U 5d5\ @s&dZddlZddlZddlZddlmZddlmZddlm Z ddlm Z ddl m Z m Z dd lmZdd lmZd d d gZeddddddddddd dd Zeddeddddddddejdd dd Zeddddddddd d!d Zd"d#Zd$d%Zd&d'Zd(d)Zd*d+Zd,d-ZdS).zg Beat and tempo ============== .. autosummary:: :toctree: generated/ beat_track plp tempo N)cache)core)onset)util) tempogramfourier_tempogram)ParameterError)deprecate_positional_args beat_tracktempoplpi"Vig^@dTframes) ysronset_envelope hop_length start_bpm tightnesstrimbpmpriorunitsc Cs|dkr,|dkrtdtj|||tjd}|sFdtjgtdfS|dkrdt|||||dd}t ||t ||||} | dkrn@| dkrt j | |d } n(| d krt j | ||d } ntd | || fS) a*Dynamic programming beat tracker. Beats are detected in three stages, following the method of [#]_: 1. Measure onset strength 2. Estimate tempo from onset correlation 3. Pick peaks in onset strength approximately consistent with estimated tempo .. [#] Ellis, Daniel PW. "Beat tracking by dynamic programming." Journal of New Music Research 36.1 (2007): 51-60. http://labrosa.ee.columbia.edu/projects/beattrack/ Parameters ---------- y : np.ndarray [shape=(n,)] or None audio time series sr : number > 0 [scalar] sampling rate of ``y`` onset_envelope : np.ndarray [shape=(n,)] or None (optional) pre-computed onset strength envelope. hop_length : int > 0 [scalar] number of audio samples between successive ``onset_envelope`` values start_bpm : float > 0 [scalar] initial guess for the tempo estimator (in beats per minute) tightness : float [scalar] tightness of beat distribution around tempo trim : bool [scalar] trim leading/trailing beats with weak onsets bpm : float [scalar] (optional) If provided, use ``bpm`` as the tempo instead of estimating it from ``onsets``. prior : scipy.stats.rv_continuous [optional] An optional prior distribution over tempo. If provided, ``start_bpm`` will be ignored. units : {'frames', 'samples', 'time'} The units to encode detected beat events in. By default, 'frames' are used. Returns ------- tempo : float [scalar, non-negative] estimated global tempo (in beats per minute) beats : np.ndarray [shape=(m,)] estimated beat event locations in the specified units (default is frame indices) .. note:: If no onset strength could be detected, beat_tracker estimates 0 BPM and returns an empty list. Raises ------ ParameterError if neither ``y`` nor ``onset_envelope`` are provided, or if ``units`` is not one of 'frames', 'samples', or 'time' See Also -------- librosa.onset.onset_strength Examples -------- Track beats using time series input >>> y, sr = librosa.load(librosa.ex('choice'), duration=10) >>> tempo, beats = librosa.beat.beat_track(y=y, sr=sr) >>> tempo 135.99917763157896 Print the frames corresponding to beats >>> beats array([ 3, 21, 40, 59, 78, 96, 116, 135, 154, 173, 192, 211, 230, 249, 268, 287, 306, 325, 344, 363]) Or print them as timestamps >>> librosa.frames_to_time(beats, sr=sr) array([0.07 , 0.488, 0.929, 1.37 , 1.811, 2.229, 2.694, 3.135, 3.576, 4.017, 4.458, 4.899, 5.341, 5.782, 6.223, 6.664, 7.105, 7.546, 7.988, 8.429]) Track beats using a pre-computed onset envelope >>> onset_env = librosa.onset.onset_strength(y=y, sr=sr, ... aggregate=np.median) >>> tempo, beats = librosa.beat.beat_track(onset_envelope=onset_env, ... sr=sr) >>> tempo 135.99917763157896 >>> beats array([ 3, 21, 40, 59, 78, 96, 116, 135, 154, 173, 192, 211, 230, 249, 268, 287, 306, 325, 344, 363]) Plot the beat events against the onset strength envelope >>> import matplotlib.pyplot as plt >>> hop_length = 512 >>> fig, ax = plt.subplots(nrows=2, sharex=True) >>> times = librosa.times_like(onset_env, sr=sr, hop_length=hop_length) >>> M = librosa.feature.melspectrogram(y=y, sr=sr, hop_length=hop_length) >>> librosa.display.specshow(librosa.power_to_db(M, ref=np.max), ... y_axis='mel', x_axis='time', hop_length=hop_length, ... ax=ax[0]) >>> ax[0].label_outer() >>> ax[0].set(title='Mel spectrogram') >>> ax[1].plot(times, librosa.util.normalize(onset_env), ... label='Onset strength') >>> ax[1].vlines(times[beats], 0, 1, alpha=0.5, color='r', ... linestyle='--', label='Beats') >>> ax[1].legend() Nz$y or onset_envelope must be providedrrr aggregaterZdtype)rrrrrrZsamples)rtimerrzInvalid unit type: {})r ronset_strengthnpmediananyarrayintr __beat_trackerfloatrZframes_to_samplesZframes_to_timeformat) rrrrrrrrrrbeatsr)0/tmp/pip-unpacked-wheel-8l90aumz/librosa/beat.pyr s> )levelxg?g @gt@) rrrrrstd_bpmac_size max_temporrc Cs|dkrtdtj|||d} t||||| d} |dk rL|| ddd} tj| jd ||d } | dkrd t| t||d } n | | } |dk rt | |k}tj | d|<t j | | jd d } tj td| | d d}t| |S)aEstimate the tempo (beats per minute) Parameters ---------- y : np.ndarray [shape=(..., n)] or None audio time series. Multi-channel is supported. sr : number > 0 [scalar] sampling rate of the time series onset_envelope : np.ndarray [shape=(..., n)] pre-computed onset strength envelope hop_length : int > 0 [scalar] hop length of the time series start_bpm : float [scalar] initial guess of the BPM std_bpm : float > 0 [scalar] standard deviation of tempo distribution ac_size : float > 0 [scalar] length (in seconds) of the auto-correlation window max_tempo : float > 0 [scalar, optional] If provided, only estimate tempo below this threshold aggregate : callable [optional] Aggregation function for estimating global tempo. If `None`, then tempo is estimated independently for each frame. prior : scipy.stats.rv_continuous [optional] A prior distribution over tempo (in beats per minute). By default, a pseudo-log-normal prior is used. If given, ``start_bpm`` and ``std_bpm`` will be ignored. Returns ------- tempo : np.ndarray estimated tempo (beats per minute). If input is multi-channel, one tempo estimate per channel is provided. See Also -------- librosa.onset.onset_strength librosa.feature.tempogram Notes ----- This function caches at level 30. Examples -------- >>> # Estimate a static tempo >>> y, sr = librosa.load(librosa.ex('nutcracker'), duration=30) >>> onset_env = librosa.onset.onset_strength(y=y, sr=sr) >>> tempo = librosa.beat.tempo(onset_envelope=onset_env, sr=sr) >>> tempo array([143.555]) >>> # Or a static tempo with a uniform prior instead >>> import scipy.stats >>> prior = scipy.stats.uniform(30, 300) # uniform over 30-300 BPM >>> utempo = librosa.beat.tempo(onset_envelope=onset_env, sr=sr, prior=prior) >>> utempo array([161.499]) >>> # Or a dynamic tempo >>> dtempo = librosa.beat.tempo(onset_envelope=onset_env, sr=sr, ... aggregate=None) >>> dtempo array([ 89.103, 89.103, 89.103, ..., 123.047, 123.047, 123.047]) >>> # Dynamic tempo with a proper log-normal prior >>> prior_lognorm = scipy.stats.lognorm(loc=np.log(120), scale=120, s=1) >>> dtempo_lognorm = librosa.beat.tempo(onset_envelope=onset_env, sr=sr, ... aggregate=None, ... prior=prior_lognorm) >>> dtempo_lognorm array([ 89.103, 89.103, 89.103, ..., 123.047, 123.047, 123.047]) Plot the estimated tempo against the onset autocorrelation >>> import matplotlib.pyplot as plt >>> # Convert to scalar >>> tempo = tempo.item() >>> utempo = utempo.item() >>> # Compute 2-second windowed autocorrelation >>> hop_length = 512 >>> ac = librosa.autocorrelate(onset_env, max_size=2 * sr // hop_length) >>> freqs = librosa.tempo_frequencies(len(ac), sr=sr, ... hop_length=hop_length) >>> # Plot on a BPM axis. We skip the first (0-lag) bin. >>> fig, ax = plt.subplots() >>> ax.semilogx(freqs[1:], librosa.util.normalize(ac)[1:], ... label='Onset autocorrelation', base=2) >>> ax.axvline(tempo, 0, 1, alpha=0.75, linestyle='--', color='r', ... label='Tempo (default prior): {:.2f} BPM'.format(tempo)) >>> ax.axvline(utempo, 0, 1, alpha=0.75, linestyle=':', color='g', ... label='Tempo (uniform prior): {:.2f} BPM'.format(utempo)) >>> ax.set(xlabel='Tempo (BPM)', title='Static tempo estimation') >>> ax.grid(True) >>> ax.legend() Plot dynamic tempo estimates over a tempogram >>> fig, ax = plt.subplots() >>> tg = librosa.feature.tempogram(onset_envelope=onset_env, sr=sr, ... hop_length=hop_length) >>> librosa.display.specshow(tg, x_axis='time', y_axis='tempo', cmap='magma', ax=ax) >>> ax.plot(librosa.times_like(dtempo), dtempo, ... color='c', linewidth=1.5, label='Tempo estimate (default prior)') >>> ax.plot(librosa.times_like(dtempo_lognorm), dtempo_lognorm, ... color='c', linewidth=1.5, linestyle='--', ... label='Tempo estimate (lognorm prior)') >>> ax.set(title='Dynamic tempo estimation') >>> ax.legend() rz#start_bpm must be strictly positive)rr)rrrr win_lengthNTaxisZkeepdimsrndimZaxes.Ar4)r rZtime_to_framesitemrtempo_frequenciesshaper log2logpdfargmaxinfr expand_tor9log1pZtake)rrrrrr.r/r0rrr1tgZbpmsZlogpriorZmax_idxZ best_periodr)r)r*r s,~ " ii,)rrrrr1 tempo_min tempo_maxrc CsR|dkrtj|||tjd}|dk rD|dk rD||krDtd||t||||d}tj|||d} |dk rd|d| |kddf<|dk rd|d| |kddf<t j | |j dd } t d t |} |dk r| || 7} | jdd d } d|| | k<|t |d t |jdd d }tj|d||jdd} t| dd| } t j| ddS)aPredominant local pulse (PLP) estimation. [#]_ The PLP method analyzes the onset strength envelope in the frequency domain to find a locally stable tempo for each frame. These local periodicities are used to synthesize local half-waves, which are combined such that peaks coincide with rhythmically salient frames (e.g. onset events on a musical time grid). The local maxima of the pulse curve can be taken as estimated beat positions. This method may be preferred over the dynamic programming method of `beat_track` when either the tempo is expected to vary significantly over time. Additionally, since `plp` does not require the entire signal to make predictions, it may be preferable when beat-tracking long recordings in a streaming setting. .. [#] Grosche, P., & Muller, M. (2011). "Extracting predominant local pulse information from music recordings." IEEE Transactions on Audio, Speech, and Language Processing, 19(6), 1688-1701. Parameters ---------- y : np.ndarray [shape=(..., n)] or None audio time series. Multi-channel is supported. sr : number > 0 [scalar] sampling rate of ``y`` onset_envelope : np.ndarray [shape=(..., n)] or None (optional) pre-computed onset strength envelope hop_length : int > 0 [scalar] number of audio samples between successive ``onset_envelope`` values win_length : int > 0 [scalar] number of frames to use for tempogram analysis. By default, 384 frames (at ``sr=22050`` and ``hop_length=512``) corresponds to about 8.9 seconds. tempo_min, tempo_max : numbers > 0 [scalar], optional Minimum and maximum permissible tempo values. ``tempo_max`` must be at least ``tempo_min``. Set either (or both) to `None` to disable this constraint. prior : scipy.stats.rv_continuous [optional] A prior distribution over tempo (in beats per minute). By default, a uniform prior over ``[tempo_min, tempo_max]`` is used. Returns ------- pulse : np.ndarray, shape=[(..., n)] The estimated pulse curve. Maxima correspond to rhythmically salient points of time. If input is multi-channel, one pulse curve per channel is computed. See Also -------- beat_track librosa.onset.onset_strength librosa.feature.fourier_tempogram Examples -------- Visualize the PLP compared to an onset strength envelope. Both are normalized here to make comparison easier. >>> y, sr = librosa.load(librosa.ex('brahms')) >>> onset_env = librosa.onset.onset_strength(y=y, sr=sr) >>> pulse = librosa.beat.plp(onset_envelope=onset_env, sr=sr) >>> # Or compute pulse with an alternate prior, like log-normal >>> import scipy.stats >>> prior = scipy.stats.lognorm(loc=np.log(120), scale=120, s=1) >>> pulse_lognorm = librosa.beat.plp(onset_envelope=onset_env, sr=sr, ... prior=prior) >>> melspec = librosa.feature.melspectrogram(y=y, sr=sr) >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(nrows=3, sharex=True) >>> librosa.display.specshow(librosa.power_to_db(melspec, ... ref=np.max), ... x_axis='time', y_axis='mel', ax=ax[0]) >>> ax[0].set(title='Mel spectrogram') >>> ax[0].label_outer() >>> ax[1].plot(librosa.times_like(onset_env), ... librosa.util.normalize(onset_env), ... label='Onset strength') >>> ax[1].plot(librosa.times_like(pulse), ... librosa.util.normalize(pulse), ... label='Predominant local pulse (PLP)') >>> ax[1].set(title='Uniform tempo prior [30, 300]') >>> ax[1].label_outer() >>> ax[2].plot(librosa.times_like(onset_env), ... librosa.util.normalize(onset_env), ... label='Onset strength') >>> ax[2].plot(librosa.times_like(pulse_lognorm), ... librosa.util.normalize(pulse_lognorm), ... label='Predominant local pulse (PLP)') >>> ax[2].set(title='Log-normal tempo prior, mean=120', xlim=[5, 20]) >>> ax[2].legend() PLP local maxima can be used as estimates of beat positions. >>> tempo, beats = librosa.beat.beat_track(onset_envelope=onset_env) >>> beats_plp = np.flatnonzero(librosa.util.localmax(pulse)) >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(nrows=2, sharex=True, sharey=True) >>> times = librosa.times_like(onset_env, sr=sr) >>> ax[0].plot(times, librosa.util.normalize(onset_env), ... label='Onset strength') >>> ax[0].vlines(times[beats], 0, 1, alpha=0.5, color='r', ... linestyle='--', label='Beats') >>> ax[0].legend() >>> ax[0].set(title='librosa.beat.beat_track') >>> ax[0].label_outer() >>> # Limit the plot to a 15-second window >>> times = librosa.times_like(pulse, sr=sr) >>> ax[1].plot(times, librosa.util.normalize(pulse), ... label='PLP') >>> ax[1].vlines(times[beats_plp], 0, 1, alpha=0.5, color='r', ... linestyle='--', label='PLP Beats') >>> ax[1].legend() >>> ax[1].set(title='librosa.beat.plp', xlim=[5, 20]) >>> ax[1].xaxis.set_major_formatter(librosa.display.TimeFormatter()) Nrz-tempo_max={} must be larger than tempo_min={})rrrr1)rrr1r.r5r8r:Tr3?rr2)rZn_fftlengthr;)rrr r!r r'rrZfourier_tempo_frequenciesrrCr9rDabsr@maxZtinyZistftr>Zclip normalize) rrrrr1rFrGrZftgramr=ZftmagZ peak_valuesZpulser)r)r*r isT   &c Cs|dkrtdtd||}t||}t|||\}}t|g} || ddkrh| || dqDtj| dddtd} t || |} | S)a)Internal function that tracks beats in an onset strength envelope. Parameters ---------- onset_envelope : np.ndarray [shape=(n,)] onset strength envelope bpm : float [scalar] tempo estimate fft_res : float [scalar] resolution of the fft (sr / hop_length) tightness : float [scalar] how closely do we adhere to bpm? trim : bool [scalar] trim leading/trailing beats with weak onsets? Returns ------- beats : np.ndarray [shape=(n,)] frame numbers of beat events rzbpm must be strictly positivegN@r2Nr) r round__beat_local_score__beat_track_dp __last_beatappendr r#r$ __trim_beats) rrZfft_resrrperiod localscorebacklinkcumscorer(r)r)r*r%)s   r%cCs |jdd}|dkr||}|S)z2Maps onset strength function into the range [0, 1]r)Zddofr)Zstd)ZonsetsZnormr)r)r*__normalize_onsets]s rWcCs<tdt| |dd|d}tjt||dS)z?Construct the local score for an onset envlope and given periodr6rg@@r7same)r exparangescipysignalconvolverW)rrSwindowr)r)r*rNfs(rNc Cstj|td}t|}tjd|t|d dtd}|dkrLtd| t| |d}d}t|D]\}} tdt |d t |} | } | | d||| d| | d<t | } | | | ||<|r| d | krd ||<n|| ||<d }|d}qr||fS) z&Core dynamic program for beat trackingrr5r7rrz#tightness must be strictly positiveTNg{Gz?r2F)r Z zeros_liker$rZrMr log enumeratemaximumminlencopyrArK) rTrSrrUrVr^ZtxwtZ first_beatiZscore_iZz_pad candidatesZ beat_locationr)r)r*rOms& $$    rOcCs8t|}t|t|}t||d|kS)z1Get the last beat from the cumulative score arrayr7)rZlocalmaxr r!argwhererK)rVZmaxesZ med_scorer)r)r*rPs rPcCs\tj||tjdd}|r6d|dd}nd}t||k}|||S)z@Final post-processing: throw out spurious leading/trailing beatsrXrHr7g) r[r\r]Zhannmeanr rgrbrK)rTr(rZ smooth_boe thresholdZvalidr)r)r*rRs rR)__doc__Znumpyr r[Z scipy.stats_cacherrrrZfeaturerrZutil.exceptionsr Zutil.decoratorsr __all__r rir r r%rWrNrOrPrRr)r)r)r*sn        &%@4 -