如何计算STFT移调后的相位？PyTorch实现及自动微分问题

我使用torch.stft()生成频谱图，希望直接对音频执行移调操作，最终得到移调后音频的STFT。由于phase_vocoder→istft→resample→stft的流程速度过慢，我编写了一段代码，通过插值原频谱的对应频率仓来生成新频谱：

def interpolate(frequencies: torch.Tensor, sgram: torch.Tensor):
    start = frequencies.int()
    frac = (frequencies - start)[:, None]
    return sgram[start, :] * (1 - frac) + sgram[start + 1, :] * frac

def pitch_shift_spectrogram(sgram: torch.Tensor, semitones: torch.Tensor):
    scaling_factor = 2 ** (-semitones / 12)
    frequencies = torch.arange(0, sgram.shape[0], 1, device=sgram.device)
    shifted_frequencies = frequencies * scaling_factor
    shifted_mags = interpolate(shifted_frequencies, sgram.abs())
    phases = sgram.angle() # ??? what do i do? help
    return torch.polar(shifted_mags, phases)

我在CantinaBand3.wav音频文件上进行了测试，生成的幅度谱效果尚可；若使用完整移调实现的相位，音频效果正常：

import torch
import torchaudio
import IPython.display as display

waveform, sample_rate = torchaudio.load("CantinaBand3.wav")
waveform = waveform[0]

shifted_waveform = torchaudio.functional.pitch_shift(waveform, sample_rate, 2)
working_sgram = torch.stft(shifted_waveform, 1024, return_complex=True)

unshifted_sgram = torch.stft(waveform, 1024, return_complex=True)
broken_sgram = pitch_shift_spectrogram(unshifted_sgram, torch.tensor(2))

broken_sgram = torch.polar(broken_sgram.abs(), working_sgram.angle())
display.display(display.Audio(torch.istft(broken_sgram, 1024), rate=sample_rate))

现提出以下问题：

• 能否仅通过STFT计算移调信号的相位信息？
• PyTorch是否提供相关内置函数？
• 当semitones作为模型参数时，插值操作能否正常支持autograd反向传播？

内容的提问来源于stack exchange，提问作者potatoportato