o ۷iӰ+@sdZddlZddlZddlmZddlmZddlm Z ddl m Z ddl m Z mZdd lmZmZdd lmZd d lmZd d lmZd dlmZd dlmZddlmZddlmZmZmZm Z d dl!m"Z"m#Z#m$Z$m%Z%gdZ&eddddddddddddddddd d!ej'd"e(d#e)d$ee$d%e)d&e)d'ee(d(e(d)ee(d*e(d+e"d,e*d-e#d.ee+d/eed0ej'f d1d2Z,eddddddddddddddddd d!ej'd"e(d#e)d$ee$d%e)d&e)d'ee(d(e(d)ee(d*e(d+e"d,e*d-e#d.e+d/eed0ej'f d3d4Z-edddddddddddddddd5 d!ej'd"e(d#e)d$ee$d%e)d&e)d'ee(d(e(d)ee(d*e(d+e"d,e*d-e#d/eed0ej'fd6d7Z.ed8ddddddddddddddd9 d:ej'd"e(d#e)d$ee$d&e)d'e(d(e(d)ee(d*e(d+e"d,e*d;ee)d.e+d/eed0ej'fddddddddddddd?d!ej'd"e(d#e)d$ee$d%e)d@ee+ee(fdAee(d&e)d'ee(d(e(d)ee(d*e(d+e"d,e*d-e#d.ee+d/eed0ej'f$dBdCZ0edDddddej1dfdEdFZ2dGe ej'd%e)d/ed0ej'fdHdIZ3 d`dKdLZ4dMdNZ5dOdPZ6edddQdRdSZ7dTdddddddddddddddUdVddWd:ej'dXe)d"e(d#e)d$ee$d&e)d'e(d(e(d)ee(d*e(d+e"d,e*d-e#d.e+d/eed;ee)dYe(dZee+d[eee)ej8j9ej8j:fd0ej'f(d\d]Z;d&e)d0ej'fd^d_Z 0 [scalar] sampling rate of ``y`` hop_length : int > 0 [scalar] number of samples between successive CQT columns. fmin : float > 0 [scalar] Minimum frequency. Defaults to `C1 ~= 32.70 Hz` n_bins : int > 0 [scalar] Number of frequency bins, starting at ``fmin`` bins_per_octave : int > 0 [scalar] Number of bins per octave tuning : None or float Tuning offset in fractions of a bin. If ``None``, tuning will be automatically estimated from the signal. The minimum frequency of the resulting CQT will be modified to ``fmin * 2**(tuning / bins_per_octave)``. filter_scale : float > 0 Filter scale factor. Small values (<1) use shorter windows for improved time resolution. norm : {inf, -inf, 0, float > 0} Type of norm to use for basis function normalization. See `librosa.util.normalize`. sparsity : float in [0, 1) Sparsify the CQT basis by discarding up to ``sparsity`` fraction of the energy in each basis. Set ``sparsity=0`` to disable sparsification. window : str, tuple, number, or function Window specification for the basis filters. See `filters.get_window` for details. scale : bool If ``True``, scale the CQT response by square-root the length of each channel's filter. This is analogous to ``norm='ortho'`` in FFT. If ``False``, do not scale the CQT. This is analogous to ``norm=None`` in FFT. pad_mode : string Padding mode for centered frame analysis. See also: `librosa.stft` and `numpy.pad`. res_type : string The resampling mode for recursive downsampling. dtype : np.dtype The (complex) data type of the output array. By default, this is inferred to match the numerical precision of the input signal. Returns ------- CQT : np.ndarray [shape=(..., n_bins, t)] Constant-Q value each frequency at each time. See Also -------- vqt librosa.resample librosa.util.normalize Notes ----- This function caches at level 20. Examples -------- Generate and plot a constant-Q power spectrum >>> import matplotlib.pyplot as plt >>> y, sr = librosa.load(librosa.ex('trumpet')) >>> C = np.abs(librosa.cqt(y, sr=sr)) >>> fig, ax = plt.subplots() >>> img = librosa.display.specshow(librosa.amplitude_to_db(C, ref=np.max), ... sr=sr, x_axis='time', y_axis='cqt_note', ax=ax) >>> ax.set_title('Constant-Q power spectrum') >>> fig.colorbar(img, ax=ax, format="%+2.0f dB") Limit the frequency range >>> C = np.abs(librosa.cqt(y, sr=sr, fmin=librosa.note_to_hz('C2'), ... n_bins=60)) >>> C array([[6.830e-04, 6.361e-04, ..., 7.362e-09, 9.102e-09], [5.366e-04, 4.818e-04, ..., 8.953e-09, 1.067e-08], ..., [4.288e-02, 4.580e-01, ..., 1.529e-05, 5.572e-06], [2.965e-03, 1.508e-01, ..., 8.965e-06, 1.455e-05]]) Using a higher frequency resolution >>> C = np.abs(librosa.cqt(y, sr=sr, fmin=librosa.note_to_hz('C2'), ... n_bins=60 * 2, bins_per_octave=12 * 2)) >>> C array([[5.468e-04, 5.382e-04, ..., 5.911e-09, 6.105e-09], [4.118e-04, 4.014e-04, ..., 7.788e-09, 8.160e-09], ..., [2.780e-03, 1.424e-01, ..., 4.225e-06, 2.388e-05], [5.147e-02, 6.959e-02, ..., 1.694e-05, 5.811e-06]]) r6r(r)r*r+ intervalsequalgammarr,r-r.r/r0r1r2r3r4r5N)r)r6r(r)r*r+r,r-r.r/r0r1r2r3r4r5r;r;L/home/ubuntu/vllm_env/lib/python3.10/site-packages/librosa/core/constantq.pyrsH     rcCs8|durtd}|durt|||d}|d||}t|||d}|dkr+t|}ntj|d}tj|||| |d\}}dtt |d |k}t t |}||}g}|d krwt ||}| t||||||||| | | | |d |d kr| tt||||||||| | | | | |d t|||d jS)a Compute the hybrid constant-Q transform of an audio signal. Here, the hybrid CQT uses the pseudo CQT for higher frequencies where the hop_length is longer than half the filter length and the full CQT for lower frequencies. Parameters ---------- y : np.ndarray [shape=(..., n)] audio time series. Multi-channel is supported. sr : number > 0 [scalar] sampling rate of ``y`` hop_length : int > 0 [scalar] number of samples between successive CQT columns. fmin : float > 0 [scalar] Minimum frequency. Defaults to `C1 ~= 32.70 Hz` n_bins : int > 0 [scalar] Number of frequency bins, starting at ``fmin`` bins_per_octave : int > 0 [scalar] Number of bins per octave tuning : None or float Tuning offset in fractions of a bin. If ``None``, tuning will be automatically estimated from the signal. The minimum frequency of the resulting CQT will be modified to ``fmin * 2**(tuning / bins_per_octave)``. filter_scale : float > 0 Filter filter_scale factor. Larger values use longer windows. norm : {inf, -inf, 0, float > 0} Type of norm to use for basis function normalization. See `librosa.util.normalize`. sparsity : float in [0, 1) Sparsify the CQT basis by discarding up to ``sparsity`` fraction of the energy in each basis. Set ``sparsity=0`` to disable sparsification. window : str, tuple, number, or function Window specification for the basis filters. See `filters.get_window` for details. scale : bool If ``True``, scale the CQT response by square-root the length of each channel's filter. This is analogous to ``norm='ortho'`` in FFT. If ``False``, do not scale the CQT. This is analogous to ``norm=None`` in FFT. pad_mode : string Padding mode for centered frame analysis. See also: `librosa.stft` and `numpy.pad`. res_type : string Resampling mode. See `librosa.cqt` for details. dtype : np.dtype, optional The complex dtype to use for computing the CQT. By default, this is inferred to match the precision of the input signal. Returns ------- CQT : np.ndarray [shape=(..., n_bins, t), dtype=np.float] Constant-Q energy for each frequency at each time. See Also -------- cqt pseudo_cqt Notes ----- This function caches at level 20. NC1r6r(r,@)r*r,rfreqs)rAr(r.r1alphar r) r(r)r*r+r,r.r/r0r1r2r3r5) r(r)r*r+r,r.r/r0r1r2r3r4r5)rr r__et_relative_bwr_relative_bandwidthwavelet_lengthsnpceillog2intsumminappendrabsr __trim_stackr5)r6r(r)r*r+r,r-r.r/r0r1r2r3r4r5rArBlengths_pseudo_filters n_bins_pseudo n_bins_fullcqt_resp fmin_pseudor;r;r<rsrh    r) r(r)r*r+r,r-r.r/r0r1r2r3r5c  Cs|durtd}|durt|||d}| durt|j} |d||}t|||d}|dkr5t|}ntj|d}tj ||| ||d\}}t ||||| || | |d \}}}t |}t ||||| d | d d }| rs|t |}|Stj||jd d}|t ||9}|S)aO Compute the pseudo constant-Q transform of an audio signal. This uses a single fft size that is the smallest power of 2 that is greater than or equal to the max of: 1. The longest CQT filter 2. 2x the hop_length Parameters ---------- y : np.ndarray [shape=(..., n)] audio time series. Multi-channel is supported. sr : number > 0 [scalar] sampling rate of ``y`` hop_length : int > 0 [scalar] number of samples between successive CQT columns. fmin : float > 0 [scalar] Minimum frequency. Defaults to `C1 ~= 32.70 Hz` n_bins : int > 0 [scalar] Number of frequency bins, starting at ``fmin`` bins_per_octave : int > 0 [scalar] Number of bins per octave tuning : None or float Tuning offset in fractions of a bin. If ``None``, tuning will be automatically estimated from the signal. The minimum frequency of the resulting CQT will be modified to ``fmin * 2**(tuning / bins_per_octave)``. filter_scale : float > 0 Filter filter_scale factor. Larger values use longer windows. norm : {inf, -inf, 0, float > 0} Type of norm to use for basis function normalization. See `librosa.util.normalize`. sparsity : float in [0, 1) Sparsify the CQT basis by discarding up to ``sparsity`` fraction of the energy in each basis. Set ``sparsity=0`` to disable sparsification. window : str, tuple, number, or function Window specification for the basis filters. See `filters.get_window` for details. scale : bool If ``True``, scale the CQT response by square-root the length of each channel's filter. This is analogous to ``norm='ortho'`` in FFT. If ``False``, do not scale the CQT. This is analogous to ``norm=None`` in FFT. pad_mode : string Padding mode for centered frame analysis. See also: `librosa.stft` and `numpy.pad`. dtype : np.dtype, optional The complex data type for CQT calculations. By default, this is inferred to match the precision of the input signal. Returns ------- CQT : np.ndarray [shape=(..., n_bins, t), dtype=np.float] Pseudo Constant-Q energy for each frequency at each time. Notes ----- This function caches at level 20. Nr=r>r?r*r+r,rr@rAr(r1r.rB)r)r1r5rBr%F)r1r5phasendimaxes)rr r dtype_r2cr5rrDrrErF__vqt_filter_fftrGrN__cqt_responsesqrt expand_tor\)r6r(r)r*r+r,r-r.r/r0r1r2r3r5rArBrPrQ fft_basisn_fftCr;r;r<rxsT`       r() r(r)r*r,r-r.r/r0r1r2lengthr4r5rergc % Cs|durtd}|d||}|jd}ttt||}t|||d}|dkr0t|}ntj |d}tj ||| ||d\}}| dur[tt| t ||}|d d|f}t |}d}|g}|g}t |dD]/}|d d d kr|d |d d |d |d d qn|d |d |d |d qntt||D]\}\}}t||||}t|||||}t||||||| ||d \}}} |j}!dtjtt|!d d}"|"|||9}"| rtjd|!|||"|d |ddfdd}#ntjd|!|"|d |ddfdd}#t|#d|| d}$tj|$d||| ddd}$|dur5|$}q|d d|$jdf|$7<q|dusLJ| rVtj|| d}|S)af Compute the inverse constant-Q transform. Given a constant-Q transform representation ``C`` of an audio signal ``y``, this function produces an approximation ``y_hat``. Parameters ---------- C : np.ndarray, [shape=(..., n_bins, n_frames)] Constant-Q representation as produced by `cqt` sr : number > 0 [scalar] sampling rate of the signal hop_length : int > 0 [scalar] number of samples between successive frames fmin : float > 0 [scalar] Minimum frequency. Defaults to `C1 ~= 32.70 Hz` bins_per_octave : int > 0 [scalar] Number of bins per octave tuning : float [scalar] Tuning offset in fractions of a bin. The minimum frequency of the CQT will be modified to ``fmin * 2**(tuning / bins_per_octave)``. filter_scale : float > 0 [scalar] Filter scale factor. Small values (<1) use shorter windows for improved time resolution. norm : {inf, -inf, 0, float > 0} Type of norm to use for basis function normalization. See `librosa.util.normalize`. sparsity : float in [0, 1) Sparsify the CQT basis by discarding up to ``sparsity`` fraction of the energy in each basis. Set ``sparsity=0`` to disable sparsification. window : str, tuple, number, or function Window specification for the basis filters. See `filters.get_window` for details. scale : bool If ``True``, scale the CQT response by square-root the length of each channel's filter. This is analogous to ``norm='ortho'`` in FFT. If ``False``, do not scale the CQT. This is analogous to ``norm=None`` in FFT. length : int > 0, optional If provided, the output ``y`` is zero-padded or clipped to exactly ``length`` samples. res_type : string Resampling mode. See `librosa.resample` for supported modes. dtype : numeric type Real numeric type for ``y``. Default is inferred to match the numerical precision of the input CQT. Returns ------- y : np.ndarray, [shape=(..., n_samples), dtype=np.float] Audio time-series reconstructed from the CQT representation. See Also -------- cqt librosa.resample Notes ----- This function caches at level 40. Examples -------- Using default parameters >>> y, sr = librosa.load(librosa.ex('trumpet')) >>> C = librosa.cqt(y=y, sr=sr) >>> y_hat = librosa.icqt(C=C, sr=sr) Or with a different hop length and frequency resolution: >>> hop_length = 256 >>> bins_per_octave = 12 * 3 >>> C = librosa.cqt(y=y, sr=sr, hop_length=256, n_bins=7*bins_per_octave, ... bins_per_octave=bins_per_octave) >>> y_hat = librosa.icqt(C=C, sr=sr, hop_length=hop_length, ... bins_per_octave=bins_per_octave) Nr=r?rZrWrr@rX.rr g?)r1rB)axiszfc,c,c,...ct->...ftT)optimizezfc,c,...ct->...ftones)r1r)r5F)orig_sr target_srr4r2fixrCsize) rshaperJrGrHfloatrrDrrErFmaxrarangeinsert enumerateziprLslicer_ conjugateTtodenserKrabs2asarrayeinsumr rresample fix_length)%rer(r)r*r,r-r.r/r0r1r2rgr4r5r+ n_octavesrArBrPf_cutoffn_framesC_scaler6srshopsimy_srmy_hop n_filtersslrcrdrQ inv_basis freq_powerD_octy_octr;r;r<rsr           rr9)r(r)r*r+r8r:r,r-r.r/r0r1r2r3r4r5r8r:c& Csxt|ts t|}ttt||}t||}|dur!td}|dur,t |||d}|dur6t |j }|d||}t ||||dd}|| d}t|}|dkr\t|}ntj|d}tj||| | ||d \}}|d}||krtd |d |d |durtjd tddd}t|||||||| \}}}g}|||}}}t|D]g}|dkrt| d}n t| |d| |}||} ||}!t|| | | | | |||!d \}"}#}$|"ddt||9<|t||#||"||d|ddkr|d}|d}tj|dd|dd}qt |||}%| r:tj||| | ||d \}}$t j!||%j"dd}|%t|}%|%S)u'Compute the variable-Q transform of an audio signal. This implementation is based on the recursive sub-sampling method described by [#]_. .. [#] Schörkhuber, Christian, Anssi Klapuri, Nicki Holighaus, and Monika Dörfler. "A Matlab toolbox for efficient perfect reconstruction time-frequency transforms with log-frequency resolution." In Audio Engineering Society Conference: 53rd International Conference: Semantic Audio. Audio Engineering Society, 2014. Parameters ---------- y : np.ndarray [shape=(..., n)] audio time series. Multi-channel is supported. sr : number > 0 [scalar] sampling rate of ``y`` hop_length : int > 0 [scalar] number of samples between successive VQT columns. fmin : float > 0 [scalar] Minimum frequency. Defaults to `C1 ~= 32.70 Hz` n_bins : int > 0 [scalar] Number of frequency bins, starting at ``fmin`` intervals : str or array of floats in [1, 2) Either a string specification for an interval set, e.g., `'equal'`, `'pythagorean'`, `'ji3'`, etc. or an array of intervals expressed as numbers between 1 and 2. .. see also:: librosa.interval_frequencies gamma : number > 0 [scalar] Bandwidth offset for determining filter lengths. If ``gamma=0``, produces the constant-Q transform. If 'gamma=None', gamma will be calculated such that filter bandwidths are equal to a constant fraction of the equivalent rectangular bandwidths (ERB). This is accomplished by solving for the gamma which gives:: B_k = alpha * f_k + gamma = C * ERB(f_k), where ``B_k`` is the bandwidth of filter ``k`` with center frequency ``f_k``, alpha is the inverse of what would be the constant Q-factor, and ``C = alpha / 0.108`` is the constant fraction across all filters. Here we use ``ERB(f_k) = 24.7 + 0.108 * f_k``, the best-fit curve derived from experimental data in [#]_. .. [#] Glasberg, Brian R., and Brian CJ Moore. "Derivation of auditory filter shapes from notched-noise data." Hearing research 47.1-2 (1990): 103-138. bins_per_octave : int > 0 [scalar] Number of bins per octave tuning : None or float Tuning offset in fractions of a bin. If ``None``, tuning will be automatically estimated from the signal. The minimum frequency of the resulting VQT will be modified to ``fmin * 2**(tuning / bins_per_octave)``. filter_scale : float > 0 Filter scale factor. Small values (<1) use shorter windows for improved time resolution. norm : {inf, -inf, 0, float > 0} Type of norm to use for basis function normalization. See `librosa.util.normalize`. sparsity : float in [0, 1) Sparsify the VQT basis by discarding up to ``sparsity`` fraction of the energy in each basis. Set ``sparsity=0`` to disable sparsification. window : str, tuple, number, or function Window specification for the basis filters. See `filters.get_window` for details. scale : bool If ``True``, scale the VQT response by square-root the length of each channel's filter. This is analogous to ``norm='ortho'`` in FFT. If ``False``, do not scale the VQT. This is analogous to ``norm=None`` in FFT. pad_mode : string Padding mode for centered frame analysis. See also: `librosa.stft` and `numpy.pad`. res_type : string The resampling mode for recursive downsampling. dtype : np.dtype The dtype of the output array. By default, this is inferred to match the numerical precision of the input signal. Returns ------- VQT : np.ndarray [shape=(..., n_bins, t), dtype=np.complex] Variable-Q value each frequency at each time. See Also -------- cqt Notes ----- This function caches at level 20. Examples -------- Generate and plot a variable-Q power spectrum >>> import matplotlib.pyplot as plt >>> y, sr = librosa.load(librosa.ex('choice'), duration=5) >>> C = np.abs(librosa.cqt(y, sr=sr)) >>> V = np.abs(librosa.vqt(y, sr=sr)) >>> fig, ax = plt.subplots(nrows=2, sharex=True, sharey=True) >>> librosa.display.specshow(librosa.amplitude_to_db(C, ref=np.max), ... sr=sr, x_axis='time', y_axis='cqt_note', ax=ax[0]) >>> ax[0].set(title='Constant-Q power spectrum', xlabel=None) >>> ax[0].label_outer() >>> img = librosa.display.specshow(librosa.amplitude_to_db(V, ref=np.max), ... sr=sr, x_axis='time', y_axis='cqt_note', ax=ax[1]) >>> ax[1].set_title('Variable-Q power spectrum') >>> fig.colorbar(img, ax=ax, format="%+2.0f dB") Nr=r>r?T)r+r*r8r,sortrr@)rAr(r1r.r:rBz!Wavelet basis with max frequency=z$ would exceed the Nyquist frequency=z,. Try reducing the number of frequency bins.zdSupport for VQT with res_type=None is deprecated in librosa 0.10 and will be removed in version 1.0.r )category stacklevelr'r)r1r:r5rBr5rkrlr4r2rZr[)# isinstancestrlenrJrGrHrqrLrr rr^r5rrrrDrrErFrwarningswarn FutureWarning__early_downsamplersrwr_rarMr`rr~rOrbr\)&r6r(r)r*r+r8r:r,r-r.r/r0r1r2r3r4r5rrrA freqs_topfmax_trBrP filter_cutoffnyquistvqt_respmy_yrrrr freqs_oct alpha_octrcrdrQVr;r;r<rs                r c  Cstj||||d||| d\} } | jd} |dur4| ddtt|kr4tddtt|} | | ddtjft| 9} t } | j | | ddddd| ddf}t j |||d}|| | fS) z6Generate the frequency domain variable-Q filter basis.T)rAr(r.r/pad_fftr1r:rBrNr?)nrhr )quantiler5) rwaveletrprGrHrIrJnewaxisrqrfftr sparsify_rows)r(rAr.r/r0r)r1r:r5rBbasisrPrdrrcr;r;r<r_s$ $( r_rUc Cstdd|D}t|dj}||d<||d<tj||dd}|}|D]8}|jd}||krE|d| d d |f|dd |d d f<n|dd |f|d|||d d f<||8}q$|S) z,Trim and stack a collection of CQT responsescss|]}|jdVqdS)rCN)rp).0c_ir;r;r< Hsz__trim_stack..rrZrCF)r5order.N)rLlistrprGempty) rUr+r5max_colrpcqt_outendrn_octr;r;r<rODs ,& rOrjc Cst||||||d}|st|}|d|jd|jdf} tj| jd|jd| jdf|jd} t| jdD] } || | | | <q:t |j} |jd| d<| | S)z3Compute the filter response with a target STFT hop.)rdr)r1r3r5rCrZrr) r rGrNreshaperprr5rsdotr) r6rdr)rcmoder1rYr5DDr output_flatrrpr;r;r<r``s    r`c CsJtdttt||dd}t|}td||d}t||S)z3Compute the number of early downsampling operationsrr)rrrJrGrHrI__num_two_factorsrL)rrr)rdownsample_count1num_twosdownsample_count2r;r;r<__early_downsample_count}s& rc Cst||||}|dkrDd|} || }|jd| kr)tdt|dd|dd|t| } tj|| d|d d }|sB|t| 9}| }|||fS) z=Perform early downsampling on an audio signal, if it applies.rr rCzInput signal length=dz is too short for z -octave CQTrTr) rrprrrqrr~rGra) r6r(r)r4rrrr2downsample_countdownsample_factornew_srr;r;r<rs(   r)nopythonr cCs<|dkrdSd}|ddkr|d7}|d}|ddks|S)zjReturn how many times integer x can be evenly divided by 2. Returns 0 for non-positive integers. rr rr;)xrr;r;r<rs  r gGz?random)n_iterr(r)r*r,r-r.r/r0r1r2r3r4r5rgmomentuminit random_staterrrrcCs|durtd}|durtj}n&t|trtjj|d}nt|tjjtjjfr-|}n t|t d||dkrHt j d|ddd n |d krTt d |d tj |j tjd }t|}|dkrztdtj|j|j d|dd<n|durd|dd<nt d|dtd}t|D]J}|}t||||||||| || || | |d}t||||j d||||| || | | | d}||d|||dd<|ddt||<qt||||||||| || || | |dS)u Approximate constant-Q magnitude spectrogram inversion using the "fast" Griffin-Lim algorithm. Given the magnitude of a constant-Q spectrogram (``C``), the algorithm randomly initializes phase estimates, and then alternates forward- and inverse-CQT operations. [#]_ This implementation is based on the (fast) Griffin-Lim method for Short-time Fourier Transforms, [#]_ but adapted for use with constant-Q spectrograms. .. [#] D. W. Griffin and J. S. Lim, "Signal estimation from modified short-time Fourier transform," IEEE Trans. ASSP, vol.32, no.2, pp.236–243, Apr. 1984. .. [#] Perraudin, N., Balazs, P., & Søndergaard, P. L. "A fast Griffin-Lim algorithm," IEEE Workshop on Applications of Signal Processing to Audio and Acoustics (pp. 1-4), Oct. 2013. Parameters ---------- C : np.ndarray [shape=(..., n_bins, n_frames)] The constant-Q magnitude spectrogram n_iter : int > 0 The number of iterations to run sr : number > 0 Audio sampling rate hop_length : int > 0 The hop length of the CQT fmin : number > 0 Minimum frequency for the CQT. If not provided, it defaults to `C1`. bins_per_octave : int > 0 Number of bins per octave tuning : float Tuning deviation from A440, in fractions of a bin filter_scale : float > 0 Filter scale factor. Small values (<1) use shorter windows for improved time resolution. norm : {inf, -inf, 0, float > 0} Type of norm to use for basis function normalization. See `librosa.util.normalize`. sparsity : float in [0, 1) Sparsify the CQT basis by discarding up to ``sparsity`` fraction of the energy in each basis. Set ``sparsity=0`` to disable sparsification. window : str, tuple, or function Window specification for the basis filters. See `filters.get_window` for details. scale : bool If ``True``, scale the CQT response by square-root the length of each channel's filter. This is analogous to ``norm='ortho'`` in FFT. If ``False``, do not scale the CQT. This is analogous to ``norm=None`` in FFT. pad_mode : string Padding mode for centered frame analysis. See also: `librosa.stft` and `numpy.pad`. res_type : string The resampling mode for recursive downsampling. See ``librosa.resample`` for a list of available options. dtype : numeric type Real numeric type for ``y``. Default is inferred to match the precision of the input CQT. length : int > 0, optional If provided, the output ``y`` is zero-padded or clipped to exactly ``length`` samples. momentum : float > 0 The momentum parameter for fast Griffin-Lim. Setting this to 0 recovers the original Griffin-Lim method. Values near 1 can lead to faster convergence, but above 1 may not converge. init : None or 'random' [default] If 'random' (the default), then phase values are initialized randomly according to ``random_state``. This is recommended when the input ``C`` is a magnitude spectrogram with no initial phase estimates. If ``None``, then the phase is initialized from ``C``. This is useful when an initial guess for phase can be provided, or when you want to resume Griffin-Lim from a previous output. random_state : None, int, np.random.RandomState, or np.random.Generator If int, random_state is the seed used by the random number generator for phase initialization. If `np.random.RandomState` or `np.random.Generator` instance, the random number generator itself. If ``None``, defaults to the `np.random.default_rng()` object. Returns ------- y : np.ndarray [shape=(..., n)] time-domain signal reconstructed from ``C`` See Also -------- cqt icqt griffinlim filters.get_window resample Examples -------- A basis CQT inverse example >>> y, sr = librosa.load(librosa.ex('trumpet', hq=True), sr=None) >>> # Get the CQT magnitude, 7 octaves at 36 bins per octave >>> C = np.abs(librosa.cqt(y=y, sr=sr, bins_per_octave=36, n_bins=7*36)) >>> # Invert using Griffin-Lim >>> y_inv = librosa.griffinlim_cqt(C, sr=sr, bins_per_octave=36) >>> # And invert without estimating phase >>> y_icqt = librosa.icqt(C, sr=sr, bins_per_octave=36) Wave-plot the results >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(nrows=3, sharex=True, sharey=True) >>> librosa.display.waveshow(y, sr=sr, color='b', ax=ax[0]) >>> ax[0].set(title='Original', xlabel=None) >>> ax[0].label_outer() >>> librosa.display.waveshow(y_inv, sr=sr, color='g', ax=ax[1]) >>> ax[1].set(title='Griffin-Lim reconstruction', xlabel=None) >>> ax[1].label_outer() >>> librosa.display.waveshow(y_icqt, sr=sr, color='r', ax=ax[2]) >>> ax[2].set(title='Magnitude-only icqt reconstruction') Nr=)seedzUnsupported random_state=rzGriffin-Lim with momentum=z+ > 1 can be unstable. Proceed with caution!r )rrz&griffinlim_cqt() called with momentum=z < 0rrrng?zinit=z must either None or 'random'r$) r(r)r,r*r-r.r1rgr4r/r2r0r5rZ) r(r,r+r)r*r-r.r1r/r2r0r3r4) r(r)r,r-r.r*r1rgr4r/r2r0r5)rrGr default_rngrrJ RandomState Generatorrrrrrrp complex64rtinyphasorpiarrayrsrrrN)rerr(r)r*r,r-r.r/r0r1r2r3r4r5rgrrrrnganglesepsrebuiltrQtprevinverser;r;r<rs,    (   rcCs*dd|}t|dd|ddS)aCompute the relative bandwidth coefficient for equal (geometric) freuqency spacing and a give number of bins per octave. This is a special case of the more general `relative_bandwidth` calculation that can be used when only a single basis frequency is used. Parameters ---------- bins_per_octave : int Returns ------- alpha : np.ndarray > 0 Value is cast up to a 1d array to allow slicing r r)rG atleast_1d)r,rr;r;r<rDs rD)rjTN)=__doc__rnumpyrGnumbarrr8rrrconvertrrspectrumr r pitchr _cacher rrutil.exceptionsr numpy.typingrtypingrrrr_typingrrrr__all__ndarrayrqrJboolrrrrrrrr_rOr`rrrrrrrrDr;r;r;r<s                %      8            b      " +   "