#!/usr/bin/env python # -*- coding: utf-8 -*- """Core IO, DSP and utility functions.""" from __future__ import annotations import os import pathlib import warnings import soundfile as sf import audioread import numpy as np import scipy import scipy.signal import soxr import lazy_loader as lazy from numba import jit, stencil, guvectorize from .fft import get_fftlib from .convert import frames_to_samples, time_to_samples from .._cache import cache from .. import util from ..util.exceptions import ParameterError from ..util.decorators import deprecated from ..util.deprecation import Deprecated, rename_kw from .._typing import _FloatLike_co, _IntLike_co, _SequenceLike from typing import Any, BinaryIO, Callable, Generator, Optional, Tuple, Union, List from numpy.typing import DTypeLike, ArrayLike # Lazy-load optional dependencies samplerate = lazy.load("samplerate") resampy = lazy.load("resampy") __all__ = [ "load", "stream", "to_mono", "resample", "get_duration", "get_samplerate", "autocorrelate", "lpc", "zero_crossings", "clicks", "tone", "chirp", "mu_compress", "mu_expand", ] # -- CORE ROUTINES --# # Load should never be cached, since we cannot verify that the contents of # 'path' are unchanged across calls. def load( path: Union[ str, int, os.PathLike[Any], sf.SoundFile, audioread.AudioFile, BinaryIO ], *, sr: Optional[float] = 22050, mono: bool = True, offset: float = 0.0, duration: Optional[float] = None, dtype: DTypeLike = np.float32, res_type: str = "soxr_hq", ) -> Tuple[np.ndarray, Union[int, float]]: """Load an audio file as a floating point time series. Audio will be automatically resampled to the given rate (default ``sr=22050``). To preserve the native sampling rate of the file, use ``sr=None``. Parameters ---------- path : string, int, pathlib.Path, soundfile.SoundFile, audioread object, or file-like object path to the input file. Any codec supported by `soundfile` or `audioread` will work. Any string file paths, or any object implementing Python's file interface (e.g. `pathlib.Path`) are supported as `path`. If the codec is supported by `soundfile`, then `path` can also be an open file descriptor (int) or an existing `soundfile.SoundFile` object. Pre-constructed audioread decoders are also supported here, see the example below. This can be used, for example, to force a specific decoder rather than relying upon audioread to select one for you. .. warning:: audioread support is deprecated as of version 0.10.0. audioread support be removed in version 1.0. sr : number > 0 [scalar] target sampling rate 'None' uses the native sampling rate mono : bool convert signal to mono offset : float start reading after this time (in seconds) duration : float only load up to this much audio (in seconds) dtype : numeric type data type of ``y`` res_type : str resample type (see note) .. note:: By default, this uses `soxr`'s high-quality mode ('HQ'). For alternative resampling modes, see `resample` .. note:: `audioread` may truncate the precision of the audio data to 16 bits. See :ref:`ioformats` for alternate loading methods. Returns ------- y : np.ndarray [shape=(n,) or (..., n)] audio time series. Multi-channel is supported. sr : number > 0 [scalar] sampling rate of ``y`` Examples -------- >>> # Load an ogg vorbis file >>> filename = librosa.ex('trumpet') >>> y, sr = librosa.load(filename) >>> y array([-1.407e-03, -4.461e-04, ..., -3.042e-05, 1.277e-05], dtype=float32) >>> sr 22050 >>> # Load a file and resample to 11 KHz >>> filename = librosa.ex('trumpet') >>> y, sr = librosa.load(filename, sr=11025) >>> y array([-8.746e-04, -3.363e-04, ..., -1.301e-05, 0.000e+00], dtype=float32) >>> sr 11025 >>> # Load 5 seconds of a file, starting 15 seconds in >>> filename = librosa.ex('brahms') >>> y, sr = librosa.load(filename, offset=15.0, duration=5.0) >>> y array([0.146, 0.144, ..., 0.128, 0.015], dtype=float32) >>> sr 22050 >>> # Load using an already open SoundFile object >>> import soundfile >>> sfo = soundfile.SoundFile(librosa.ex('brahms')) >>> y, sr = librosa.load(sfo) >>> # Load using an already open audioread object >>> import audioread.ffdec # Use ffmpeg decoder >>> aro = audioread.ffdec.FFmpegAudioFile(librosa.ex('brahms')) >>> y, sr = librosa.load(aro) """ if isinstance(path, tuple(audioread.available_backends())): # Force the audioread loader if we have a reader object already y, sr_native = __audioread_load(path, offset, duration, dtype) else: # Otherwise try soundfile first, and then fall back if necessary try: y, sr_native = __soundfile_load(path, offset, duration, dtype) except sf.SoundFileRuntimeError as exc: # If soundfile failed, try audioread instead if isinstance(path, (str, pathlib.PurePath)): warnings.warn( "PySoundFile failed. Trying audioread instead.", stacklevel=2 ) y, sr_native = __audioread_load(path, offset, duration, dtype) else: raise exc # Final cleanup for dtype and contiguity if mono: y = to_mono(y) if sr is not None: y = resample(y, orig_sr=sr_native, target_sr=sr, res_type=res_type) else: sr = sr_native return y, sr def __soundfile_load(path, offset, duration, dtype): """Load an audio buffer using soundfile.""" if isinstance(path, sf.SoundFile): # If the user passed an existing soundfile object, # we can use it directly context = path else: # Otherwise, create the soundfile object context = sf.SoundFile(path) with context as sf_desc: sr_native = sf_desc.samplerate if offset: # Seek to the start of the target read sf_desc.seek(int(offset * sr_native)) if duration is not None: frame_duration = int(duration * sr_native) else: frame_duration = -1 # Load the target number of frames, and transpose to match librosa form y = sf_desc.read(frames=frame_duration, dtype=dtype, always_2d=False).T return y, sr_native @deprecated(version="0.10.0", version_removed="1.0") def __audioread_load(path, offset, duration, dtype: DTypeLike): """Load an audio buffer using audioread. This loads one block at a time, and then concatenates the results. """ buf = [] if isinstance(path, tuple(audioread.available_backends())): # If we have an audioread object already, don't bother opening reader = path else: # If the input was not an audioread object, try to open it reader = audioread.audio_open(path) with reader as input_file: sr_native = input_file.samplerate n_channels = input_file.channels s_start = int(sr_native * offset) * n_channels if duration is None: s_end = np.inf else: s_end = s_start + (int(sr_native * duration) * n_channels) n = 0 for frame in input_file: frame = util.buf_to_float(frame, dtype=dtype) n_prev = n n = n + len(frame) if n < s_start: # offset is after the current frame # keep reading continue if s_end < n_prev: # we're off the end. stop reading break if s_end < n: # the end is in this frame. crop. frame = frame[: int(s_end - n_prev)] # pragma: no cover if n_prev <= s_start <= n: # beginning is in this frame frame = frame[(s_start - n_prev) :] # tack on the current frame buf.append(frame) if buf: y = np.concatenate(buf) if n_channels > 1: y = y.reshape((-1, n_channels)).T else: y = np.empty(0, dtype=dtype) return y, sr_native def stream( path: Union[str, int, sf.SoundFile, BinaryIO], *, block_length: int, frame_length: int, hop_length: int, mono: bool = True, offset: float = 0.0, duration: Optional[float] = None, fill_value: Optional[float] = None, dtype: DTypeLike = np.float32, ) -> Generator[np.ndarray, None, None]: """Stream audio in fixed-length buffers. This is primarily useful for processing large files that won't fit entirely in memory at once. Instead of loading the entire audio signal into memory (as in `load`, this function produces *blocks* of audio spanning a fixed number of frames at a specified frame length and hop length. While this function strives for similar behavior to `load`, there are a few caveats that users should be aware of: 1. This function does not return audio buffers directly. It returns a generator, which you can iterate over to produce blocks of audio. A *block*, in this context, refers to a buffer of audio which spans a given number of (potentially overlapping) frames. 2. Automatic sample-rate conversion is not supported. Audio will be streamed in its native sample rate, so no default values are provided for ``frame_length`` and ``hop_length``. It is recommended that you first get the sampling rate for the file in question, using `get_samplerate`, and set these parameters accordingly. 3. Many analyses require access to the entire signal to behave correctly, such as `resample`, `cqt`, or `beat_track`, so these methods will not be appropriate for streamed data. 4. The ``block_length`` parameter specifies how many frames of audio will be produced per block. Larger values will consume more memory, but will be more efficient to process down-stream. The best value will ultimately depend on your application and other system constraints. 5. By default, most librosa analyses (e.g., short-time Fourier transform) assume centered frames, which requires padding the signal at the beginning and end. This will not work correctly when the signal is carved into blocks, because it would introduce padding in the middle of the signal. To disable this feature, use ``center=False`` in all frame-based analyses. See the examples below for proper usage of this function. Parameters ---------- path : string, int, sf.SoundFile, or file-like object path to the input file to stream. Any codec supported by `soundfile` is permitted here. An existing `soundfile.SoundFile` object may also be provided. block_length : int > 0 The number of frames to include in each block. Note that at the end of the file, there may not be enough data to fill an entire block, resulting in a shorter block by default. To pad the signal out so that blocks are always full length, set ``fill_value`` (see below). frame_length : int > 0 The number of samples per frame. hop_length : int > 0 The number of samples to advance between frames. Note that by when ``hop_length < frame_length``, neighboring frames will overlap. Similarly, the last frame of one *block* will overlap with the first frame of the next *block*. mono : bool Convert the signal to mono during streaming offset : float Start reading after this time (in seconds) duration : float Only load up to this much audio (in seconds) fill_value : float [optional] If padding the signal to produce constant-length blocks, this value will be used at the end of the signal. In most cases, ``fill_value=0`` (silence) is expected, but you may specify any value here. dtype : numeric type data type of audio buffers to be produced Yields ------ y : np.ndarray An audio buffer of (at most) ``(block_length-1) * hop_length + frame_length`` samples. See Also -------- load get_samplerate soundfile.blocks Examples -------- Apply a short-term Fourier transform to blocks of 256 frames at a time. Note that streaming operation requires left-aligned frames, so we must set ``center=False`` to avoid padding artifacts. >>> filename = librosa.ex('brahms') >>> sr = librosa.get_samplerate(filename) >>> stream = librosa.stream(filename, ... block_length=256, ... frame_length=4096, ... hop_length=1024) >>> for y_block in stream: ... D_block = librosa.stft(y_block, center=False) Or compute a mel spectrogram over a stream, using a shorter frame and non-overlapping windows >>> filename = librosa.ex('brahms') >>> sr = librosa.get_samplerate(filename) >>> stream = librosa.stream(filename, ... block_length=256, ... frame_length=2048, ... hop_length=2048) >>> for y_block in stream: ... m_block = librosa.feature.melspectrogram(y=y_block, sr=sr, ... n_fft=2048, ... hop_length=2048, ... center=False) """ if not util.is_positive_int(block_length): raise ParameterError(f"block_length={block_length} must be a positive integer") if not util.is_positive_int(frame_length): raise ParameterError(f"frame_length={frame_length} must be a positive integer") if not util.is_positive_int(hop_length): raise ParameterError(f"hop_length={hop_length} must be a positive integer") if isinstance(path, sf.SoundFile): sfo = path else: sfo = sf.SoundFile(path) # Get the sample rate from the file info sr = sfo.samplerate # Construct the stream if offset: start = int(offset * sr) else: start = 0 if duration: frames = int(duration * sr) else: frames = -1 # Seek the soundfile object to the starting frame sfo.seek(start) blocks = sfo.blocks( blocksize=frame_length + (block_length - 1) * hop_length, overlap=frame_length - hop_length, frames=frames, dtype=dtype, always_2d=False, fill_value=fill_value, ) for block in blocks: if mono: yield to_mono(block.T) else: yield block.T @cache(level=20) def to_mono(y: np.ndarray) -> np.ndarray: """Convert an audio signal to mono by averaging samples across channels. Parameters ---------- y : np.ndarray [shape=(..., n)] audio time series. Multi-channel is supported. Returns ------- y_mono : np.ndarray [shape=(n,)] ``y`` as a monophonic time-series Notes ----- This function caches at level 20. Examples -------- >>> y, sr = librosa.load(librosa.ex('trumpet', hq=True), mono=False) >>> y.shape (2, 117601) >>> y_mono = librosa.to_mono(y) >>> y_mono.shape (117601,) """ # Validate the buffer. Stereo is ok here. util.valid_audio(y, mono=False) if y.ndim > 1: y = np.mean(y, axis=tuple(range(y.ndim - 1))) return y @cache(level=20) def resample( y: np.ndarray, *, orig_sr: float, target_sr: float, res_type: str = "soxr_hq", fix: bool = True, scale: bool = False, axis: int = -1, **kwargs: Any, ) -> np.ndarray: """Resample a time series from orig_sr to target_sr By default, this uses a high-quality method (`soxr_hq`) for band-limited sinc interpolation. The alternate ``res_type`` values listed below offer different trade-offs of speed and quality. Parameters ---------- y : np.ndarray [shape=(..., n, ...)] audio time series, with `n` samples along the specified axis. orig_sr : number > 0 [scalar] original sampling rate of ``y`` target_sr : number > 0 [scalar] target sampling rate res_type : str (default: `soxr_hq`) resample type 'soxr_vhq', 'soxr_hq', 'soxr_mq' or 'soxr_lq' `soxr` Very high-, High-, Medium-, Low-quality FFT-based bandlimited interpolation. ``'soxr_hq'`` is the default setting of `soxr`. 'soxr_qq' `soxr` Quick cubic interpolation (very fast, but not bandlimited) 'kaiser_best' `resampy` high-quality mode 'kaiser_fast' `resampy` faster method 'fft' or 'scipy' `scipy.signal.resample` Fourier method. 'polyphase' `scipy.signal.resample_poly` polyphase filtering. (fast) 'linear' `samplerate` linear interpolation. (very fast, but not bandlimited) 'zero_order_hold' `samplerate` repeat the last value between samples. (very fast, but not bandlimited) 'sinc_best', 'sinc_medium' or 'sinc_fastest' `samplerate` high-, medium-, and low-quality bandlimited sinc interpolation. .. note:: Not all options yield a bandlimited interpolator. If you use `soxr_qq`, `polyphase`, `linear`, or `zero_order_hold`, you need to be aware of possible aliasing effects. .. note:: `samplerate` and `resampy` are not installed with `librosa`. To use `samplerate` or `resampy`, they should be installed manually:: $ pip install samplerate $ pip install resampy .. note:: When using ``res_type='polyphase'``, only integer sampling rates are supported. fix : bool adjust the length of the resampled signal to be of size exactly ``ceil(target_sr * len(y) / orig_sr)`` scale : bool Scale the resampled signal so that ``y`` and ``y_hat`` have approximately equal total energy. axis : int The target axis along which to resample. Defaults to the trailing axis. **kwargs : additional keyword arguments If ``fix==True``, additional keyword arguments to pass to `librosa.util.fix_length`. Returns ------- y_hat : np.ndarray [shape=(..., n * target_sr / orig_sr, ...)] ``y`` resampled from ``orig_sr`` to ``target_sr`` along the target axis Raises ------ ParameterError If ``res_type='polyphase'`` and ``orig_sr`` or ``target_sr`` are not both integer-valued. See Also -------- librosa.util.fix_length scipy.signal.resample resampy samplerate.converters.resample soxr.resample Notes ----- This function caches at level 20. Examples -------- Downsample from 22 KHz to 8 KHz >>> y, sr = librosa.load(librosa.ex('trumpet'), sr=22050) >>> y_8k = librosa.resample(y, orig_sr=sr, target_sr=8000) >>> y.shape, y_8k.shape ((117601,), (42668,)) """ # First, validate the audio buffer util.valid_audio(y, mono=False) if orig_sr == target_sr: return y ratio = float(target_sr) / orig_sr n_samples = int(np.ceil(y.shape[axis] * ratio)) if res_type in ("scipy", "fft"): y_hat = scipy.signal.resample(y, n_samples, axis=axis) elif res_type == "polyphase": if int(orig_sr) != orig_sr or int(target_sr) != target_sr: raise ParameterError( "polyphase resampling is only supported for integer-valued sampling rates." ) # For polyphase resampling, we need up- and down-sampling ratios # We can get those from the greatest common divisor of the rates # as long as the rates are integrable orig_sr = int(orig_sr) target_sr = int(target_sr) gcd = np.gcd(orig_sr, target_sr) y_hat = scipy.signal.resample_poly( y, target_sr // gcd, orig_sr // gcd, axis=axis ) elif res_type in ( "linear", "zero_order_hold", "sinc_best", "sinc_fastest", "sinc_medium", ): # Use numpy to vectorize the resampler along the target axis # This is because samplerate does not support ndim>2 generally. y_hat = np.apply_along_axis( samplerate.resample, axis=axis, arr=y, ratio=ratio, converter_type=res_type ) elif res_type.startswith("soxr"): # Use numpy to vectorize the resampler along the target axis # This is because soxr does not support ndim>2 generally. y_hat = np.apply_along_axis( soxr.resample, axis=axis, arr=y, in_rate=orig_sr, out_rate=target_sr, quality=res_type, ) else: y_hat = resampy.resample(y, orig_sr, target_sr, filter=res_type, axis=axis) if fix: y_hat = util.fix_length(y_hat, size=n_samples, axis=axis, **kwargs) if scale: y_hat /= np.sqrt(ratio) # Match dtypes return np.asarray(y_hat, dtype=y.dtype) def get_duration( *, y: Optional[np.ndarray] = None, sr: float = 22050, S: Optional[np.ndarray] = None, n_fft: int = 2048, hop_length: int = 512, center: bool = True, path: Optional[Union[str, os.PathLike[Any]]] = None, filename: Optional[Union[str, os.PathLike[Any], Deprecated]] = Deprecated(), ) -> float: """Compute the duration (in seconds) of an audio time series, feature matrix, or filename. Examples -------- >>> # Load an example audio file >>> y, sr = librosa.load(librosa.ex('trumpet')) >>> librosa.get_duration(y=y, sr=sr) 5.333378684807256 >>> # Or directly from an audio file >>> librosa.get_duration(filename=librosa.ex('trumpet')) 5.333378684807256 >>> # Or compute duration from an STFT matrix >>> y, sr = librosa.load(librosa.ex('trumpet')) >>> S = librosa.stft(y) >>> librosa.get_duration(S=S, sr=sr) 5.317369614512471 >>> # Or a non-centered STFT matrix >>> S_left = librosa.stft(y, center=False) >>> librosa.get_duration(S=S_left, sr=sr) 5.224489795918367 Parameters ---------- y : np.ndarray [shape=(..., n)] or None audio time series. Multi-channel is supported. sr : number > 0 [scalar] audio sampling rate of ``y`` S : np.ndarray [shape=(..., d, t)] or None STFT matrix, or any STFT-derived matrix (e.g., chromagram or mel spectrogram). Durations calculated from spectrogram inputs are only accurate up to the frame resolution. If high precision is required, it is better to use the audio time series directly. n_fft : int > 0 [scalar] FFT window size for ``S`` hop_length : int > 0 [ scalar] number of audio samples between columns of ``S`` center : boolean - If ``True``, ``S[:, t]`` is centered at ``y[t * hop_length]`` - If ``False``, then ``S[:, t]`` begins at ``y[t * hop_length]`` path : str, path, or file-like If provided, all other parameters are ignored, and the duration is calculated directly from the audio file. Note that this avoids loading the contents into memory, and is therefore useful for querying the duration of long files. As in ``load``, this can also be an integer or open file-handle that can be processed by ``soundfile``. filename : Deprecated Equivalent to ``path`` .. warning:: This parameter has been renamed to ``path`` in 0.10. Support for ``filename=`` will be removed in 1.0. Returns ------- d : float >= 0 Duration (in seconds) of the input time series or spectrogram. Raises ------ ParameterError if none of ``y``, ``S``, or ``path`` are provided. Notes ----- `get_duration` can be applied to a file (``path``), a spectrogram (``S``), or audio buffer (``y, sr``). Only one of these three options should be provided. If you do provide multiple options (e.g., ``path`` and ``S``), then ``path`` takes precedence over ``S``, and ``S`` takes precedence over ``(y, sr)``. """ path = rename_kw( old_name="filename", old_value=filename, new_name="path", new_value=path, version_deprecated="0.10.0", version_removed="1.0", ) if path is not None: try: return sf.info(path).duration # type: ignore except sf.SoundFileRuntimeError: warnings.warn( "PySoundFile failed. Trying audioread instead." "\n\tAudioread support is deprecated in librosa 0.10.0" " and will be removed in version 1.0.", stacklevel=2, category=FutureWarning, ) with audioread.audio_open(path) as fdesc: return fdesc.duration # type: ignore if y is None: if S is None: raise ParameterError("At least one of (y, sr), S, or path must be provided") n_frames = S.shape[-1] n_samples = n_fft + hop_length * (n_frames - 1) # If centered, we lose half a window from each end of S if center: n_samples = n_samples - 2 * int(n_fft // 2) else: n_samples = y.shape[-1] return float(n_samples) / sr def get_samplerate(path: Union[str, int, sf.SoundFile, BinaryIO]) -> float: """Get the sampling rate for a given file. Parameters ---------- path : string, int, soundfile.SoundFile, or file-like The path to the file to be loaded As in ``load``, this can also be an integer or open file-handle that can be processed by `soundfile`. An existing `soundfile.SoundFile` object can also be supplied. Returns ------- sr : number > 0 The sampling rate of the given audio file Examples -------- Get the sampling rate for the included audio file >>> path = librosa.ex('trumpet') >>> librosa.get_samplerate(path) 22050 """ try: if isinstance(path, sf.SoundFile): return path.samplerate # type: ignore return sf.info(path).samplerate # type: ignore except sf.SoundFileRuntimeError: warnings.warn( "PySoundFile failed. Trying audioread instead." "\n\tAudioread support is deprecated in librosa 0.10.0" " and will be removed in version 1.0.", stacklevel=2, category=FutureWarning, ) with audioread.audio_open(path) as fdesc: return fdesc.samplerate # type: ignore @cache(level=20) def autocorrelate( y: np.ndarray, *, max_size: Optional[int] = None, axis: int = -1 ) -> np.ndarray: """Bounded-lag auto-correlation Parameters ---------- y : np.ndarray array to autocorrelate max_size : int > 0 or None maximum correlation lag. If unspecified, defaults to ``y.shape[axis]`` (unbounded) axis : int The axis along which to autocorrelate. By default, the last axis (-1) is taken. Returns ------- z : np.ndarray truncated autocorrelation ``y*y`` along the specified axis. If ``max_size`` is specified, then ``z.shape[axis]`` is bounded to ``max_size``. Notes ----- This function caches at level 20. Examples -------- Compute full autocorrelation of ``y`` >>> y, sr = librosa.load(librosa.ex('trumpet')) >>> librosa.autocorrelate(y) array([ 6.899e+02, 6.236e+02, ..., 3.710e-08, -1.796e-08]) Compute onset strength auto-correlation up to 4 seconds >>> import matplotlib.pyplot as plt >>> odf = librosa.onset.onset_strength(y=y, sr=sr, hop_length=512) >>> ac = librosa.autocorrelate(odf, max_size=4 * sr // 512) >>> fig, ax = plt.subplots() >>> ax.plot(ac) >>> ax.set(title='Auto-correlation', xlabel='Lag (frames)') """ if max_size is None: max_size = y.shape[axis] max_size = int(min(max_size, y.shape[axis])) fft = get_fftlib() real = not np.iscomplexobj(y) # Pad out the signal to support full-length auto-correlation if hasattr(scipy.fft, "next_fast_len"): n_pad = scipy.fft.next_fast_len(2 * y.shape[axis] - 1, real=real) else: # TODO: Bump to scipy>=1.4.0 and remove this branch n_pad = scipy.fftpack.next_fast_len(2 * y.shape[axis] - 1) if real: # Compute the power spectrum along the chosen axis powspec = util.abs2(fft.rfft(y, n=n_pad, axis=axis)) # Convert back to time domain autocorr = fft.irfft(powspec, n=n_pad, axis=axis) else: # Compute the power spectrum along the chosen axis powspec = util.abs2(fft.fft(y, n=n_pad, axis=axis)) # Convert back to time domain autocorr = fft.ifft(powspec, n=n_pad, axis=axis) # Slice down to max_size subslice = [slice(None)] * autocorr.ndim subslice[axis] = slice(max_size) autocorr_slice: np.ndarray = autocorr[tuple(subslice)] return autocorr_slice def lpc(y: np.ndarray, *, order: int, axis: int = -1) -> np.ndarray: """Linear Prediction Coefficients via Burg's method This function applies Burg's method to estimate coefficients of a linear filter on ``y`` of order ``order``. Burg's method is an extension to the Yule-Walker approach, which are both sometimes referred to as LPC parameter estimation by autocorrelation. It follows the description and implementation approach described in the introduction by Marple. [#]_ N.B. This paper describes a different method, which is not implemented here, but has been chosen for its clear explanation of Burg's technique in its introduction. .. [#] Larry Marple. A New Autoregressive Spectrum Analysis Algorithm. IEEE Transactions on Acoustics, Speech, and Signal Processing vol 28, no. 4, 1980. Parameters ---------- y : np.ndarray [shape=(..., n)] Time series to fit. Multi-channel is supported.. order : int > 0 Order of the linear filter axis : int Axis along which to compute the coefficients Returns ------- a : np.ndarray [shape=(..., order + 1)] LP prediction error coefficients, i.e. filter denominator polynomial. Note that the length along the specified ``axis`` will be ``order+1``. Raises ------ ParameterError - If ``y`` is not valid audio as per `librosa.util.valid_audio` - If ``order < 1`` or not integer FloatingPointError - If ``y`` is ill-conditioned See Also -------- scipy.signal.lfilter Examples -------- Compute LP coefficients of y at order 16 on entire series >>> y, sr = librosa.load(librosa.ex('libri1')) >>> librosa.lpc(y, order=16) Compute LP coefficients, and plot LP estimate of original series >>> import matplotlib.pyplot as plt >>> import scipy >>> y, sr = librosa.load(librosa.ex('libri1'), duration=0.020) >>> a = librosa.lpc(y, order=2) >>> b = np.hstack([[0], -1 * a[1:]]) >>> y_hat = scipy.signal.lfilter(b, [1], y) >>> fig, ax = plt.subplots() >>> ax.plot(y) >>> ax.plot(y_hat, linestyle='--') >>> ax.legend(['y', 'y_hat']) >>> ax.set_title('LP Model Forward Prediction') """ if not util.is_positive_int(order): raise ParameterError(f"order={order} must be an integer > 0") util.valid_audio(y, mono=False) # Move the lpc axis around front, because numba is silly y = y.swapaxes(axis, 0) dtype = y.dtype shape = list(y.shape) shape[0] = order + 1 ar_coeffs = np.zeros(tuple(shape), dtype=dtype) ar_coeffs[0] = 1 ar_coeffs_prev = ar_coeffs.copy() shape[0] = 1 reflect_coeff = np.zeros(shape, dtype=dtype) den = reflect_coeff.copy() epsilon = util.tiny(den) # Call the helper, and swap the results back to the target axis position return np.swapaxes( __lpc(y, order, ar_coeffs, ar_coeffs_prev, reflect_coeff, den, epsilon), 0, axis ) @jit(nopython=True, cache=True) # type: ignore def __lpc( y: np.ndarray, order: int, ar_coeffs: np.ndarray, ar_coeffs_prev: np.ndarray, reflect_coeff: np.ndarray, den: np.ndarray, epsilon: float, ) -> np.ndarray: # This implementation follows the description of Burg's algorithm given in # section III of Marple's paper referenced in the docstring. # # We use the Levinson-Durbin recursion to compute AR coefficients for each # increasing model order by using those from the last. We maintain two # arrays and then flip them each time we increase the model order so that # we may use all the coefficients from the previous order while we compute # those for the new one. These two arrays hold ar_coeffs for order M and # order M-1. (Corresponding to a_{M,k} and a_{M-1,k} in eqn 5) # These two arrays hold the forward and backward prediction error. They # correspond to f_{M-1,k} and b_{M-1,k} in eqns 10, 11, 13 and 14 of # Marple. First they are used to compute the reflection coefficient at # order M from M-1 then are re-used as f_{M,k} and b_{M,k} for each # iteration of the below loop fwd_pred_error = y[1:] bwd_pred_error = y[:-1] # DEN_{M} from eqn 16 of Marple. den[0] = np.sum(fwd_pred_error**2 + bwd_pred_error**2, axis=0) for i in range(order): # can be removed if we keep the epsilon bias # if np.any(den <= 0): # raise FloatingPointError("numerical error, input ill-conditioned?") # Eqn 15 of Marple, with fwd_pred_error and bwd_pred_error # corresponding to f_{M-1,k+1} and b{M-1,k} and the result as a_{M,M} reflect_coeff[0] = np.sum(bwd_pred_error * fwd_pred_error, axis=0) reflect_coeff[0] *= -2 reflect_coeff[0] /= den[0] + epsilon # Now we use the reflection coefficient and the AR coefficients from # the last model order to compute all of the AR coefficients for the # current one. This is the Levinson-Durbin recursion described in # eqn 5. # Note 1: We don't have to care about complex conjugates as our signals # are all real-valued # Note 2: j counts 1..order+1, i-j+1 counts order..0 # Note 3: The first element of ar_coeffs* is always 1, which copies in # the reflection coefficient at the end of the new AR coefficient array # after the preceding coefficients ar_coeffs_prev, ar_coeffs = ar_coeffs, ar_coeffs_prev for j in range(1, i + 2): # reflection multiply should be broadcast ar_coeffs[j] = ( ar_coeffs_prev[j] + reflect_coeff[0] * ar_coeffs_prev[i - j + 1] ) # Update the forward and backward prediction errors corresponding to # eqns 13 and 14. We start with f_{M-1,k+1} and b_{M-1,k} and use them # to compute f_{M,k} and b_{M,k} fwd_pred_error_tmp = fwd_pred_error fwd_pred_error = fwd_pred_error + reflect_coeff * bwd_pred_error bwd_pred_error = bwd_pred_error + reflect_coeff * fwd_pred_error_tmp # SNIP - we are now done with order M and advance. M-1 <- M # Compute DEN_{M} using the recursion from eqn 17. # # reflect_coeff = a_{M-1,M-1} (we have advanced M) # den = DEN_{M-1} (rhs) # bwd_pred_error = b_{M-1,N-M+1} (we have advanced M) # fwd_pred_error = f_{M-1,k} (we have advanced M) # den <- DEN_{M} (lhs) # q = 1.0 - reflect_coeff[0] ** 2 den[0] = q * den[0] - bwd_pred_error[-1] ** 2 - fwd_pred_error[0] ** 2 # Shift up forward error. # # fwd_pred_error <- f_{M-1,k+1} # bwd_pred_error <- b_{M-1,k} # # N.B. We do this after computing the denominator using eqn 17 but # before using it in the numerator in eqn 15. fwd_pred_error = fwd_pred_error[1:] bwd_pred_error = bwd_pred_error[:-1] return ar_coeffs @stencil # type: ignore def _zc_stencil(x: np.ndarray, threshold: float, zero_pos: bool) -> np.ndarray: """Stencil to compute zero crossings""" x0 = x[0] if -threshold <= x0 <= threshold: x0 = 0 x1 = x[-1] if -threshold <= x1 <= threshold: x1 = 0 if zero_pos: return np.signbit(x0) != np.signbit(x1) # type: ignore else: return np.sign(x0) != np.sign(x1) # type: ignore @guvectorize( [ "void(float32[:], float32, bool_, bool_[:])", "void(float64[:], float64, bool_, bool_[:])", ], "(n),(),()->(n)", cache=True, nopython=True, ) # type: ignore def _zc_wrapper( x: np.ndarray, threshold: float, zero_pos: bool, y: np.ndarray, ) -> None: # pragma: no cover """Vectorized wrapper for zero crossing stencil""" y[:] = _zc_stencil(x, threshold, zero_pos) @cache(level=20) def zero_crossings( y: np.ndarray, *, threshold: float = 1e-10, ref_magnitude: Optional[Union[float, Callable]] = None, pad: bool = True, zero_pos: bool = True, axis: int = -1, ) -> np.ndarray: """Find the zero-crossings of a signal ``y``: indices ``i`` such that ``sign(y[i]) != sign(y[j])``. If ``y`` is multi-dimensional, then zero-crossings are computed along the specified ``axis``. Parameters ---------- y : np.ndarray The input array threshold : float >= 0 If non-zero, values where ``-threshold <= y <= threshold`` are clipped to 0. ref_magnitude : float > 0 or callable If numeric, the threshold is scaled relative to ``ref_magnitude``. If callable, the threshold is scaled relative to ``ref_magnitude(np.abs(y))``. pad : boolean If ``True``, then ``y[0]`` is considered a valid zero-crossing. zero_pos : boolean If ``True`` then the value 0 is interpreted as having positive sign. If ``False``, then 0, -1, and +1 all have distinct signs. axis : int Axis along which to compute zero-crossings. Returns ------- zero_crossings : np.ndarray [shape=y.shape, dtype=boolean] Indicator array of zero-crossings in ``y`` along the selected axis. Notes ----- This function caches at level 20. Examples -------- >>> # Generate a time-series >>> y = np.sin(np.linspace(0, 4 * 2 * np.pi, 20)) >>> y array([ 0.000e+00, 9.694e-01, 4.759e-01, -7.357e-01, -8.372e-01, 3.247e-01, 9.966e-01, 1.646e-01, -9.158e-01, -6.142e-01, 6.142e-01, 9.158e-01, -1.646e-01, -9.966e-01, -3.247e-01, 8.372e-01, 7.357e-01, -4.759e-01, -9.694e-01, -9.797e-16]) >>> # Compute zero-crossings >>> z = librosa.zero_crossings(y) >>> z array([ True, False, False, True, False, True, False, False, True, False, True, False, True, False, False, True, False, True, False, True], dtype=bool) >>> # Stack y against the zero-crossing indicator >>> librosa.util.stack([y, z], axis=-1) array([[ 0.000e+00, 1.000e+00], [ 9.694e-01, 0.000e+00], [ 4.759e-01, 0.000e+00], [ -7.357e-01, 1.000e+00], [ -8.372e-01, 0.000e+00], [ 3.247e-01, 1.000e+00], [ 9.966e-01, 0.000e+00], [ 1.646e-01, 0.000e+00], [ -9.158e-01, 1.000e+00], [ -6.142e-01, 0.000e+00], [ 6.142e-01, 1.000e+00], [ 9.158e-01, 0.000e+00], [ -1.646e-01, 1.000e+00], [ -9.966e-01, 0.000e+00], [ -3.247e-01, 0.000e+00], [ 8.372e-01, 1.000e+00], [ 7.357e-01, 0.000e+00], [ -4.759e-01, 1.000e+00], [ -9.694e-01, 0.000e+00], [ -9.797e-16, 1.000e+00]]) >>> # Find the indices of zero-crossings >>> np.nonzero(z) (array([ 0, 3, 5, 8, 10, 12, 15, 17, 19]),) """ if callable(ref_magnitude): threshold = threshold * ref_magnitude(np.abs(y)) elif ref_magnitude is not None: threshold = threshold * ref_magnitude yi = y.swapaxes(-1, axis) z = np.empty_like(y, dtype=bool) zi = z.swapaxes(-1, axis) _zc_wrapper(yi, threshold, zero_pos, zi) zi[..., 0] = pad return z def clicks( *, times: Optional[_SequenceLike[_FloatLike_co]] = None, frames: Optional[_SequenceLike[_IntLike_co]] = None, sr: float = 22050, hop_length: int = 512, click_freq: float = 1000.0, click_duration: float = 0.1, click: Optional[np.ndarray] = None, length: Optional[int] = None, ) -> np.ndarray: """Construct a "click track". This returns a signal with the signal ``click`` sound placed at each specified time. Parameters ---------- times : np.ndarray or None times to place clicks, in seconds frames : np.ndarray or None frame indices to place clicks sr : number > 0 desired sampling rate of the output signal hop_length : int > 0 if positions are specified by ``frames``, the number of samples between frames. click_freq : float > 0 frequency (in Hz) of the default click signal. Default is 1KHz. click_duration : float > 0 duration (in seconds) of the default click signal. Default is 100ms. click : np.ndarray or None (optional) click signal sample to use instead of the default click. Multi-channel is supported. length : int > 0 desired number of samples in the output signal Returns ------- click_signal : np.ndarray Synthesized click signal. This will be monophonic by default, or match the number of channels to a provided ``click`` signal. Raises ------ ParameterError - If neither ``times`` nor ``frames`` are provided. - If any of ``click_freq``, ``click_duration``, or ``length`` are out of range. Examples -------- >>> # Sonify detected beat events >>> y, sr = librosa.load(librosa.ex('choice'), duration=10) >>> tempo, beats = librosa.beat.beat_track(y=y, sr=sr) >>> y_beats = librosa.clicks(frames=beats, sr=sr) >>> # Or generate a signal of the same length as y >>> y_beats = librosa.clicks(frames=beats, sr=sr, length=len(y)) >>> # Or use timing instead of frame indices >>> times = librosa.frames_to_time(beats, sr=sr) >>> y_beat_times = librosa.clicks(times=times, sr=sr) >>> # Or with a click frequency of 880Hz and a 500ms sample >>> y_beat_times880 = librosa.clicks(times=times, sr=sr, ... click_freq=880, click_duration=0.5) Display click waveform next to the spectrogram >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(nrows=2, sharex=True) >>> S = librosa.feature.melspectrogram(y=y, sr=sr) >>> librosa.display.specshow(librosa.power_to_db(S, ref=np.max), ... x_axis='time', y_axis='mel', ax=ax[0]) >>> librosa.display.waveshow(y_beat_times, sr=sr, label='Beat clicks', ... ax=ax[1]) >>> ax[1].legend() >>> ax[0].label_outer() >>> ax[0].set_title(None) """ # Compute sample positions from time or frames positions: np.ndarray if times is None: if frames is None: raise ParameterError('either "times" or "frames" must be provided') positions = frames_to_samples(frames, hop_length=hop_length) else: # Convert times to positions positions = time_to_samples(times, sr=sr) if click is not None: # Check that we have a well-formed audio buffer util.valid_audio(click, mono=False) else: # Create default click signal if click_duration <= 0: raise ParameterError("click_duration must be strictly positive") if click_freq <= 0: raise ParameterError("click_freq must be strictly positive") angular_freq = 2 * np.pi * click_freq / float(sr) click = np.logspace(0, -10, num=int(sr * click_duration), base=2.0) click *= np.sin(angular_freq * np.arange(len(click))) # Set default length if length is None: length = positions.max() + click.shape[-1] else: if length < 1: raise ParameterError("length must be a positive integer") # Filter out any positions past the length boundary positions = positions[positions < length] # Pre-allocate click signal shape = list(click.shape) shape[-1] = length click_signal = np.zeros(shape, dtype=np.float32) # Place clicks for start in positions: # Compute the end-point of this click end = start + click.shape[-1] if end >= length: click_signal[..., start:] += click[..., : length - start] else: # Normally, just add a click here click_signal[..., start:end] += click return click_signal def tone( frequency: _FloatLike_co, *, sr: float = 22050, length: Optional[int] = None, duration: Optional[float] = None, phi: Optional[float] = None, ) -> np.ndarray: """Construct a pure tone (cosine) signal at a given frequency. Parameters ---------- frequency : float > 0 frequency sr : number > 0 desired sampling rate of the output signal length : int > 0 desired number of samples in the output signal. When both ``duration`` and ``length`` are defined, ``length`` takes priority. duration : float > 0 desired duration in seconds. When both ``duration`` and ``length`` are defined, ``length`` takes priority. phi : float or None phase offset, in radians. If unspecified, defaults to ``-np.pi * 0.5``. Returns ------- tone_signal : np.ndarray [shape=(length,), dtype=float64] Synthesized pure sine tone signal Raises ------ ParameterError - If ``frequency`` is not provided. - If neither ``length`` nor ``duration`` are provided. Examples -------- Generate a pure sine tone A4 >>> tone = librosa.tone(440, duration=1, sr=22050) Or generate the same signal using `length` >>> tone = librosa.tone(440, sr=22050, length=22050) Display spectrogram >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots() >>> S = librosa.feature.melspectrogram(y=tone) >>> librosa.display.specshow(librosa.power_to_db(S, ref=np.max), ... x_axis='time', y_axis='mel', ax=ax) """ if frequency is None: raise ParameterError('"frequency" must be provided') # Compute signal length if length is None: if duration is None: raise ParameterError('either "length" or "duration" must be provided') length = int(duration * sr) if phi is None: phi = -np.pi * 0.5 y: np.ndarray = np.cos(2 * np.pi * frequency * np.arange(length) / sr + phi) return y def chirp( *, fmin: _FloatLike_co, fmax: _FloatLike_co, sr: float = 22050, length: Optional[int] = None, duration: Optional[float] = None, linear: bool = False, phi: Optional[float] = None, ) -> np.ndarray: """Construct a "chirp" or "sine-sweep" signal. The chirp sweeps from frequency ``fmin`` to ``fmax`` (in Hz). Parameters ---------- fmin : float > 0 initial frequency fmax : float > 0 final frequency sr : number > 0 desired sampling rate of the output signal length : int > 0 desired number of samples in the output signal. When both ``duration`` and ``length`` are defined, ``length`` takes priority. duration : float > 0 desired duration in seconds. When both ``duration`` and ``length`` are defined, ``length`` takes priority. linear : boolean - If ``True``, use a linear sweep, i.e., frequency changes linearly with time - If ``False``, use a exponential sweep. Default is ``False``. phi : float or None phase offset, in radians. If unspecified, defaults to ``-np.pi * 0.5``. Returns ------- chirp_signal : np.ndarray [shape=(length,), dtype=float64] Synthesized chirp signal Raises ------ ParameterError - If either ``fmin`` or ``fmax`` are not provided. - If neither ``length`` nor ``duration`` are provided. See Also -------- scipy.signal.chirp Examples -------- Generate a exponential chirp from A2 to A8 >>> exponential_chirp = librosa.chirp(fmin=110, fmax=110*64, duration=1, sr=22050) Or generate the same signal using ``length`` >>> exponential_chirp = librosa.chirp(fmin=110, fmax=110*64, sr=22050, length=22050) Or generate a linear chirp instead >>> linear_chirp = librosa.chirp(fmin=110, fmax=110*64, duration=1, linear=True, sr=22050) Display spectrogram for both exponential and linear chirps. >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(nrows=2, sharex=True, sharey=True) >>> S_exponential = np.abs(librosa.stft(y=exponential_chirp)) >>> librosa.display.specshow(librosa.amplitude_to_db(S_exponential, ref=np.max), ... x_axis='time', y_axis='linear', ax=ax[0]) >>> ax[0].set(title='Exponential chirp', xlabel=None) >>> ax[0].label_outer() >>> S_linear = np.abs(librosa.stft(y=linear_chirp)) >>> librosa.display.specshow(librosa.amplitude_to_db(S_linear, ref=np.max), ... x_axis='time', y_axis='linear', ax=ax[1]) >>> ax[1].set(title='Linear chirp') """ if fmin is None or fmax is None: raise ParameterError('both "fmin" and "fmax" must be provided') # Compute signal duration period = 1.0 / sr if length is None: if duration is None: raise ParameterError('either "length" or "duration" must be provided') else: duration = period * length if phi is None: phi = -np.pi * 0.5 method = "linear" if linear else "logarithmic" y: np.ndarray = scipy.signal.chirp( np.arange(int(duration * sr)) / sr, fmin, duration, fmax, method=method, phi=phi / np.pi * 180, # scipy.signal.chirp uses degrees for phase offset ) return y def mu_compress( x: Union[np.ndarray, _FloatLike_co], *, mu: float = 255, quantize: bool = True ) -> np.ndarray: """mu-law compression Given an input signal ``-1 <= x <= 1``, the mu-law compression is calculated by:: sign(x) * ln(1 + mu * abs(x)) / ln(1 + mu) Parameters ---------- x : np.ndarray with values in [-1, +1] The input signal to compress mu : positive number The compression parameter. Values of the form ``2**n - 1`` (e.g., 15, 31, 63, etc.) are most common. quantize : bool If ``True``, quantize the compressed values into ``1 + mu`` distinct integer values. If ``False``, mu-law compression is applied without quantization. Returns ------- x_compressed : np.ndarray The compressed signal. Raises ------ ParameterError If ``x`` has values outside the range [-1, +1] If ``mu <= 0`` See Also -------- mu_expand Examples -------- Compression without quantization >>> x = np.linspace(-1, 1, num=16) >>> x array([-1. , -0.86666667, -0.73333333, -0.6 , -0.46666667, -0.33333333, -0.2 , -0.06666667, 0.06666667, 0.2 , 0.33333333, 0.46666667, 0.6 , 0.73333333, 0.86666667, 1. ]) >>> y = librosa.mu_compress(x, quantize=False) >>> y array([-1. , -0.97430198, -0.94432361, -0.90834832, -0.86336132, -0.80328309, -0.71255496, -0.52124063, 0.52124063, 0.71255496, 0.80328309, 0.86336132, 0.90834832, 0.94432361, 0.97430198, 1. ]) Compression with quantization >>> y = librosa.mu_compress(x, quantize=True) >>> y array([-128, -124, -120, -116, -110, -102, -91, -66, 66, 91, 102, 110, 116, 120, 124, 127]) Compression with quantization and a smaller range >>> y = librosa.mu_compress(x, mu=15, quantize=True) >>> y array([-8, -7, -7, -6, -6, -5, -4, -2, 2, 4, 5, 6, 6, 7, 7, 7]) """ if mu <= 0: raise ParameterError( f"mu-law compression parameter mu={mu} must be strictly positive." ) if np.any(x < -1) or np.any(x > 1): raise ParameterError(f"mu-law input x={x} must be in the range [-1, +1].") x_comp: np.ndarray = np.sign(x) * np.log1p(mu * np.abs(x)) / np.log1p(mu) if quantize: y: np.ndarray = ( np.digitize( x_comp, np.linspace(-1, 1, num=int(1 + mu), endpoint=True), right=True ) - int(mu + 1) // 2 ) return y return x_comp def mu_expand( x: Union[np.ndarray, _FloatLike_co], *, mu: float = 255.0, quantize: bool = True ) -> np.ndarray: """mu-law expansion This function is the inverse of ``mu_compress``. Given a mu-law compressed signal ``-1 <= x <= 1``, the mu-law expansion is calculated by:: sign(x) * (1 / mu) * ((1 + mu)**abs(x) - 1) Parameters ---------- x : np.ndarray The compressed signal. If ``quantize=True``, values must be in the range [-1, +1]. mu : positive number The compression parameter. Values of the form ``2**n - 1`` (e.g., 15, 31, 63, etc.) are most common. quantize : boolean If ``True``, the input is assumed to be quantized to ``1 + mu`` distinct integer values. Returns ------- x_expanded : np.ndarray with values in the range [-1, +1] The mu-law expanded signal. Raises ------ ParameterError If ``x`` has values outside the range [-1, +1] and ``quantize=False`` If ``mu <= 0`` See Also -------- mu_compress Examples -------- Compress and expand without quantization >>> x = np.linspace(-1, 1, num=16) >>> x array([-1. , -0.86666667, -0.73333333, -0.6 , -0.46666667, -0.33333333, -0.2 , -0.06666667, 0.06666667, 0.2 , 0.33333333, 0.46666667, 0.6 , 0.73333333, 0.86666667, 1. ]) >>> y = librosa.mu_compress(x, quantize=False) >>> y array([-1. , -0.97430198, -0.94432361, -0.90834832, -0.86336132, -0.80328309, -0.71255496, -0.52124063, 0.52124063, 0.71255496, 0.80328309, 0.86336132, 0.90834832, 0.94432361, 0.97430198, 1. ]) >>> z = librosa.mu_expand(y, quantize=False) >>> z array([-1. , -0.86666667, -0.73333333, -0.6 , -0.46666667, -0.33333333, -0.2 , -0.06666667, 0.06666667, 0.2 , 0.33333333, 0.46666667, 0.6 , 0.73333333, 0.86666667, 1. ]) Compress and expand with quantization. Note that this necessarily incurs quantization error, particularly for values near +-1. >>> y = librosa.mu_compress(x, quantize=True) >>> y array([-128, -124, -120, -116, -110, -102, -91, -66, 66, 91, 102, 110, 116, 120, 124, 127]) >>> z = librosa.mu_expand(y, quantize=True) array([-1. , -0.84027248, -0.70595818, -0.59301377, -0.4563785 , -0.32155973, -0.19817918, -0.06450245, 0.06450245, 0.19817918, 0.32155973, 0.4563785 , 0.59301377, 0.70595818, 0.84027248, 0.95743702]) """ if mu <= 0: raise ParameterError( f"Inverse mu-law compression parameter mu={mu} must be strictly positive." ) if quantize: x = x * 2.0 / (1 + mu) if np.any(x < -1) or np.any(x > 1): raise ParameterError( f"Inverse mu-law input x={x} must be in the range [-1, +1]." ) return np.sign(x) / mu * (np.power(1 + mu, np.abs(x)) - 1)