modules/parallel_wavegan/models/source.py

import torch
import numpy as np
import sys
import torch.nn.functional as torch_nn_func


class SineGen(torch.nn.Module):
    """ Definition of sine generator
    SineGen(samp_rate, harmonic_num = 0,
            sine_amp = 0.1, noise_std = 0.003,
            voiced_threshold = 0,
            flag_for_pulse=False)

    samp_rate: sampling rate in Hz
    harmonic_num: number of harmonic overtones (default 0)
    sine_amp: amplitude of sine-wavefrom (default 0.1)
    noise_std: std of Gaussian noise (default 0.003)
    voiced_thoreshold: F0 threshold for U/V classification (default 0)
    flag_for_pulse: this SinGen is used inside PulseGen (default False)

    Note: when flag_for_pulse is True, the first time step of a voiced
        segment is always sin(np.pi) or cos(0)
    """

    def __init__(self, samp_rate, harmonic_num=0,
                 sine_amp=0.1, noise_std=0.003,
                 voiced_threshold=0,
                 flag_for_pulse=False):
        super(SineGen, self).__init__()
        self.sine_amp = sine_amp
        self.noise_std = noise_std
        self.harmonic_num = harmonic_num
        self.dim = self.harmonic_num + 1
        self.sampling_rate = samp_rate
        self.voiced_threshold = voiced_threshold
        self.flag_for_pulse = flag_for_pulse

    def _f02uv(self, f0):
        # generate uv signal
        uv = torch.ones_like(f0)
        uv = uv * (f0 > self.voiced_threshold)
        return uv

    def _f02sine(self, f0_values):
        """ f0_values: (batchsize, length, dim)
            where dim indicates fundamental tone and overtones
        """
        # convert to F0 in rad. The interger part n can be ignored
        # because 2 * np.pi * n doesn't affect phase
        rad_values = (f0_values / self.sampling_rate) % 1

        # initial phase noise (no noise for fundamental component)
        rand_ini = torch.rand(f0_values.shape[0], f0_values.shape[2], \
                              device=f0_values.device)
        rand_ini[:, 0] = 0
        rad_values[:, 0, :] = rad_values[:, 0, :] + rand_ini

        # instantanouse phase sine[t] = sin(2*pi \sum_i=1 ^{t} rad)
        if not self.flag_for_pulse:
            # for normal case

            # To prevent torch.cumsum numerical overflow,
            # it is necessary to add -1 whenever \sum_k=1^n rad_value_k > 1.
            # Buffer tmp_over_one_idx indicates the time step to add -1.
            # This will not change F0 of sine because (x-1) * 2*pi = x * 2*pi
            tmp_over_one = torch.cumsum(rad_values, 1) % 1
            tmp_over_one_idx = (tmp_over_one[:, 1:, :] -
                                tmp_over_one[:, :-1, :]) < 0
            cumsum_shift = torch.zeros_like(rad_values)
            cumsum_shift[:, 1:, :] = tmp_over_one_idx * -1.0

            sines = torch.sin(torch.cumsum(rad_values + cumsum_shift, dim=1)
                              * 2 * np.pi)
        else:
            # If necessary, make sure that the first time step of every
            # voiced segments is sin(pi) or cos(0)
            # This is used for pulse-train generation

            # identify the last time step in unvoiced segments
            uv = self._f02uv(f0_values)
            uv_1 = torch.roll(uv, shifts=-1, dims=1)
            uv_1[:, -1, :] = 1
            u_loc = (uv < 1) * (uv_1 > 0)

            # get the instantanouse phase
            tmp_cumsum = torch.cumsum(rad_values, dim=1)
            # different batch needs to be processed differently
            for idx in range(f0_values.shape[0]):
                temp_sum = tmp_cumsum[idx, u_loc[idx, :, 0], :]
                temp_sum[1:, :] = temp_sum[1:, :] - temp_sum[0:-1, :]
                # stores the accumulation of i.phase within
                # each voiced segments
                tmp_cumsum[idx, :, :] = 0
                tmp_cumsum[idx, u_loc[idx, :, 0], :] = temp_sum

            # rad_values - tmp_cumsum: remove the accumulation of i.phase
            # within the previous voiced segment.
            i_phase = torch.cumsum(rad_values - tmp_cumsum, dim=1)

            # get the sines
            sines = torch.cos(i_phase * 2 * np.pi)
        return sines

    def forward(self, f0):
        """ sine_tensor, uv = forward(f0)
        input F0: tensor(batchsize=1, length, dim=1)
                  f0 for unvoiced steps should be 0
        output sine_tensor: tensor(batchsize=1, length, dim)
        output uv: tensor(batchsize=1, length, 1)
        """
        with torch.no_grad():
            f0_buf = torch.zeros(f0.shape[0], f0.shape[1], self.dim,
                                 device=f0.device)
            # fundamental component
            f0_buf[:, :, 0] = f0[:, :, 0]
            for idx in np.arange(self.harmonic_num):
                # idx + 2: the (idx+1)-th overtone, (idx+2)-th harmonic
                f0_buf[:, :, idx + 1] = f0_buf[:, :, 0] * (idx + 2)

            # generate sine waveforms
            sine_waves = self._f02sine(f0_buf) * self.sine_amp

            # generate uv signal
            # uv = torch.ones(f0.shape)
            # uv = uv * (f0 > self.voiced_threshold)
            uv = self._f02uv(f0)

            # noise: for unvoiced should be similar to sine_amp
            #        std = self.sine_amp/3 -> max value ~ self.sine_amp
            # .       for voiced regions is self.noise_std
            noise_amp = uv * self.noise_std + (1 - uv) * self.sine_amp / 3
            noise = noise_amp * torch.randn_like(sine_waves)

            # first: set the unvoiced part to 0 by uv
            # then: additive noise
            sine_waves = sine_waves * uv + noise
        return sine_waves, uv, noise


class PulseGen(torch.nn.Module):
    """ Definition of Pulse train generator

    There are many ways to implement pulse generator.
    Here, PulseGen is based on SinGen. For a perfect
    """
    def __init__(self, samp_rate, pulse_amp = 0.1,
                 noise_std = 0.003, voiced_threshold = 0):
        super(PulseGen, self).__init__()
        self.pulse_amp = pulse_amp
        self.sampling_rate = samp_rate
        self.voiced_threshold = voiced_threshold
        self.noise_std = noise_std
        self.l_sinegen = SineGen(self.sampling_rate, harmonic_num=0, \
                                 sine_amp=self.pulse_amp, noise_std=0, \
                                 voiced_threshold=self.voiced_threshold, \
                                 flag_for_pulse=True)

    def forward(self, f0):
        """ Pulse train generator
        pulse_train, uv = forward(f0)
        input F0: tensor(batchsize=1, length, dim=1)
                  f0 for unvoiced steps should be 0
        output pulse_train: tensor(batchsize=1, length, dim)
        output uv: tensor(batchsize=1, length, 1)

        Note: self.l_sine doesn't make sure that the initial phase of
        a voiced segment is np.pi, the first pulse in a voiced segment
        may not be at the first time step within a voiced segment
        """
        with torch.no_grad():
            sine_wav, uv, noise = self.l_sinegen(f0)

            # sine without additive noise
            pure_sine = sine_wav - noise

            # step t corresponds to a pulse if
            # sine[t] > sine[t+1] & sine[t] > sine[t-1]
            # & sine[t-1], sine[t+1], and sine[t] are voiced
            # or
            # sine[t] is voiced, sine[t-1] is unvoiced
            # we use torch.roll to simulate sine[t+1] and sine[t-1]
            sine_1 = torch.roll(pure_sine, shifts=1, dims=1)
            uv_1 = torch.roll(uv, shifts=1, dims=1)
            uv_1[:, 0, :] = 0
            sine_2 = torch.roll(pure_sine, shifts=-1, dims=1)
            uv_2 = torch.roll(uv, shifts=-1, dims=1)
            uv_2[:, -1, :] = 0

            loc = (pure_sine > sine_1) * (pure_sine > sine_2) \
                  * (uv_1 > 0) * (uv_2 > 0) * (uv > 0) \
                  + (uv_1 < 1) * (uv > 0)

            # pulse train without noise
            pulse_train = pure_sine * loc

            # additive noise to pulse train
            # note that noise from sinegen is zero in voiced regions
            pulse_noise = torch.randn_like(pure_sine) * self.noise_std

            # with additive noise on pulse, and unvoiced regions
            pulse_train += pulse_noise * loc + pulse_noise * (1 - uv)
        return pulse_train, sine_wav, uv, pulse_noise


class SignalsConv1d(torch.nn.Module):
    """ Filtering input signal with time invariant filter
    Note: FIRFilter conducted filtering given fixed FIR weight
          SignalsConv1d convolves two signals
    Note: this is based on torch.nn.functional.conv1d

    """

    def __init__(self):
        super(SignalsConv1d, self).__init__()

    def forward(self, signal, system_ir):
        """ output = forward(signal, system_ir)

        signal:    (batchsize, length1, dim)
        system_ir: (length2, dim)

        output:    (batchsize, length1, dim)
        """
        if signal.shape[-1] != system_ir.shape[-1]:
            print("Error: SignalsConv1d expects shape:")
            print("signal    (batchsize, length1, dim)")
            print("system_id (batchsize, length2, dim)")
            print("But received signal: {:s}".format(str(signal.shape)))
            print(" system_ir: {:s}".format(str(system_ir.shape)))
            sys.exit(1)
        padding_length = system_ir.shape[0] - 1
        groups = signal.shape[-1]

        # pad signal on the left
        signal_pad = torch_nn_func.pad(signal.permute(0, 2, 1), \
                                       (padding_length, 0))
        # prepare system impulse response as (dim, 1, length2)
        # also flip the impulse response
        ir = torch.flip(system_ir.unsqueeze(1).permute(2, 1, 0), \
                        dims=[2])
        # convolute
        output = torch_nn_func.conv1d(signal_pad, ir, groups=groups)
        return output.permute(0, 2, 1)


class CyclicNoiseGen_v1(torch.nn.Module):
    """ CyclicnoiseGen_v1
    Cyclic noise with a single parameter of beta.
    Pytorch v1 implementation assumes f_t is also fixed
    """

    def __init__(self, samp_rate,
                 noise_std=0.003, voiced_threshold=0):
        super(CyclicNoiseGen_v1, self).__init__()
        self.samp_rate = samp_rate
        self.noise_std = noise_std
        self.voiced_threshold = voiced_threshold

        self.l_pulse = PulseGen(samp_rate, pulse_amp=1.0,
                                noise_std=noise_std,
                                voiced_threshold=voiced_threshold)
        self.l_conv = SignalsConv1d()

    def noise_decay(self, beta, f0mean):
        """ decayed_noise = noise_decay(beta, f0mean)
        decayed_noise =  n[t]exp(-t * f_mean / beta / samp_rate)

        beta: (dim=1) or (batchsize=1, 1, dim=1)
        f0mean (batchsize=1, 1, dim=1)

        decayed_noise (batchsize=1, length, dim=1)
        """
        with torch.no_grad():
            # exp(-1.0 n / T) < 0.01 => n > -log(0.01)*T = 4.60*T
            # truncate the noise when decayed by -40 dB
            length = 4.6 * self.samp_rate / f0mean
            length = length.int()
            time_idx = torch.arange(0, length, device=beta.device)
            time_idx = time_idx.unsqueeze(0).unsqueeze(2)
            time_idx = time_idx.repeat(beta.shape[0], 1, beta.shape[2])

        noise = torch.randn(time_idx.shape, device=beta.device)

        # due to Pytorch implementation, use f0_mean as the f0 factor
        decay = torch.exp(-time_idx * f0mean / beta / self.samp_rate)
        return noise * self.noise_std * decay

    def forward(self, f0s, beta):
        """ Producde cyclic-noise
        """
        # pulse train
        pulse_train, sine_wav, uv, noise = self.l_pulse(f0s)
        pure_pulse = pulse_train - noise

        # decayed_noise (length, dim=1)
        if (uv < 1).all():
            # all unvoiced
            cyc_noise = torch.zeros_like(sine_wav)
        else:
            f0mean = f0s[uv > 0].mean()

            decayed_noise = self.noise_decay(beta, f0mean)[0, :, :]
            # convolute
            cyc_noise = self.l_conv(pure_pulse, decayed_noise)

        # add noise in invoiced segments
        cyc_noise = cyc_noise + noise * (1.0 - uv)
        return cyc_noise, pulse_train, sine_wav, uv, noise


class SineGen(torch.nn.Module):
    """ Definition of sine generator
    SineGen(samp_rate, harmonic_num = 0,
            sine_amp = 0.1, noise_std = 0.003,
            voiced_threshold = 0,
            flag_for_pulse=False)

    samp_rate: sampling rate in Hz
    harmonic_num: number of harmonic overtones (default 0)
    sine_amp: amplitude of sine-wavefrom (default 0.1)
    noise_std: std of Gaussian noise (default 0.003)
    voiced_thoreshold: F0 threshold for U/V classification (default 0)
    flag_for_pulse: this SinGen is used inside PulseGen (default False)

    Note: when flag_for_pulse is True, the first time step of a voiced
        segment is always sin(np.pi) or cos(0)
    """

    def __init__(self, samp_rate, harmonic_num=0,
                 sine_amp=0.1, noise_std=0.003,
                 voiced_threshold=0,
                 flag_for_pulse=False):
        super(SineGen, self).__init__()
        self.sine_amp = sine_amp
        self.noise_std = noise_std
        self.harmonic_num = harmonic_num
        self.dim = self.harmonic_num + 1
        self.sampling_rate = samp_rate
        self.voiced_threshold = voiced_threshold
        self.flag_for_pulse = flag_for_pulse

    def _f02uv(self, f0):
        # generate uv signal
        uv = torch.ones_like(f0)
        uv = uv * (f0 > self.voiced_threshold)
        return uv

    def _f02sine(self, f0_values):
        """ f0_values: (batchsize, length, dim)
            where dim indicates fundamental tone and overtones
        """
        # convert to F0 in rad. The interger part n can be ignored
        # because 2 * np.pi * n doesn't affect phase
        rad_values = (f0_values / self.sampling_rate) % 1

        # initial phase noise (no noise for fundamental component)
        rand_ini = torch.rand(f0_values.shape[0], f0_values.shape[2], \
                              device=f0_values.device)
        rand_ini[:, 0] = 0
        rad_values[:, 0, :] = rad_values[:, 0, :] + rand_ini

        # instantanouse phase sine[t] = sin(2*pi \sum_i=1 ^{t} rad)
        if not self.flag_for_pulse:
            # for normal case

            # To prevent torch.cumsum numerical overflow,
            # it is necessary to add -1 whenever \sum_k=1^n rad_value_k > 1.
            # Buffer tmp_over_one_idx indicates the time step to add -1.
            # This will not change F0 of sine because (x-1) * 2*pi = x * 2*pi
            tmp_over_one = torch.cumsum(rad_values, 1) % 1
            tmp_over_one_idx = (tmp_over_one[:, 1:, :] -
                                tmp_over_one[:, :-1, :]) < 0
            cumsum_shift = torch.zeros_like(rad_values)
            cumsum_shift[:, 1:, :] = tmp_over_one_idx * -1.0

            sines = torch.sin(torch.cumsum(rad_values + cumsum_shift, dim=1)
                              * 2 * np.pi)
        else:
            # If necessary, make sure that the first time step of every
            # voiced segments is sin(pi) or cos(0)
            # This is used for pulse-train generation

            # identify the last time step in unvoiced segments
            uv = self._f02uv(f0_values)
            uv_1 = torch.roll(uv, shifts=-1, dims=1)
            uv_1[:, -1, :] = 1
            u_loc = (uv < 1) * (uv_1 > 0)

            # get the instantanouse phase
            tmp_cumsum = torch.cumsum(rad_values, dim=1)
            # different batch needs to be processed differently
            for idx in range(f0_values.shape[0]):
                temp_sum = tmp_cumsum[idx, u_loc[idx, :, 0], :]
                temp_sum[1:, :] = temp_sum[1:, :] - temp_sum[0:-1, :]
                # stores the accumulation of i.phase within
                # each voiced segments
                tmp_cumsum[idx, :, :] = 0
                tmp_cumsum[idx, u_loc[idx, :, 0], :] = temp_sum

            # rad_values - tmp_cumsum: remove the accumulation of i.phase
            # within the previous voiced segment.
            i_phase = torch.cumsum(rad_values - tmp_cumsum, dim=1)

            # get the sines
            sines = torch.cos(i_phase * 2 * np.pi)
        return sines

    def forward(self, f0):
        """ sine_tensor, uv = forward(f0)
        input F0: tensor(batchsize=1, length, dim=1)
                  f0 for unvoiced steps should be 0
        output sine_tensor: tensor(batchsize=1, length, dim)
        output uv: tensor(batchsize=1, length, 1)
        """
        with torch.no_grad():
            f0_buf = torch.zeros(f0.shape[0], f0.shape[1], self.dim, \
                                 device=f0.device)
            # fundamental component
            f0_buf[:, :, 0] = f0[:, :, 0]
            for idx in np.arange(self.harmonic_num):
                # idx + 2: the (idx+1)-th overtone, (idx+2)-th harmonic
                f0_buf[:, :, idx + 1] = f0_buf[:, :, 0] * (idx + 2)

            # generate sine waveforms
            sine_waves = self._f02sine(f0_buf) * self.sine_amp

            # generate uv signal
            # uv = torch.ones(f0.shape)
            # uv = uv * (f0 > self.voiced_threshold)
            uv = self._f02uv(f0)

            # noise: for unvoiced should be similar to sine_amp
            #        std = self.sine_amp/3 -> max value ~ self.sine_amp
            # .       for voiced regions is self.noise_std
            noise_amp = uv * self.noise_std + (1 - uv) * self.sine_amp / 3
            noise = noise_amp * torch.randn_like(sine_waves)

            # first: set the unvoiced part to 0 by uv
            # then: additive noise
            sine_waves = sine_waves * uv + noise
        return sine_waves, uv, noise


class SourceModuleCycNoise_v1(torch.nn.Module):
    """ SourceModuleCycNoise_v1
    SourceModule(sampling_rate, noise_std=0.003, voiced_threshod=0)
    sampling_rate: sampling_rate in Hz

    noise_std: std of Gaussian noise (default: 0.003)
    voiced_threshold: threshold to set U/V given F0 (default: 0)

    cyc, noise, uv = SourceModuleCycNoise_v1(F0_upsampled, beta)
    F0_upsampled (batchsize, length, 1)
    beta (1)
    cyc (batchsize, length, 1)
    noise (batchsize, length, 1)
    uv (batchsize, length, 1)
    """

    def __init__(self, sampling_rate, noise_std=0.003, voiced_threshod=0):
        super(SourceModuleCycNoise_v1, self).__init__()
        self.sampling_rate = sampling_rate
        self.noise_std = noise_std
        self.l_cyc_gen = CyclicNoiseGen_v1(sampling_rate, noise_std,
                                           voiced_threshod)

    def forward(self, f0_upsamped, beta):
        """
        cyc, noise, uv = SourceModuleCycNoise_v1(F0, beta)
        F0_upsampled (batchsize, length, 1)
        beta (1)
        cyc (batchsize, length, 1)
        noise (batchsize, length, 1)
        uv (batchsize, length, 1)
        """
        # source for harmonic branch
        cyc, pulse, sine, uv, add_noi = self.l_cyc_gen(f0_upsamped, beta)

        # source for noise branch, in the same shape as uv
        noise = torch.randn_like(uv) * self.noise_std / 3
        return cyc, noise, uv


class SourceModuleHnNSF(torch.nn.Module):
    """ SourceModule for hn-nsf
    SourceModule(sampling_rate, harmonic_num=0, sine_amp=0.1,
                 add_noise_std=0.003, voiced_threshod=0)
    sampling_rate: sampling_rate in Hz
    harmonic_num: number of harmonic above F0 (default: 0)
    sine_amp: amplitude of sine source signal (default: 0.1)
    add_noise_std: std of additive Gaussian noise (default: 0.003)
        note that amplitude of noise in unvoiced is decided
        by sine_amp
    voiced_threshold: threhold to set U/V given F0 (default: 0)

    Sine_source, noise_source = SourceModuleHnNSF(F0_sampled)
    F0_sampled (batchsize, length, 1)
    Sine_source (batchsize, length, 1)
    noise_source (batchsize, length 1)
    uv (batchsize, length, 1)
    """

    def __init__(self, sampling_rate, harmonic_num=0, sine_amp=0.1,
                 add_noise_std=0.003, voiced_threshod=0):
        super(SourceModuleHnNSF, self).__init__()

        self.sine_amp = sine_amp
        self.noise_std = add_noise_std

        # to produce sine waveforms
        self.l_sin_gen = SineGen(sampling_rate, harmonic_num,
                                 sine_amp, add_noise_std, voiced_threshod)

        # to merge source harmonics into a single excitation
        self.l_linear = torch.nn.Linear(harmonic_num + 1, 1)
        self.l_tanh = torch.nn.Tanh()

    def forward(self, x):
        """
        Sine_source, noise_source = SourceModuleHnNSF(F0_sampled)
        F0_sampled (batchsize, length, 1)
        Sine_source (batchsize, length, 1)
        noise_source (batchsize, length 1)
        """
        # source for harmonic branch
        sine_wavs, uv, _ = self.l_sin_gen(x)
        sine_merge = self.l_tanh(self.l_linear(sine_wavs))

        # source for noise branch, in the same shape as uv
        noise = torch.randn_like(uv) * self.sine_amp / 3
        return sine_merge, noise, uv


if __name__ == '__main__':
    source = SourceModuleCycNoise_v1(24000)
    x = torch.randn(16, 25600, 1)