U 9%e@s dZddlZddlZddlmZddlmZddlm 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%ddddddgZ&eddddddddddd d!d"d#d$dd%ej'e(e)ee$e)e)ee(e(ee(e(e"e*e#ee+eeej'd&d'dZ,eddddddddddd d!d"d#d$dd%ej'e(e)ee$e)e)ee(e(ee(e(e"e*e#e+eeej'd&d(dZ-eddddddddddd d!d"d#dd) ej'e(e)ee$e)e)ee(e(ee(e(e"e*e#eeej'd*d+dZ.ed,ddddddddd d!d"dd$dd- ej'e(e)ee$e)e(e(ee(e(e"e*ee)e+eeej'd.d/dZ/eddddddd0dddddd d!d"d#d$dd1ej'e(e)ee$e)ee+ee(fee(e)ee(e(ee(e(e"e*e#ee+eeej'd2d3dZ0ed4ddd!dej1dfd5d6Z2e ej'e)eej'd7d8d9Z3dMd;d<Z4d=d>Z5d?d@Z6ed"d"dAdBdCZ7dDdddddddd d!d"d#d$dddEdFddGej'e)e(e)ee$e)e(e(ee(e(e"e*e#e+eeee)e(ee+eee)ej8j9ej8j:fej'dHdIdZ;e)ej'dJdKdLZ 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]]) equalr)r5r'r(r)r* intervalsgammar+r,r-r.r/r0r1r2r3r4)r)r5r'r(r)r*r+r,r-r.r/r0r1r2r3r4r:U/var/www/html/Darija-Ai-API/env/lib/python3.8/site-packages/librosa/core/constantq.pyrs(cCs:|dkrtd}|dkr&t|||d}|d||}t|||d}|dkrVt|}n tj|d}tj|||| |d\}}dtt |d |k}t t |}||}g}|d krt ||}| 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. NC1r5r'r+@)r)r+rfreqs)r@r'r-r0alphar r) r'r(r)r*r+r-r.r/r0r1r2r4) r'r(r)r*r+r-r.r/r0r1r2r3r4)rr r__et_relative_bwr_relative_bandwidthwavelet_lengthsnpceillog2intsumminappendrabsr __trim_stackr4)r5r'r(r)r*r+r,r-r.r/r0r1r2r3r4r@rAlengths_Zpseudo_filtersZ n_bins_pseudoZ n_bins_fullcqt_respZ fmin_pseudor:r:r;rszh    ) r'r(r)r*r+r,r-r.r/r0r1r2r4)r5r'r(r)r*r+r,r-r.r/r0r1r2r4r6c  Cs |dkrtd}|dkr&t|||d}| dkr:t|j} |d||}t|||d}|dkrjt|}n tj|d}tj ||| ||d\}}t ||||| || | |d \}}}t |}t ||||| d | d d }| r|t |}n$tj||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?r@r'r0r-rA)r(r0r4rAr%F)r0r4phasendimZaxes)rr r dtype_r2cr4rrCrrDrE__vqt_filter_fftrFrM__cqt_responsesqrt expand_torW)r5r'r(r)r*r+r,r-r.r/r0r1r2r4r@rArOrP fft_basisn_fftCr:r:r;rxsZ`      () r'r(r)r+r,r-r.r/r0r1lengthr3r4)r_r'r(r)r+r,r-r.r/r0r1rar3r4r6c % Cs|dkrtd}|d||}|jd}ttt||}t|||d}|dkr`t|}n tj |d}tj ||| ||d\}}| dk rtt| t ||}|d d|f}t |}d}|g}|g}t |dD]`}|d d d kr|d |d d |d |d d q|d |d |d |d qtt||D]>\}\}}t||||}t|||||}t||||||| | ||d \}}} |j}!dtjtt|!d d}"|"|||9}"| rtjd|!|||"|d |ddfdd}#n"tjd|!|"|d |ddfdd}#t|#d|| d}$tj|$d||| ddd}$|dkrl|$}n|d d|$jdf|$7<qL|dk st| rtj|| 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>rUrRrr?rS.rr g?)r0r4rA)axiszfc,c,c,...ct->...ftT)optimizezfc,c,...ct->...ftones)r0r(r4F)orig_sr target_srr3r1ZfixrBsize) rshaperIrFrGfloatrrCrrDrEmaxr[rangeinsert enumerateziprKslicerYHZtodenserJrZabs2ZasarrayZeinsumr rresampleAssertionErrorZ fix_length)%r_r'r(r)r+r,r-r.r/r0r1rar3r4r* n_octavesr@rArOZf_cutoffZn_framesZC_scaler5ZsrsZhopsimy_srmy_hop n_filtersslr]r^rPZ inv_basisZ freq_powerZD_octZy_octr:r:r;rsr        "r7)r'r(r)r*r8r9r+r,r-r.r/r0r1r2r3r4)r5r'r(r)r*r8r9r+r,r-r.r/r0r1r2r3r4r6c& Cst|tst|}ttt||}t||}|dkrBtd}|dkrXt |||d}|dkrlt |j }|d||}t ||||dd}|| d}t|}|dkrt|}n tj|d}tj||| | ||d \}}|d}||krtd |d |d |dkr$tjd tddd}t|||||||| \}}}g}|||}}}t|D]}|dkrxt| d}nt| |d| |}||} ||}!t|| | | | | |||!d \}"}#}$|"ddt||9<|t||#||"||d|ddkr\|d}|d}tj|dd|dd}q\t |||}%| r|tj||| | ||d \}}$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?)r@r'r0r-r9rAz!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)r0r9r4rAr4rerfr3r1rUrV)# isinstancestrlenrIrFrGrjrKrr rrXr4rrkrCrrDrErwarningswarn FutureWarning__early_downsamplerlrprYr[rLrZrrrrNr\rW)&r5r'r(r)r*r8r9r+r,r-r.r/r0r1r2r3r4rtrxr@Z freqs_topZfmax_trArO filter_cutoffnyquistZvqt_respZmy_yrvrwruryZ freqs_octZ alpha_octr]r^rPVr:r:r;rs                 c  Cstj||||d||| d\} } | jd} |dk rh| ddtt|krhtddtt|} | | ddtjft| 9} t } | j | | ddddd| ddf}t j |||d}|| | fS) z6Generate the frequency domain variable-Q filter basis.T)r@r'r-r.Zpad_fftr0r9rArNr>)nrbr )Zquantiler4) rZwaveletrirFrGrHrIZnewaxisrjrfftrZ sparsify_rows)r'r@r-r.r/r(r0r9r4rAZbasisrOr^rr]r:r:r;rYs$ $(rY)rQr*r4r6c Cstdd|D}t|dj}||d<||d<tj||dd}|}|D]p}|jd}||kr|d| d d |f|dd |d d f<n&|dd |f|d|||d d f<||8}qH|S) z,Trim and stack a collection of CQT responsescss|]}|jdVqdS)rBN)ri).0c_ir:r:r; Isz__trim_stack..rrUrBF)r4order.N)rKlistrirFempty) rQr*r4Zmax_colriZcqt_outendrZn_octr:r:r;rNEs ,& rNrdc Cst||||||d}|s"t|}|d|jd|jdf} tj| jd|jd| jdf|jd} t| jdD]} || | | | <qtt |j} |jd| d<| | S)z3Compute the filter response with a target STFT hop.)r^r(r0r2r4rBrUrr}) r rFrMZreshaperirr4rldotr) r5r^r(r]moder0rTr4DZDrZ output_flatrurir:r:r;rZas(  rZc CsJtdttt||dd}t|}td||d}t||S)z3Compute the number of early downsampling operationsrr)rkrIrFrGrH__num_two_factorsrK)rrr(rtZdownsample_count1num_twosZdownsample_count2r:r:r;__early_downsample_count~s&rc Cst||||}|dkrd|} || }|jd| krRtdt|dd|dd|t| } tj|| d|d d }|s|t| 9}| }|||fS) z=Perform early downsampling on an audio signal, if it applies.rr rBzInput signal length=dz is too short for z -octave CQTrTr~) rrirrrjrrrrFr[) r5r'r(r3rtrrr1Zdownsample_countZdownsample_factorZnew_srr:r:r;rs2 r)Znopythonr cCs2|dkr dSd}|ddkr.|d7}|d}q|S)zjReturn how many times integer x can be evenly divided by 2. Returns 0 for non-positive integers. rr rr:)xrr:r:r;rs  r gGz?random)n_iterr'r(r)r+r,r-r.r/r0r1r2r3r4ramomentuminit random_state)r_rr'r(r)r+r,r-r.r/r0r1r2r3r4rarrrr6cCs|dkrtd}|dkr$tj}nLt|tr>tjj|d}n2t|tjjtjjfrZ|}nt|t d||dkrt j d|ddd n|d krt d |d tj |j tjd }t|}|dkrtdtj|j|j d|dd<n(|dkr d|dd<nt d|dtd}t|D]}|}t||||||||| || || | |d}t||||j d||||| || | | | d}||d|||dd<|ddt||<q.t||||||||| || || | |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. 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