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+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# GAN Vocoders 总览\n",
+    "\n",
+    "Loss 函数简称与全称的对应关系\n",
+    "\n",
+    "|Short Name|Full Name|\n",
+    ":-----:|:-----|\n",
+    "|adv|adversial loss|\n",
+    "|FM|Feature Matching|\n",
+    "|MSD|Multi-Scale Discriminator|\n",
+    "|mr-STFT|Multi-resolution STFT loss|\n",
+    "|fmr-STFT|full band Multi-resolution STFT loss|\n",
+    "|smr-STFT|sub band Multi-resolution STFT loss|\n",
+    "|Mel|Mel-Spectrogram Loss|\n",
+    "|MPD|Multi-Period Discriminator|\n",
+    "|FB-RAWs|Filter Bank Random Window Discriminators|\n",
+    "\n",
+    "<br></br>\n",
+    "csmsc 数据集上 GAN Vocoder 整体对比\n",
+    "\n",
+    "Model|Date|Input|Generator<br>Loss|Discriminator<br>Loss|Need<br>Finetune|Training<br>Steps|Finetune<br>Steps|Batch<br>Size|ips<br>(gen only)<br>(gen + dis)|Static Model<br>Size (gen)|RTF<br>(GPU)|\n",
+    ":-----:|:-----:|:-----:|:-----:|:-----:|:-----:|:-----:|:-----:|:-----:|:-----:|:-----:|:-----:|\n",
+    "Mel GAN|9 Dec 2019|mel|adv<br>FM |MSD|——|——|——|——|——|——|——|\n",
+    "Parallel Wave GAN |6 Feb 2020|mel<br>noise|adv<br>mr-STFT|adv|No|40W|——|8|18<br>10|5.1MB|0.01786|\n",
+    "HiFi GAN|23 Oct 2020|mel|adv<br>FM<br>Mel|MSD<br>MPD|Yes|250W|no need|16|——<br>31|50MB|0.00825|\n",
+    "Multi-Band Mel GAN|17 Nov 2020|mel|adv<br>fmr-STFT<br>smr-STFT|MSD|Yes|100W|100W<br><font size=1>(not good enough,<br>need to adjust parameters)</font>|64|305<br>148|8.2MB|0.00457|\n",
+    "Style Mel GAN|12 Feb 2021|mel<br>noise|adv<br>mr-STFT|FB-RAWs|No|150W|——|32|58<br>24|——|0.01343|\n",
+    "\n"
+   ]
+  },
+  {
+   "attachments": {},
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# 网络结构\n",
+    "## Mel GAN\n",
+    "<center><img src=\"./imgs/melgan.png\"></center>\n",
+    "<br><center>Mel GAN 网络结构图</center></br>\n",
+    "\n",
+    "## Parallel Wave GAN\n",
+    "<center><img src=\"./imgs/pwg.png\"></center>\n",
+    "<br><center>Parallel Wave GAN 网络结构图</center></br>\n",
+    "\n",
+    "## HiFi GAN\n",
+    "<center><img src=\"./imgs/hifigan_gen.png\" width=900></center>\n",
+    "<br><center>HiFi GAN 生成器网络结构图</center></br>\n",
+    "\n",
+    "<br></br>\n",
+    "\n",
+    "<center><img src=\"./imgs/hifigan_dis.png\" width=900></center>\n",
+    "<br><center>HiFi GAN 判别器网络结构图</center></br>\n",
+    "\n",
+    "## Multi-Band Mel GAN\n",
+    "<center><img src=\"./imgs/mb_melgan.png\" width=500></center>\n",
+    "<br><center>Multi-Band Mel GAN 网络结构图</center></br>\n",
+    "\n",
+    "## Style Mel GAN\n",
+    "<center><img src=\"./imgs/style_melgan_TADE.png\" width=500></center>\n",
+    "<br><center>Style Mel GAN TADE 网络结构图</center></br>\n",
+    "\n",
+    "<br></br>\n",
+    "\n",
+    "<center><img src=\"./imgs/style_melgan_gen.png\" width=500></center>\n",
+    "<br><center>Style Mel GAN 生成器网络结构图</center></br>\n",
+    "\n",
+    "<br></br>\n",
+    "\n",
+    "<center><img src=\"./imgs/style_melgan_dis.png\" width=500></center>\n",
+    "<br><center>Style Mel GAN 判别器网络结构图</center></br>"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# 需要注意的点\n",
+    "## 输入\n",
+    "1. 一般情况下，若训练时输入中没有 `noise`，容易过拟合，需要 finetune\n",
+    "    - 参考 [espent issue](https://github.com/espnet/espnet/issues/3536)\n",
+    "2. 若输入中有 `noise`, 在预测时需要自己在 `inference` 代码中生成 `noise`, 而不能作为参数输入给 `inference`, 否则动转静可能走不通\n",
+    "    - 参考 [pwgan 动转静修复 pr](https://github.com/PaddlePaddle/Parakeet/pull/132/files)\n",
+    "\n",
+    "\n",
+    "## 生成器\n",
+    "1. `hop_size` 和 `n_shift` 的含义一样\n",
+    "2. `upsample_scales` 的乘积一定等于 `hop_size`\n",
+    "3. `采样点 = hop_size * 帧数`\n",
+    "4. `librosa 帧数 = 采样点 // hop_size + 1`, 具体要不要 `+1` 看不同的库，看 `center` 这个参数 \n",
+    "5. `Mel GAN` 和 `Multi-Band Mel GAN` 生成器的代码是一样的，只是参数不一样，通道数不一样\n",
+    "6. `Parallel Wave GAN` 的生成器是 `WaveNet` like\n",
+    "    - 用非因果卷积替换了因果卷积\n",
+    "    - 输入是满足高斯分布的随机噪声\n",
+    "    - 训练和预测时都是非自回归的\n",
+    "7. `Style MelGAN` 的 noise 的上采样需要额外注意，输入的长度是固定的\n",
+    "    - `batch_max_steps(24000) == prod(noise_upsample_scales)(80) * prod(upsample_scales)(300, n_shift)`\n",
+    "\n",
+    "## 判别器\n",
+    "1. HiFi GAN 判别器的能力很强\n",
+    "\n",
+    "## 速度\n",
+    "1. 为什么 `Multi-Band Mel GAN` 的预测会更快？因为上采样的倍数变为了原来的 `1/4`"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# FFT 在语音合成声码器上的应用\n",
+    "\n",
+    "语音合成是一种将任意文本转换成语音的技术，目前在深度学习领域，语音合成主要分为 `3` 个模块:\n",
+    "- 文本前端\n",
+    "- 声学模型\n",
+    "- 声码器\n",
+    "\n",
+    "其中，文本前端模块将输入文本转换为音素序列或语言学特征；声学模型将音素序列或语言学特征转换为声学特征，在语音合成领域，常用的声学特征是 mel 频谱；声码器将声学特征转换为语音波形。\n",
+    "\n",
+    "声码器的输入是频域特征 mel 频谱图，输出是对应的语音波形。\n",
+    "\n",
+    "STFT 全称 Short-Time Fourier Transform，短时傅里叶变换，它是用滑动帧 FFT 生成频率与时间的 2D 矩阵，通常被称为频谱图（Spectrogram）, 而人耳对于频率的敏感程度是非线性的，可以通过 mel 三角滤波器对频谱图处理，生成 mel 频谱图。\n",
+    "\n",
+    "生成 mel 频谱图的计算离不开 fft 系列的算子，若模型的输入是 mel 频谱图，可以使用 `librosa` 等科学计算库进行计算再输入模型。然而，现有的大多数基于 `GAN` 的声码器模型，在计算 `loss` 时需要将生成器合成的音频及原始音频转换到频率域再做计算，这时需要用到短时傅里叶变换算子 `stft`，且由于 `stft` 算子出现在了模型图中，其需要参与到模型的前向和反向计算过程中，此时，则需要深度学习框架提供 `stft` 算子。\n",
+    "\n",
+    "最新的 `PaddleSpeech` 语音合成模块的声码器，用到了 paddle 2.2.0 提供的 fft 系列算子 `paddle.signal.stft`。\n",
+    "\n",
+    "`PaddleSpeech` 模型库目前已经实现的基于 `GAN` 的声码器包括 `Parallel WaveGAN`、`Multi Band MelGAN`、`HiFiGAN` 和 `Style MelGAN`，这些模型的 `loss` 中都包含基于 `stft` 算子的 `loss`，其中主要包含 `Multi-resolution STFT loss` 和 `Mel-Spectrogram Loss`。\n",
+    "\n",
+    "`Multi-resolution STFT loss` 公式如下所示：\n",
+    "\n",
+    "![image](./imgs/stft_loss_0.png)\n",
+    "\n",
+    "![image](./imgs/stft_loss_1.png)\n",
+    "\n",
+    "![image](./imgs/stft_loss_2.png)\n",
+    "\n",
+    "\n",
+    "`Mel-Spectrogram Loss` 公式如下所示：\n",
+    "\n",
+    "![image](./imgs/mel_loss.png)\n",
+    "\n",
+    "\n",
+    "其中 `Φ` 表示将音频转换为对应 mel 频谱的函数。\n",
+    "\n",
+    "如上述公式所示，现在主流的基于 `GAN` 的声码器的 `loss` 设计需要用到 `stft`，在 Paddle 中尚未实现 fft 系列算子时，`PaddleSpeech` 模型库使用基于 `Conv1D` 算子的函数来模拟 `stft` 算子，然而经过计算，该模拟函数前向结果正确，反向梯度计算结果不正确，这导致了模型收敛效果不佳，听感略差于竞品。\n",
+    "\n",
+    "Paddle 主框架中加入 fft 系列算子后，我们将语音合成声码器 loss 模块中的基于 `Conv1D` 的 `stft` 均替换为 `paddle.signal.stft`，在模型收敛效果和合成音频听感上，`paddle.signal.stft` 的效果明显优于基于 `Conv1D` 的 `stft` 实现。\n",
+    "\n",
+    "以 `Parallel WaveGAN` 模型为例，我们复现了基于 `Pytorch` 和基于 `Paddle` 的 `Parallel WaveGAN`，并保持模型结构完全一致，在相同的实验环境下，基于 `Paddle` 的模型收敛速度比基于 `Pytorch` 的模型快 `10.4%`, 而基于 `Conv1D` 的 `stft` 实现的 Paddle 模型的收敛速度和收敛效果和收敛速度差于基于 `Pytorch` 的模型，更明显差于基于 `Paddle` 的模型，所以可以认为 `paddle.signal.stft` 算子大幅度提升了 `Parallel WaveGAN` 模型的效果。\n",
+    "\n",
+    "![image](https://paddlespeech.bj.bcebos.com/Parakeet/docs/images/pwg_vs.png)\n"
+   ]
+  }
+ ],
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