)
# Build a frequency interpolator
f_interp = interp1d(
times * fs,
2 * np.pi * frequencies / fs,
kind=kind,
fill_value=0.0,
bounds_error=False,
copy=False,
)
# Estimate frequency at sample points
f_est = f_interp(np.arange(length))
if amplitudes is None:
a_est = np.ones((length,))
else:
# build an amplitude interpolator
a_interp = interp1d(
times * fs,
amplitudes,
kind=kind,
fill_value=0.0,
bounds_error=False,
copy=False,
)
a_est = a_interp(np.arange(length))
# Sonify the waveform
return a_est * function(np.cumsum(f_est))
def chroma(chromagram, times, fs, **kwargs):
"""Reverse synthesis of a chromagram (semitone matrix)
Parameters
----------
chromagram : np.ndarray, shape=(12, times.shape[0])
Chromagram matrix, where each row represents a semitone [C->Bb]
i.e., ``chromagram[3, j]`` is the magnitude of D# from ``times[j]`` to
``times[j + 1]``
times : np.ndarray, shape=(len(chord_labels),) or (len(chord_labels), 2)
Either the start time of each column in the chromagram,
or the time interval corresponding to each column.
fs : int
Sampling rate to synthesize audio data at
**kwargs
Additional keyword arguments to pass to
:func:`mir_eval.sonify.time_frequency`
Returns
-------
output : np.ndarray
Synthesized chromagram
"""
# We'll just use time_frequency with a Shepard tone-gram
# To create the Shepard tone-gram, we copy the chromagram across 7 octaves
n_octaves = 7
# starting from C2
base_note = 24
# and weight each octave by a normal distribution
# The normal distribution has mean 72 (one octave above middle C)
# and std 6 (one half octave)
mean = 72
std = 6
notes = np.arange(12 * n_octaves) + base_note
shepard_weight = np.exp(-((notes - mean) ** 2.0) / (2.0 * std**2.0))
# Copy the chromagram matrix vertically n_octaves times
gram = np.tile(chromagram.T, n_octaves).T
# This fixes issues if the supplied chromagram is int type
gram = gram.astype(float)
# Apply Sheppard weighting
gram *= shepard_weight.reshape(-1, 1)
# Compute frequencies
frequencies = 440.0 * (2.0 ** ((notes - 69) / 12.0))
return time_frequency(gram, frequencies, times, fs, **kwargs)
def chords(chord_labels, intervals, fs, **kwargs):
"""Synthesizes chord labels
Parameters
----------
chord_labels : list of str
List of chord label strings.
intervals : np.ndarray, shape=(len(chord_labels), 2)
Start and end times of each chord label
fs : int
Sampling rate to synthesize at
**kwargs
Additional keyword arguments to pass to
:func:`mir_eval.sonify.time_frequency`
Returns
-------
output : np.ndarray
Synthesized chord labels
"""
util.validate_intervals(intervals)
# Convert from labels to chroma
roots, interval_bitmaps, _ = chord.encode_many(chord_labels)
chromagram = np.array(
[
np.roll(interval_bitmap, root)
for (interval_bitmap, root) in zip(interval_bitmaps, roots)
]
).T
return chroma(chromagram, intervals, fs, **kwargs)
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