import torch.nn as nn import torch import numpy as np from time import time from ..utils import * from ..utils import * class CQT1992(nn.Module): """ This alogrithm uses the method proposed in [1], which would run extremely slow if low frequencies (below 220Hz) are included in the frequency bins. Please refer to :func:`~nnAudio.Spectrogram.CQT1992v2` for a more computational and memory efficient version. [1] Brown, Judith C.C. and Miller Puckette. “An efficient algorithm for the calculation of a constant Q transform.” (1992). This function is to calculate the CQT of the input signal. Input signal should be in either of the following shapes.\n 1. ``(len_audio)``\n 2. ``(num_audio, len_audio)``\n 3. ``(num_audio, 1, len_audio)`` The correct shape will be inferred autommatically if the input follows these 3 shapes. Most of the arguments follow the convention from librosa. This class inherits from ``nn.Module``, therefore, the usage is same as ``nn.Module``. Parameters ---------- sr : int The sampling rate for the input audio. It is used to calucate the correct ``fmin`` and ``fmax``. Setting the correct sampling rate is very important for calculating the correct frequency. hop_length : int The hop (or stride) size. Default value is 512. fmin : float The frequency for the lowest CQT bin. Default is 32.70Hz, which coresponds to the note C0. fmax : float The frequency for the highest CQT bin. Default is ``None``, therefore the higest CQT bin is inferred from the ``n_bins`` and ``bins_per_octave``. If ``fmax`` is not ``None``, then the argument ``n_bins`` will be ignored and ``n_bins`` will be calculated automatically. Default is ``None`` n_bins : int The total numbers of CQT bins. Default is 84. Will be ignored if ``fmax`` is not ``None``. bins_per_octave : int Number of bins per octave. Default is 12. trainable_STFT : bool Determine if the time to frequency domain transformation kernel for the input audio is trainable or not. Default is ``False`` trainable_CQT : bool Determine if the frequency domain CQT kernel is trainable or not. Default is ``False`` norm : int Normalization for the CQT kernels. ``1`` means L1 normalization, and ``2`` means L2 normalization. Default is ``1``, which is same as the normalization used in librosa. window : str The windowing function for CQT. It uses ``scipy.signal.get_window``, please refer to scipy documentation for possible windowing functions. The default value is 'hann'. center : bool Putting the CQT keneral at the center of the time-step or not. If ``False``, the time index is the beginning of the CQT kernel, if ``True``, the time index is the center of the CQT kernel. Default value if ``True``. pad_mode : str The padding method. Default value is 'reflect'. trainable : bool Determine if the CQT kernels are trainable or not. If ``True``, the gradients for CQT kernels will also be caluclated and the CQT kernels will be updated during model training. Default value is ``False``. output_format : str Determine the return type. ``Magnitude`` will return the magnitude of the STFT result, shape = ``(num_samples, freq_bins,time_steps)``; ``Complex`` will return the STFT result in complex number, shape = ``(num_samples, freq_bins,time_steps, 2)``; ``Phase`` will return the phase of the STFT reuslt, shape = ``(num_samples, freq_bins,time_steps, 2)``. The complex number is stored as ``(real, imag)`` in the last axis. Default value is 'Magnitude'. verbose : bool If ``True``, it shows layer information. If ``False``, it suppresses all prints Returns ------- spectrogram : torch.tensor It returns a tensor of spectrograms. shape = ``(num_samples, freq_bins,time_steps)`` if ``output_format='Magnitude'``; shape = ``(num_samples, freq_bins,time_steps, 2)`` if ``output_format='Complex' or 'Phase'``; Examples -------- >>> spec_layer = Spectrogram.CQT1992v2() >>> specs = spec_layer(x) """ def __init__( self, sr=22050, hop_length=512, fmin=220, fmax=None, n_bins=84, trainable_STFT=False, trainable_CQT=False, bins_per_octave=12, filter_scale=1, output_format="Magnitude", norm=1, window="hann", center=True, pad_mode="reflect", ): super().__init__() # norm arg is not functioning self.hop_length = hop_length self.center = center self.pad_mode = pad_mode self.norm = norm self.output_format = output_format # creating kernels for CQT Q = float(filter_scale) / (2 ** (1 / bins_per_octave) - 1) print("Creating CQT kernels ...", end="\r") start = time() cqt_kernels, self.kernel_width, lenghts, freqs = create_cqt_kernels( Q, sr, fmin, n_bins, bins_per_octave, norm, window, fmax ) self.register_buffer("lenghts", lenghts) self.frequencies = freqs cqt_kernels = fft(cqt_kernels)[:, : self.kernel_width // 2 + 1] print("CQT kernels created, time used = {:.4f} seconds".format(time() - start)) # creating kernels for stft # self.cqt_kernels_real*=lenghts.unsqueeze(1)/self.kernel_width # Trying to normalize as librosa # self.cqt_kernels_imag*=lenghts.unsqueeze(1)/self.kernel_width print("Creating STFT kernels ...", end="\r") start = time() kernel_sin, kernel_cos, self.bins2freq, _, window = create_fourier_kernels( self.kernel_width, window="ones", freq_scale="no" ) # Converting kernels from numpy arrays to torch tensors wsin = torch.tensor(kernel_sin * window) wcos = torch.tensor(kernel_cos * window) cqt_kernels_real = torch.tensor(cqt_kernels.real) cqt_kernels_imag = torch.tensor(cqt_kernels.imag) if trainable_STFT: wsin = nn.Parameter(wsin, requires_grad=trainable_STFT) wcos = nn.Parameter(wcos, requires_grad=trainable_STFT) self.register_parameter("wsin", wsin) self.register_parameter("wcos", wcos) else: self.register_buffer("wsin", wsin) self.register_buffer("wcos", wcos) if trainable_CQT: cqt_kernels_real = nn.Parameter( cqt_kernels_real, requires_grad=trainable_CQT ) cqt_kernels_imag = nn.Parameter( cqt_kernels_imag, requires_grad=trainable_CQT ) self.register_parameter("cqt_kernels_real", cqt_kernels_real) self.register_parameter("cqt_kernels_imag", cqt_kernels_imag) else: self.register_buffer("cqt_kernels_real", cqt_kernels_real) self.register_buffer("cqt_kernels_imag", cqt_kernels_imag) print("STFT kernels created, time used = {:.4f} seconds".format(time() - start)) def forward(self, x, output_format=None, normalization_type="librosa"): """ Convert a batch of waveforms to CQT spectrograms. Parameters ---------- x : torch tensor Input signal should be in either of the following shapes.\n 1. ``(len_audio)``\n 2. ``(num_audio, len_audio)``\n 3. ``(num_audio, 1, len_audio)`` It will be automatically broadcast to the right shape """ output_format = output_format or self.output_format x = broadcast_dim(x) if self.center: if self.pad_mode == "constant": padding = nn.ConstantPad1d(self.kernel_width // 2, 0) elif self.pad_mode == "reflect": padding = nn.ReflectionPad1d(self.kernel_width // 2) x = padding(x) # STFT fourier_real = conv1d(x, self.wcos, stride=self.hop_length) fourier_imag = conv1d(x, self.wsin, stride=self.hop_length) # CQT CQT_real, CQT_imag = complex_mul( (self.cqt_kernels_real, self.cqt_kernels_imag), (fourier_real, fourier_imag) ) CQT = torch.stack((CQT_real, -CQT_imag), -1) if normalization_type == "librosa": CQT *= torch.sqrt(self.lenghts.view(-1, 1, 1)) / self.kernel_width elif normalization_type == "convolutional": pass elif normalization_type == "wrap": CQT *= 2 / self.kernel_width else: raise ValueError( "The normalization_type %r is not part of our current options." % normalization_type ) # if self.norm: # CQT = CQT/self.kernel_width*torch.sqrt(self.lenghts.view(-1,1,1)) # else: # CQT = CQT*torch.sqrt(self.lenghts.view(-1,1,1)) if output_format == "Magnitude": # Getting CQT Amplitude return torch.sqrt(CQT.pow(2).sum(-1)) elif output_format == "Complex": return CQT elif output_format == "Phase": phase_real = torch.cos(torch.atan2(CQT_imag, CQT_real)) phase_imag = torch.sin(torch.atan2(CQT_imag, CQT_real)) return torch.stack((phase_real, phase_imag), -1) def extra_repr(self) -> str: return "STFT kernel size = {}, CQT kernel size = {}".format( (*self.wcos.shape,), (*self.cqt_kernels_real.shape,) ) class CQT2010(nn.Module): """ This algorithm is using the resampling method proposed in [1]. Instead of convoluting the STFT results with a gigantic CQT kernel covering the full frequency spectrum, we make a small CQT kernel covering only the top octave. Then we keep downsampling the input audio by a factor of 2 to convoluting it with the small CQT kernel. Everytime the input audio is downsampled, the CQT relative to the downsampled input is equavalent to the next lower octave. The kernel creation process is still same as the 1992 algorithm. Therefore, we can reuse the code from the 1992 alogrithm [2] [1] Schörkhuber, Christian. “CONSTANT-Q TRANSFORM TOOLBOX FOR MUSIC PROCESSING.” (2010). [2] Brown, Judith C.C. and Miller Puckette. “An efficient algorithm for the calculation of a constant Q transform.” (1992). early downsampling factor is to downsample the input audio to reduce the CQT kernel size. The result with and without early downsampling are more or less the same except in the very low frequency region where freq < 40Hz. """ def __init__( self, sr=22050, hop_length=512, fmin=32.70, fmax=None, n_bins=84, bins_per_octave=12, norm=True, basis_norm=1, window="hann", pad_mode="reflect", trainable_STFT=False, filter_scale=1, trainable_CQT=False, output_format="Magnitude", earlydownsample=True, verbose=True, ): super().__init__() self.norm = ( norm # Now norm is used to normalize the final CQT result by dividing n_fft ) # basis_norm is for normalizing basis self.hop_length = hop_length self.pad_mode = pad_mode self.n_bins = n_bins self.output_format = output_format self.earlydownsample = ( earlydownsample # TODO: activate early downsampling later if possible ) # This will be used to calculate filter_cutoff and creating CQT kernels Q = float(filter_scale) / (2 ** (1 / bins_per_octave) - 1) # Creating lowpass filter and make it a torch tensor if verbose == True: print("Creating low pass filter ...", end="\r") start = time() lowpass_filter = torch.tensor( create_lowpass_filter( band_center=0.5, kernelLength=256, transitionBandwidth=0.001 ) ) # Broadcast the tensor to the shape that fits conv1d self.register_buffer("lowpass_filter", lowpass_filter[None, None, :]) if verbose == True: print( "Low pass filter created, time used = {:.4f} seconds".format( time() - start ) ) # Calculate num of filter requires for the kernel # n_octaves determines how many resampling requires for the CQT n_filters = min(bins_per_octave, n_bins) self.n_octaves = int(np.ceil(float(n_bins) / bins_per_octave)) # print("n_octaves = ", self.n_octaves) # Calculate the lowest frequency bin for the top octave kernel self.fmin_t = fmin * 2 ** (self.n_octaves - 1) remainder = n_bins % bins_per_octave # print("remainder = ", remainder) if remainder == 0: # Calculate the top bin frequency fmax_t = self.fmin_t * 2 ** ((bins_per_octave - 1) / bins_per_octave) else: # Calculate the top bin frequency fmax_t = self.fmin_t * 2 ** ((remainder - 1) / bins_per_octave) self.fmin_t = fmax_t / 2 ** ( 1 - 1 / bins_per_octave ) # Adjusting the top minium bins if fmax_t > sr / 2: raise ValueError( "The top bin {}Hz has exceeded the Nyquist frequency, \ please reduce the n_bins".format( fmax_t ) ) if ( self.earlydownsample == True ): # Do early downsampling if this argument is True if verbose == True: print("Creating early downsampling filter ...", end="\r") start = time() ( sr, self.hop_length, self.downsample_factor, early_downsample_filter, self.earlydownsample, ) = get_early_downsample_params( sr, hop_length, fmax_t, Q, self.n_octaves, verbose ) self.register_buffer("early_downsample_filter", early_downsample_filter) if verbose == True: print( "Early downsampling filter created, \ time used = {:.4f} seconds".format( time() - start ) ) else: self.downsample_factor = 1.0 # Preparing CQT kernels if verbose == True: print("Creating CQT kernels ...", end="\r") start = time() # print("Q = {}, fmin_t = {}, n_filters = {}".format(Q, self.fmin_t, n_filters)) basis, self.n_fft, _, _ = create_cqt_kernels( Q, sr, self.fmin_t, n_filters, bins_per_octave, norm=basis_norm, topbin_check=False, ) # This is for the normalization in the end freqs = fmin * 2.0 ** (np.r_[0:n_bins] / np.double(bins_per_octave)) self.frequencies = freqs lenghts = np.ceil(Q * sr / freqs) lenghts = torch.tensor(lenghts).float() self.register_buffer("lenghts", lenghts) self.basis = basis fft_basis = fft(basis)[ :, : self.n_fft // 2 + 1 ] # Convert CQT kenral from time domain to freq domain # These cqt_kernel is already in the frequency domain cqt_kernels_real = torch.tensor(fft_basis.real) cqt_kernels_imag = torch.tensor(fft_basis.imag) if verbose == True: print( "CQT kernels created, time used = {:.4f} seconds".format(time() - start) ) # print("Getting cqt kernel done, n_fft = ",self.n_fft) # Preparing kernels for Short-Time Fourier Transform (STFT) # We set the frequency range in the CQT filter instead of here. if verbose == True: print("Creating STFT kernels ...", end="\r") start = time() kernel_sin, kernel_cos, self.bins2freq, _, window = create_fourier_kernels( self.n_fft, window="ones", freq_scale="no" ) wsin = kernel_sin * window wcos = kernel_cos * window wsin = torch.tensor(wsin) wcos = torch.tensor(wcos) if verbose == True: print( "STFT kernels created, time used = {:.4f} seconds".format( time() - start ) ) if trainable_STFT: wsin = nn.Parameter(wsin, requires_grad=trainable_STFT) wcos = nn.Parameter(wcos, requires_grad=trainable_STFT) self.register_parameter("wsin", wsin) self.register_parameter("wcos", wcos) else: self.register_buffer("wsin", wsin) self.register_buffer("wcos", wcos) if trainable_CQT: cqt_kernels_real = nn.Parameter( cqt_kernels_real, requires_grad=trainable_CQT ) cqt_kernels_imag = nn.Parameter( cqt_kernels_imag, requires_grad=trainable_CQT ) self.register_parameter("cqt_kernels_real", cqt_kernels_real) self.register_parameter("cqt_kernels_imag", cqt_kernels_imag) else: self.register_buffer("cqt_kernels_real", cqt_kernels_real) self.register_buffer("cqt_kernels_imag", cqt_kernels_imag) # If center==True, the STFT window will be put in the middle, and paddings at the beginning # and ending are required. if self.pad_mode == "constant": self.padding = nn.ConstantPad1d(self.n_fft // 2, 0) elif self.pad_mode == "reflect": self.padding = nn.ReflectionPad1d(self.n_fft // 2) def forward(self, x, output_format=None, normalization_type="librosa"): """ Convert a batch of waveforms to CQT spectrograms. Parameters ---------- x : torch tensor Input signal should be in either of the following shapes.\n 1. ``(len_audio)``\n 2. ``(num_audio, len_audio)``\n 3. ``(num_audio, 1, len_audio)`` It will be automatically broadcast to the right shape """ output_format = output_format or self.output_format x = broadcast_dim(x) if self.earlydownsample == True: x = downsampling_by_n( x, self.early_downsample_filter, self.downsample_factor ) hop = self.hop_length CQT = get_cqt_complex2( x, self.cqt_kernels_real, self.cqt_kernels_imag, hop, self.padding, wcos=self.wcos, wsin=self.wsin, ) x_down = x # Preparing a new variable for downsampling for i in range(self.n_octaves - 1): hop = hop // 2 x_down = downsampling_by_2(x_down, self.lowpass_filter) CQT1 = get_cqt_complex2( x_down, self.cqt_kernels_real, self.cqt_kernels_imag, hop, self.padding, wcos=self.wcos, wsin=self.wsin, ) CQT = torch.cat((CQT1, CQT), 1) CQT = CQT[:, -self.n_bins :, :] # Removing unwanted top bins if normalization_type == "librosa": CQT *= torch.sqrt(self.lenghts.view(-1, 1, 1)) / self.n_fft elif normalization_type == "convolutional": pass elif normalization_type == "wrap": CQT *= 2 / self.n_fft else: raise ValueError( "The normalization_type %r is not part of our current options." % normalization_type ) if output_format == "Magnitude": # Getting CQT Amplitude return torch.sqrt(CQT.pow(2).sum(-1)) elif output_format == "Complex": return CQT elif output_format == "Phase": phase_real = torch.cos(torch.atan2(CQT[:, :, :, 1], CQT[:, :, :, 0])) phase_imag = torch.sin(torch.atan2(CQT[:, :, :, 1], CQT[:, :, :, 0])) return torch.stack((phase_real, phase_imag), -1) def extra_repr(self) -> str: return "STFT kernel size = {}, CQT kernel size = {}".format( (*self.wcos.shape,), (*self.cqt_kernels_real.shape,) ) class CQT1992v2(nn.Module): """This function is to calculate the CQT of the input signal. Input signal should be in either of the following shapes.\n 1. ``(len_audio)``\n 2. ``(num_audio, len_audio)``\n 3. ``(num_audio, 1, len_audio)`` The correct shape will be inferred autommatically if the input follows these 3 shapes. Most of the arguments follow the convention from librosa. This class inherits from ``nn.Module``, therefore, the usage is same as ``nn.Module``. This alogrithm uses the method proposed in [1]. I slightly modify it so that it runs faster than the original 1992 algorithm, that is why I call it version 2. [1] Brown, Judith C.C. and Miller Puckette. “An efficient algorithm for the calculation of a constant Q transform.” (1992). Parameters ---------- sr : int The sampling rate for the input audio. It is used to calucate the correct ``fmin`` and ``fmax``. Setting the correct sampling rate is very important for calculating the correct frequency. hop_length : int The hop (or stride) size. Default value is 512. fmin : float The frequency for the lowest CQT bin. Default is 32.70Hz, which coresponds to the note C0. fmax : float The frequency for the highest CQT bin. Default is ``None``, therefore the higest CQT bin is inferred from the ``n_bins`` and ``bins_per_octave``. If ``fmax`` is not ``None``, then the argument ``n_bins`` will be ignored and ``n_bins`` will be calculated automatically. Default is ``None`` n_bins : int The total numbers of CQT bins. Default is 84. Will be ignored if ``fmax`` is not ``None``. bins_per_octave : int Number of bins per octave. Default is 12. filter_scale : float > 0 Filter scale factor. Values of filter_scale smaller than 1 can be used to improve the time resolution at the cost of degrading the frequency resolution. Important to note is that setting for example filter_scale = 0.5 and bins_per_octave = 48 leads to exactly the same time-frequency resolution trade-off as setting filter_scale = 1 and bins_per_octave = 24, but the former contains twice more frequency bins per octave. In this sense, values filter_scale < 1 can be seen to implement oversampling of the frequency axis, analogously to the use of zero padding when calculating the DFT. norm : int Normalization for the CQT kernels. ``1`` means L1 normalization, and ``2`` means L2 normalization. Default is ``1``, which is same as the normalization used in librosa. window : string, float, or tuple The windowing function for CQT. If it is a string, It uses ``scipy.signal.get_window``. If it is a tuple, only the gaussian window wanrantees constant Q factor. Gaussian window should be given as a tuple ('gaussian', att) where att is the attenuation in the border given in dB. Please refer to scipy documentation for possible windowing functions. The default value is 'hann'. center : bool Putting the CQT keneral at the center of the time-step or not. If ``False``, the time index is the beginning of the CQT kernel, if ``True``, the time index is the center of the CQT kernel. Default value if ``True``. pad_mode : str The padding method. Default value is 'reflect'. trainable : bool Determine if the CQT kernels are trainable or not. If ``True``, the gradients for CQT kernels will also be caluclated and the CQT kernels will be updated during model training. Default value is ``False``. output_format : str Determine the return type. ``Magnitude`` will return the magnitude of the STFT result, shape = ``(num_samples, freq_bins,time_steps)``; ``Complex`` will return the STFT result in complex number, shape = ``(num_samples, freq_bins,time_steps, 2)``; ``Phase`` will return the phase of the STFT reuslt, shape = ``(num_samples, freq_bins,time_steps, 2)``. The complex number is stored as ``(real, imag)`` in the last axis. Default value is 'Magnitude'. verbose : bool If ``True``, it shows layer information. If ``False``, it suppresses all prints Returns ------- spectrogram : torch.tensor It returns a tensor of spectrograms. shape = ``(num_samples, freq_bins,time_steps)`` if ``output_format='Magnitude'``; shape = ``(num_samples, freq_bins,time_steps, 2)`` if ``output_format='Complex' or 'Phase'``; Examples -------- >>> spec_layer = Spectrogram.CQT1992v2() >>> specs = spec_layer(x) """ def __init__( self, sr=22050, hop_length=512, fmin=32.70, fmax=None, n_bins=84, bins_per_octave=12, filter_scale=1, norm=1, window="hann", center=True, pad_mode="reflect", trainable=False, output_format="Magnitude", verbose=True, ): super().__init__() self.trainable = trainable self.hop_length = hop_length self.center = center self.pad_mode = pad_mode self.output_format = output_format # creating kernels for CQT Q = float(filter_scale) / (2 ** (1 / bins_per_octave) - 1) if verbose == True: print("Creating CQT kernels ...", end="\r") start = time() cqt_kernels, self.kernel_width, lenghts, freqs = create_cqt_kernels( Q, sr, fmin, n_bins, bins_per_octave, norm, window, fmax ) self.register_buffer("lenghts", lenghts) self.frequencies = freqs cqt_kernels_real = torch.tensor(cqt_kernels.real).unsqueeze(1) cqt_kernels_imag = torch.tensor(cqt_kernels.imag).unsqueeze(1) if trainable: cqt_kernels_real = nn.Parameter(cqt_kernels_real, requires_grad=trainable) cqt_kernels_imag = nn.Parameter(cqt_kernels_imag, requires_grad=trainable) self.register_parameter("cqt_kernels_real", cqt_kernels_real) self.register_parameter("cqt_kernels_imag", cqt_kernels_imag) else: self.register_buffer("cqt_kernels_real", cqt_kernels_real) self.register_buffer("cqt_kernels_imag", cqt_kernels_imag) if verbose == True: print( "CQT kernels created, time used = {:.4f} seconds".format(time() - start) ) def forward(self, x, output_format=None, normalization_type="librosa"): """ Convert a batch of waveforms to CQT spectrograms. Parameters ---------- x : torch tensor Input signal should be in either of the following shapes.\n 1. ``(len_audio)``\n 2. ``(num_audio, len_audio)``\n 3. ``(num_audio, 1, len_audio)`` It will be automatically broadcast to the right shape normalization_type : str Type of the normalisation. The possible options are: \n 'librosa' : the output fits the librosa one \n 'convolutional' : the output conserves the convolutional inequalities of the wavelet transform:\n for all p ϵ [1, inf] \n - || CQT ||_p <= || f ||_p || g ||_1 \n - || CQT ||_p <= || f ||_1 || g ||_p \n - || CQT ||_2 = || f ||_2 || g ||_2 \n 'wrap' : wraps positive and negative frequencies into positive frequencies. This means that the CQT of a sinus (or a cosinus) with a constant amplitude equal to 1 will have the value 1 in the bin corresponding to its frequency. """ output_format = output_format or self.output_format x = broadcast_dim(x) if self.center: if self.pad_mode == "constant": padding = nn.ConstantPad1d(self.kernel_width // 2, 0) elif self.pad_mode == "reflect": padding = nn.ReflectionPad1d(self.kernel_width // 2) x = padding(x) # CQT CQT_real = conv1d(x, self.cqt_kernels_real, stride=self.hop_length) CQT_imag = -conv1d(x, self.cqt_kernels_imag, stride=self.hop_length) if normalization_type == "librosa": CQT_real *= torch.sqrt(self.lenghts.view(-1, 1)) CQT_imag *= torch.sqrt(self.lenghts.view(-1, 1)) elif normalization_type == "convolutional": pass elif normalization_type == "wrap": CQT_real *= 2 CQT_imag *= 2 else: raise ValueError( "The normalization_type %r is not part of our current options." % normalization_type ) if output_format == "Magnitude": if self.trainable == False: # Getting CQT Amplitude CQT = torch.sqrt(CQT_real.pow(2) + CQT_imag.pow(2)) else: CQT = torch.sqrt(CQT_real.pow(2) + CQT_imag.pow(2) + 1e-8) return CQT elif output_format == "Complex": return torch.stack((CQT_real, CQT_imag), -1) elif output_format == "Phase": phase_real = torch.cos(torch.atan2(CQT_imag, CQT_real)) phase_imag = torch.sin(torch.atan2(CQT_imag, CQT_real)) return torch.stack((phase_real, phase_imag), -1) def forward_manual(self, x): """ Method for debugging """ x = broadcast_dim(x) if self.center: if self.pad_mode == "constant": padding = nn.ConstantPad1d(self.kernel_width // 2, 0) elif self.pad_mode == "reflect": padding = nn.ReflectionPad1d(self.kernel_width // 2) x = padding(x) # CQT CQT_real = conv1d(x, self.cqt_kernels_real, stride=self.hop_length) CQT_imag = conv1d(x, self.cqt_kernels_imag, stride=self.hop_length) # Getting CQT Amplitude CQT = torch.sqrt(CQT_real.pow(2) + CQT_imag.pow(2)) return CQT * torch.sqrt(self.lenghts.view(-1, 1)) class CQT2010v2(nn.Module): """This function is to calculate the CQT of the input signal. Input signal should be in either of the following shapes.\n 1. ``(len_audio)``\n 2. ``(num_audio, len_audio)``\n 3. ``(num_audio, 1, len_audio)`` The correct shape will be inferred autommatically if the input follows these 3 shapes. Most of the arguments follow the convention from librosa. This class inherits from ``nn.Module``, therefore, the usage is same as ``nn.Module``. This alogrithm uses the resampling method proposed in [1]. Instead of convoluting the STFT results with a gigantic CQT kernel covering the full frequency spectrum, we make a small CQT kernel covering only the top octave. Then we keep downsampling the input audio by a factor of 2 to convoluting it with the small CQT kernel. Everytime the input audio is downsampled, the CQT relative to the downsampled input is equivalent to the next lower octave. The kernel creation process is still same as the 1992 algorithm. Therefore, we can reuse the code from the 1992 alogrithm [2] [1] Schörkhuber, Christian. “CONSTANT-Q TRANSFORM TOOLBOX FOR MUSIC PROCESSING.” (2010). [2] Brown, Judith C.C. and Miller Puckette. “An efficient algorithm for the calculation of a constant Q transform.” (1992). Early downsampling factor is to downsample the input audio to reduce the CQT kernel size. The result with and without early downsampling are more or less the same except in the very low frequency region where freq < 40Hz. Parameters ---------- sr : int The sampling rate for the input audio. It is used to calucate the correct ``fmin`` and ``fmax``. Setting the correct sampling rate is very important for calculating the correct frequency. hop_length : int The hop (or stride) size. Default value is 512. fmin : float The frequency for the lowest CQT bin. Default is 32.70Hz, which coresponds to the note C0. fmax : float The frequency for the highest CQT bin. Default is ``None``, therefore the higest CQT bin is inferred from the ``n_bins`` and ``bins_per_octave``. If ``fmax`` is not ``None``, then the argument ``n_bins`` will be ignored and ``n_bins`` will be calculated automatically. Default is ``None`` n_bins : int The total numbers of CQT bins. Default is 84. Will be ignored if ``fmax`` is not ``None``. bins_per_octave : int Number of bins per octave. Default is 12. norm : bool Normalization for the CQT result. basis_norm : int Normalization for the CQT kernels. ``1`` means L1 normalization, and ``2`` means L2 normalization. Default is ``1``, which is same as the normalization used in librosa. window : str The windowing function for CQT. It uses ``scipy.signal.get_window``, please refer to scipy documentation for possible windowing functions. The default value is 'hann' pad_mode : str The padding method. Default value is 'reflect'. trainable : bool Determine if the CQT kernels are trainable or not. If ``True``, the gradients for CQT kernels will also be caluclated and the CQT kernels will be updated during model training. Default value is ``False`` output_format : str Determine the return type. 'Magnitude' will return the magnitude of the STFT result, shape = ``(num_samples, freq_bins, time_steps)``; 'Complex' will return the STFT result in complex number, shape = ``(num_samples, freq_bins, time_steps, 2)``; 'Phase' will return the phase of the STFT reuslt, shape = ``(num_samples, freq_bins,time_steps, 2)``. The complex number is stored as ``(real, imag)`` in the last axis. Default value is 'Magnitude'. verbose : bool If ``True``, it shows layer information. If ``False``, it suppresses all prints. Returns ------- spectrogram : torch.tensor It returns a tensor of spectrograms. shape = ``(num_samples, freq_bins,time_steps)`` if ``output_format='Magnitude'``; shape = ``(num_samples, freq_bins,time_steps, 2)`` if ``output_format='Complex' or 'Phase'``; Examples -------- >>> spec_layer = Spectrogram.CQT2010v2() >>> specs = spec_layer(x) """ # To DO: # need to deal with the filter and other tensors def __init__( self, sr=22050, hop_length=512, fmin=32.70, fmax=None, n_bins=84, filter_scale=1, bins_per_octave=12, norm=True, basis_norm=1, window="hann", pad_mode="reflect", earlydownsample=True, trainable=False, output_format="Magnitude", verbose=True, ): super().__init__() self.norm = ( norm # Now norm is used to normalize the final CQT result by dividing n_fft ) # basis_norm is for normalizing basis self.hop_length = hop_length self.pad_mode = pad_mode self.n_bins = n_bins self.earlydownsample = ( earlydownsample # We will activate early downsampling later if possible ) self.trainable = trainable self.output_format = output_format # It will be used to calculate filter_cutoff and creating CQT kernels Q = float(filter_scale) / (2 ** (1 / bins_per_octave) - 1) # Creating lowpass filter and make it a torch tensor if verbose == True: print("Creating low pass filter ...", end="\r") start = time() # self.lowpass_filter = torch.tensor( # create_lowpass_filter( # band_center = 0.50, # kernelLength=256, # transitionBandwidth=0.001)) lowpass_filter = torch.tensor( create_lowpass_filter( band_center=0.50, kernelLength=256, transitionBandwidth=0.001 ) ) # Broadcast the tensor to the shape that fits conv1d self.register_buffer("lowpass_filter", lowpass_filter[None, None, :]) if verbose == True: print( "Low pass filter created, time used = {:.4f} seconds".format( time() - start ) ) # Caluate num of filter requires for the kernel # n_octaves determines how many resampling requires for the CQT n_filters = min(bins_per_octave, n_bins) self.n_octaves = int(np.ceil(float(n_bins) / bins_per_octave)) if verbose == True: print("num_octave = ", self.n_octaves) # Calculate the lowest frequency bin for the top octave kernel self.fmin_t = fmin * 2 ** (self.n_octaves - 1) remainder = n_bins % bins_per_octave # print("remainder = ", remainder) if remainder == 0: # Calculate the top bin frequency fmax_t = self.fmin_t * 2 ** ((bins_per_octave - 1) / bins_per_octave) else: # Calculate the top bin frequency fmax_t = self.fmin_t * 2 ** ((remainder - 1) / bins_per_octave) self.fmin_t = fmax_t / 2 ** ( 1 - 1 / bins_per_octave ) # Adjusting the top minium bins if fmax_t > sr / 2: raise ValueError( "The top bin {}Hz has exceeded the Nyquist frequency, \ please reduce the n_bins".format( fmax_t ) ) if ( self.earlydownsample == True ): # Do early downsampling if this argument is True if verbose == True: print("Creating early downsampling filter ...", end="\r") start = time() ( sr, self.hop_length, self.downsample_factor, early_downsample_filter, self.earlydownsample, ) = get_early_downsample_params( sr, hop_length, fmax_t, Q, self.n_octaves, verbose ) self.register_buffer("early_downsample_filter", early_downsample_filter) if verbose == True: print( "Early downsampling filter created, \ time used = {:.4f} seconds".format( time() - start ) ) else: self.downsample_factor = 1.0 # Preparing CQT kernels if verbose == True: print("Creating CQT kernels ...", end="\r") start = time() basis, self.n_fft, lenghts, _ = create_cqt_kernels( Q, sr, self.fmin_t, n_filters, bins_per_octave, norm=basis_norm, topbin_check=False, ) # For normalization in the end # The freqs returned by create_cqt_kernels cannot be used # Since that returns only the top octave bins # We need the information for all freq bin freqs = fmin * 2.0 ** (np.r_[0:n_bins] / np.double(bins_per_octave)) self.frequencies = freqs lenghts = np.ceil(Q * sr / freqs) lenghts = torch.tensor(lenghts).float() self.register_buffer("lenghts", lenghts) self.basis = basis # These cqt_kernel is already in the frequency domain cqt_kernels_real = torch.tensor(basis.real).unsqueeze(1) cqt_kernels_imag = torch.tensor(basis.imag).unsqueeze(1) if trainable: cqt_kernels_real = nn.Parameter(cqt_kernels_real, requires_grad=trainable) cqt_kernels_imag = nn.Parameter(cqt_kernels_imag, requires_grad=trainable) self.register_parameter("cqt_kernels_real", cqt_kernels_real) self.register_parameter("cqt_kernels_imag", cqt_kernels_imag) else: self.register_buffer("cqt_kernels_real", cqt_kernels_real) self.register_buffer("cqt_kernels_imag", cqt_kernels_imag) if verbose == True: print( "CQT kernels created, time used = {:.4f} seconds".format(time() - start) ) # print("Getting cqt kernel done, n_fft = ",self.n_fft) # If center==True, the STFT window will be put in the middle, and paddings at the beginning # and ending are required. if self.pad_mode == "constant": self.padding = nn.ConstantPad1d(self.n_fft // 2, 0) elif self.pad_mode == "reflect": self.padding = nn.ReflectionPad1d(self.n_fft // 2) def forward(self, x, output_format=None, normalization_type="librosa"): """ Convert a batch of waveforms to CQT spectrograms. Parameters ---------- x : torch tensor Input signal should be in either of the following shapes.\n 1. ``(len_audio)``\n 2. ``(num_audio, len_audio)``\n 3. ``(num_audio, 1, len_audio)`` It will be automatically broadcast to the right shape """ output_format = output_format or self.output_format x = broadcast_dim(x) if self.earlydownsample == True: x = downsampling_by_n( x, self.early_downsample_filter, self.downsample_factor ) hop = self.hop_length CQT = get_cqt_complex( x, self.cqt_kernels_real, self.cqt_kernels_imag, hop, self.padding ) # Getting the top octave CQT x_down = x # Preparing a new variable for downsampling for i in range(self.n_octaves - 1): hop = hop // 2 x_down = downsampling_by_2(x_down, self.lowpass_filter) CQT1 = get_cqt_complex( x_down, self.cqt_kernels_real, self.cqt_kernels_imag, hop, self.padding ) CQT = torch.cat((CQT1, CQT), 1) CQT = CQT[:, -self.n_bins :, :] # Removing unwanted bottom bins # print("downsample_factor = ",self.downsample_factor) # print(CQT.shape) # print(self.lenghts.view(-1,1).shape) # Normalizing the output with the downsampling factor, 2**(self.n_octaves-1) is make it # same mag as 1992 CQT = CQT * self.downsample_factor # Normalize again to get same result as librosa if normalization_type == "librosa": CQT = CQT * torch.sqrt(self.lenghts.view(-1, 1, 1)) elif normalization_type == "convolutional": pass elif normalization_type == "wrap": CQT *= 2 else: raise ValueError( "The normalization_type %r is not part of our current options." % normalization_type ) if output_format == "Magnitude": if self.trainable == False: # Getting CQT Amplitude return torch.sqrt(CQT.pow(2).sum(-1)) else: return torch.sqrt(CQT.pow(2).sum(-1) + 1e-8) elif output_format == "Complex": return CQT elif output_format == "Phase": phase_real = torch.cos(torch.atan2(CQT[:, :, :, 1], CQT[:, :, :, 0])) phase_imag = torch.sin(torch.atan2(CQT[:, :, :, 1], CQT[:, :, :, 0])) return torch.stack((phase_real, phase_imag), -1) class CQT(CQT1992v2): """An abbreviation for :func:`~nnAudio.Spectrogram.CQT1992v2`. Please refer to the :func:`~nnAudio.Spectrogram.CQT1992v2` documentation""" pass