}Kgǰ+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%gdZ&edddddddddddddddd d!ejNd"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/eed0ejNf d1Z,edddddddddddddddd d!ejNd"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/eed0ejNf d2Z-eddddddddddddddd3 d!ejNd"e(d#e)d$ee$d%e)d&e)d'ee(d(e(d)ee(d*e(d+e"d,e*d-e#d/eed0ejNfd4Z.ed5dddddddddddddd6 d7ejNd"e(d#e)d$ee$d&e)d'e(d(e(d)ee(d*e(d+e"d,e*d8ee)d.e+d/eed0ejNfd9Z/edddddd:dddddddddddd;d!ejNd"e(d#e)d$ee$d%e)dZ0ed?dddejbdfd@Z2dAe ejNd%e)d/ed0ejNfdBZ3 dRdCZ4dDZ5dEZ6eddFdGZ7dHdddddddddddddddIdJddKd7ejNdLe)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/eed8ee)dMe(dNee+dOeee)ejpjrejpjtfd0ejNf(dPZ;d&e)d0ejNfdQZ 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]]) r7r)r*r+r, intervalsequalgammarr-r.r/r0r1r2r3r4r5r6)r )r7r)r*r+r,r-r.r/r0r1r2r3r4r5r6s Z/home/alanp/www/video.onchill/myenv/lib/python3.12/site-packages/librosa/core/constantq.pyrrs`                (  "       ! "# c| td}|t|||}|d||z zz}t|||}|dk(r t|}nt j |}t j |||| |\}}dtjtj|zd|zk}ttj|}||z }g}|d kDr?tj||}|jt||||||||| | | | | |d kDr;|jtjt!||||||||| | | | | | t#|||d j$S) 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. C1r7r)r-@)r+r-rfreqs)rEr)r/r2alphar r) r)r*r+r,r-r/r0r1r2r3r4r6) r)r*r+r,r-r/r0r1r2r3r4r5r6)r r r__et_relative_bwr_relative_bandwidthwavelet_lengthsnpceillog2intsumminappendrabsr __trim_stackr6)r7r)r*r+r,r-r.r/r0r1r2r3r4r5r6rErFlengths_pseudo_filters n_bins_pseudo n_bins_fullcqt_resp fmin_pseudos r>rrsP |$ ~ 1_M #&?23 3D F OE{ 1++%8((fEJGQ BGGBGGG$455JFN~./M=(KHqffU>23  % $ /)!!  $Q FF)&$3!-%!%%  , &(2,*<*< ==r?) r)r*r+r,r-r.r/r0r1r2r3r4r6c n| td}|t|||}| tj|j} |d||z zz}t |||}|dk(r t |}ntj|}tj||| ||\}}t||||| || | | \}}}tj|}t||||| d | d }| r|tj|z}|Stj||j d }|tj||z z}|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. rArBrCr+r,r-rrDrEr)r2r/rF)r*r2r6rFr&F)r2r6phasendimaxes)r r r dtype_r2cr6rrHrrIrJ__vqt_filter_fftrKrR__cqt_responsesqrt expand_tora)r7r)r*r+r,r-r.r/r0r1r2r3r4r6rErFrTrU fft_basisn_fftCs r>rrxsV@ |$ ~ 1_M }qww' #&?23 3D fo VE { 1++%8((6 EJGQ+    Iuay!I#   A  RWWU^ H ..qvvB? RWWWu_ %% Hr?() r)r*r+r-r.r/r0r1r2r3lengthr5r6rjrlc | td}|d||z zz}|jd}ttjt ||z }t |||}|dk(r t|}ntj|}tj||| ||\}}| 6ttj| t|z|z }|d d|f}tj|}d}|g}|g}t|dz D]h}|d d zd k(r1|jd |d d z|jd |d d z?|jd |d |jd |d jtt!||D]M\}\}}t#||||zz }t%||z||z|z}t'||||||| || \}}} |j(j+}!dtj,t/j0tj2|!d z }"|"|||z z}"| r'tj4d|!|||"|d |ddfd}#n"tj4d|!|"|d |ddfd}#t7|#d|| }$t9j:|$d||z| dd}$||$}0|d d|$jdfxx|$z cc<P|J| rt/j<|| }|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) NrArCr_r\rrDr].rr g?)r2rF)axiszfc,c,c,...ct->...ftT)optimizezfc,c,...ct->...ftones)r2r*r6F)orig_sr target_srr5r3fixrGsize)r shaperNrKrLfloatrrHrrIrJmaxrfrangeinsert enumerateziprPslicerdHtodenserOrabs2asarrayeinsumr rresample fix_length)%rjr)r*r+r-r.r/r0r1r2r3rlr5r6r, n_octavesrErFrTf_cutoffn_framesC_scaler7srshopsimy_srmy_hop n_filtersslrhrirU inv_basis freq_powerD_octy_octs% r>rrs0d |$ #&?23 3DWWR[FBGGE&MO;<=I fo VE { 1++%8//6 EGX rwwW 5CDE c9H9n gggG#A $C |dd|d}tA|||}%| rXt!j$||| | || \}}$tjB||%jDd}|%t j6|z}%|%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") NrArBrCT)r,r+r:r-sortrrD)rEr)r2r/r<rFz!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)r2r<r6rFr6rqrrr5r3r_r`)# isinstancestrlenrNrKrLrwrPr r rrcr6rrxrHrrIrJrwarningswarn FutureWarning__early_downsampleryr}rdrfrQrerrrSrgra)&r7r)r*r+r,r:r<r-r.r/r0r1r2r3r4r5r6rrrE freqs_topfmax_trFrT filter_cutoffnyquistvqt_respmy_yrrrr freqs_oct alpha_octrhrirUVs& r>r r sz i %i.BGGE&MO;<=IOV,I |$ ~ 1_M }qww' #&?23 3D ! '   E&'(IFF9%F { 1++%8$44 ! G]3hGw/x7[\c[de9 9    2"  * 2z8YAr:HR%D 9  6 z4(B zQU+iZ!^>a1xtDEL Xvu-A ,,%  ..qvvB? RWWW  Hr? c tj||||d||| \} } | jd} |h| ddtjtj |zzkr7t ddtjtj |zz} | | ddtjft| z z} t} | j| | dddd| dzdzf}tj|||}|| | fS) z6Generate the frequency domain variable-Q filter basis.T)rEr)r/r0pad_fftr2r<rFrNrC)nrnr )quantiler6) rwaveletrvrKrLrMrNnewaxisrwrfftr sparsify_rows)r)rEr/r0r1r*r2r<r6rFbasisrTrirrhs r>rdrds__ !  NE7 KKNE%#!bggbggj>Q6R2R*S"SCA (; <<=> WQ ] #eEl 22E ,CQ/3EeqjA5E3E0EFI""9xuMI eW $$r?rYc>td|D}t|dj}||d<||d<tj||d}|}|D]I}|jd}||kr|d| dd|f|dd|ddf<n|dd|f|d||z |ddf<||z}K|S) z,Trim and stack a collection of CQT responsesc3:K|]}|jdyw)rGN)rv).0c_is r> z__trim_stack..Hs48C#))B-8srr_rGF)r6order.N)rPlistrvrKempty) rYr,r6max_colrvcqt_outendrn_octs r>rSrSDs4844G !"" #EE"IE"IhhuE5G C "  ;$'cTUHWH(<$=GC#qL !14S(7(]1CGCus*A- . u  Nr?ct||||||}|stj|}|jd|jd|jdf} tj | jd|jd| jdf|j } t| jdD]} |j| | | | <t|j} |jd| d<| j| S)z3Compute the filter response with a target STFT hop.)rir*r2r4r6rGr_rr) r rKrRreshapervrr6rydotr) r7rir*rhmoder2r^r6DDr output_flatrrvs r>rere`s  :ftSX A  FF1I B QWWR[1 2B(( !iooa("((2,7qwwK 288A; "r!u- A  ME"E"I   u %%r?c tdttjtj||z dz dz }t |}td||z dz}t ||S)z3Compute the number of early downsampling operationsrr)rxrNrKrLrM__num_two_factorsrP)rrr*rdownsample_count1num_twosdownsample_count2s r>__early_downsample_countr}sfAs2772777]3J+K#Lq#PQTUUV ,HAx)3a78  "3 44r?c,t||||}|dkDr}d|z} || z}|jd| krtdt|dd|dd|t | z } t j || d|d }|s|tj| z}| }|||fS) z=Perform early downsampling on an audio signal, if it applies.rr rGzInput signal length=dz is too short for z -octave CQTrTr) rrvrrrwrrrKrf) r7r)r*r5rrrr3downsample_countdownsample_factornew_srs r>rrs0 I!"23(( 772;* * &s1vaj0BQ-{,  e-.. NN (APT   *+ +A  b* r?)nopythonrcL|dkryd}|dzdk(r|dz }|dz}|dzdk(r|S)zjReturn how many times integer x can be evenly divided by 2. Returns 0 for non-positive integers. rr rr=)xrs r>rrsD  AvH a%1*A  a a%1* Or? gGz?random)n_iterr)r*r+r-r.r/r0r1r2r3r4r5r6rlmomentuminit random_staterrrrc| td}|tjj}nt |t r!tjj |}nZt |tjj tjjfr|}nt|td||dkDrtjd|dd n|d krtd |d tj|jtj }tj |}|dk(rGtj"dtj$z|j|jz|ddn|d|ddntd|dtj&d}t)|D]{}|}t+||z||||||| || || | |}t-||||jd||||| || | | | }||d|zz |zz |dd|ddxxxtj.||zzccc}t+||z||||||| || || | |S)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') NrA)seedzUnsupported random_state=rzGriffin-Lim with momentum=z+ > 1 can be unstable. Proceed with caution!r )rrz&griffinlim_cqt() called with momentum=z < 0rrrtg?zinit=z must either None or 'random'r%) r)r*r-r+r.r/r2rlr5r0r3r1r6r_) r)r-r,r*r+r.r/r2r0r3r1r4r5) r)r*r-r.r/r+r2rlr5r0r3r1r6)r rKr default_rngrrN RandomState Generatorrrrrrrv complex64rtinyphasorpiarrayryrrrR)rjrr)r*r+r-r.r/r0r1r2r3r4r5r6rlrrrrnganglesepsrebuiltrUtprevinverses r>rrsiV |$ii##% L# &ii###6 L299#8#8")):M:M"N Ol+88HIJJ!| ( 3$ $ AEhZtTUUXXaggR\\ 2F ))F C xKKBEE CJJAGGJ,D DEq q uTF*GHII((3-G 6] J!+% $ +772;!% $x1x<8EAAq q RVVF^c)) UZ  F '!   r?cZdd|z z}tj|dzdz |dzdzz S)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)rK atleast_1d)r-rs r>rHrHs7$ a/!"A ==!Q$(q!tax0 11r?)rpTN)=__doc__rnumpyrKnumbarrr:rrrconvertrr spectrumr r pitchr _cacherrrutil.exceptionsr numpy.typingrtypingrrrr_typingrrrr__all__ndarrayrwrNboolrrrrrr rrdrSrerrrrrrrrHr=r?r>rs+0!","44QQ N R$(! #'!%!a zza a a = ! a  aa UOaa 5/aa a aasma I !a"ZZ#aaHR$(! #!%!t> zzt> t> t> = ! t>  t>t> UOt>t> 5/t>t> t> t>t>t> I !t>"ZZ#t>t>nR$(! #!%Y  zzY  Y  Y = ! Y  Y Y  UOY Y  5/Y Y  Y  Y Y  I Y ZZ!Y Y xR$(  !%^  zz^  ^  ^ = ! ^  ^  ^ ^  5/^ ^  ^  ^  SM^ ^  I ^ ZZ!^ ^ BR$(/6!! #'!%%]  zz]  ]  ] = ! ]  ] S*U++,]  E?] ]  UO] ]  5/] ]  ]  ] !] "sm#] $ I %] &ZZ'] ] @ R  ,, (%(%V2::(+4=ZZ:MQ&:5Dd$   $$( #!% " -M zzM M  M  M = ! MM MM 5/MM M MMM I !M" SM#M$%M& 3-'M( c299(("))*=*==>)M.ZZ/M`2c2bjj2r?