Summary
Although phase-aware speech processing has received increasing attention in recent years, most narrow-band STFT methods with frame lengths around 32 ms show a rather limited impact of phase on overall performance. At the same time, modern deep neural network (DNN) based methods, such as Conv-TasNet, implicitly modify the magnitude and phase, yielding excellent performance on very short frames (2 ms).
Inspired by this observation, this paper systematically investigates the role of phase and amplitude in DNN speech enhancement with different frame lengths. The results show that phase-aware neural networks can take full advantage of previous research on clean speech reconstruction showing that when short frames are used, the phase spectrum becomes more important, while the magnitude spectrum becomes less important . Experiments show that shorter frames can significantly improve the performance of DNNs with explicit phase estimation when both magnitude and phase are estimated simultaneously. Conversely, 32 ms frames give the best performance if only the magnitude is processed and the phase is not estimated. DNN-based phase estimation benefits from using shorter frames, and a frame length of about 4 ms is recommended for neural network-based phase-aware speech enhancement methods.
Index Terms: Speech Enhancement, Neural Networks, Frame Length, Phase Awareness
1 Introduction
Single-channel speech enhancement is usually performed in the time-frequency domain, and to obtain a time-frequency representation, a transform with multiple free parameters such as the short-time Fourier transform (STFT) can be applied. These parameters (ie frame length, frame shift and window function, see Section 2) have to be chosen appropriately. However, not only the signal itself, but also the algorithm applied to the time-frequency representation must be considered; the choice of STFT parameters should yield the most useful representation for the current algorithm [1].
This paper focuses on the choice of frame length for speech enhancement algorithms based on deep neural networks (DNNs) , especially for phase-aware methods. The STFT representation is complex and is usually divided into a magnitude spectrum and a phase spectrum. The relevance of phase spectra to speech enhancement tasks has been a topic of debate. Traditionally, it has been considered unimportant due to empirical studies [2] and theoretical results [3]. However, recent studies have shown that phase does carry speech-related information [4], [5]. Motivated by these findings, phase-aware speech processing has been somewhat revived, and various phase-aware speech processing methods have been proposed, such as [6]–[10].
In recent years, deep neural networks have rapidly become the tool of choice in many fields, including audio and speech processing. Therefore, many recent phase-aware speech enhancement and sound source separation methods use deep neural networks to directly estimate the phase spectrum [11]–[13], or estimate the phase derivative and reconstruct the phase from it [14], [15]. Other DNN-based approaches include operating directly on the complex spectrum without splitting [16]–[18] into magnitude and phase, or considering only phase to improve magnitude estimation [19].
Some authors have taken a different approach, completely replacing STFT-based representations with a learned encoder-decoder mechanism, which often results in real representations [20]–[22]. An interesting aspect of these encoder-decoder methods is that they show very good performance when using very short frames of around 2ms, even as short as 0.125ms [21]. This is in stark contrast to STFT-based methods, which typically use frame lengths of around 20 ms to 60 ms. Note that although learned encoder-decoder methods were originally proposed for source separation, they also show good performance on speech enhancement tasks [23], [24].
Following the publication of the seminal learning encoder-decoder Conv-TasNet model [20], several authors proposed extensions and analyzes. Among other results, it has been shown that ConvTasNet's performance is dominated by the use of short frames and temporal loss functions rather than the learned encoder-decoder [25], [26]. Studies have also shown that when replacing the learned encoder with STFT, the optimal set of input features depends on the chosen frame length [26], [27]; for longer frames (25 ms to 64 ms), the magnitude spectrum works quite well, while shorter frames (2 ms to 4 ms) only show better performance when they take the full spectrum of complex numbers as input (in the form of concatenated real and imaginary parts) . This observation is particularly important because it implies that phase-aware speech processing (whether implicit or explicit phase estimation) should possibly employ a different frame length than magnitude-only processing.
While the paper [24] has studied the impact of the choice of loss function in phase-aware speech enhancement DNNs on perceptual measurements, we are not yet aware of such an analysis on the choice of frame length. Previous DNN-independent studies have shown that the importance of phase for speech-related tasks varies with the choice of STFT parameters. In particular, without using the typical frame length (corresponding to about 20 ms to 40 ms), using shorter frames [28], [29] or using effectively shortened frames [4], it is possible to obtain very good Signal reconstruction. Similar results are observed for longer typical frames [28], [30]. However, we choose to focus on short frames for practical reasons due to the algorithmic delay that long frames create, which can be prohibitive for many real-time speech processing devices. Figure 1 reproduced from [28] shows how the contribution of phase and magnitude to the intelligibility of reconstructed clean speech varies with frame length. It is observed that as the frame gets shorter, the phase becomes more important while the magnitude gradually loses its correlation. Note, however, that these findings are based on some artificial signal reconstruction experiments on oracle data - whether they also apply to practical speech enhancement, source separation, etc. is unclear.
Figure 1: An excerpt of the results reproduced from [28] and shown here for illustration purposes.
When reconstructing speech from magnitude spectrum or phase spectrum (replacing other components with noise), the intelligibility of the resulting speech signal depends largely on the choice of frame length. See [28, Fig. 2] for the complete figure and details.
语音处理中典型的帧长(约32 ms)可以被认为是准平稳的，但又足够长，可以覆盖多个浊音的基本周期(基本周期在2 ms到12.5 ms之间)[31]。这些考虑适用于幅度谱，但不一定适用于相位谱。事实上，似乎相位谱的不相关性部分是由于实验中帧长的选择。
基于之前的结果和观察，本文试图回答的问题是：哪种帧长对基于STFT的相位感知语音增强DNN最有利？以具有显式相位估计的深度神经网络为例，分析和比较了不同帧长下的性能。为了获得进一步的见解，本文还试图描述每个帧长上的幅度和相位谱的相对贡献，并表明上述关于短帧中相位重要性的观察在语音增强的背景下也是相关和有用的。
2 预备知识
将时域信号$x(n)$分割为长度为$M$、位移为$H$的重叠帧，计算其STFT，对每一帧应用窗函数$w(n)$，然后对其进行离散傅里叶变换(DFT)，将其转换到频域。假设采用单边$M$点DFT，得到复数谱$x\in C^{K*L}$，定义为
$$公式1：X_{k,l}=\sum_{n=0}^{M-1}x(lH+n)w(n)e^{-j2\pi \frac{kn}{M}}$$
其中$k$是频率索引，$l$是帧索引，$K=\frac{M}{2}+1$是频点的数量，$L$是时间帧的数量。除非另有说明，否则我们总是考虑整个频谱，因此忽略下面的索引。为了方便起见，我们还定义了重叠率$R=\frac{M-H}{M}$。由于$M$是单个帧中的样本数量，我们定义$M_t=\frac{M}{f_s}$(其中$f_s$是采样频率)为物理帧长度(以秒为单位)。从这一点开始，术语帧长度将指的是$M_t$。
复数谱在极坐标下可以表示为幅度谱$|X|$和相位谱$\phi X$：
$$公式2：X=|X|e^{j\phi X}$$
在语音增强的背景下，我们考虑了一个加性噪声模型
$$公式3：X=S+V$$
其中$S$和$V$分别是纯净语音信号和加性噪声分量。给定噪声信号$X$，任务是计算估计$\hat{S}=|\hat{S}|e^{j\hat{\phi }S}$，随后将其转换回时域，得到估计的干净信号$\hat{s}$。
3 神经网络框架
本文提出的DNN架构是[12]中提出的用于视听语音分离和增强的模型的改编，由耦合的幅值和相位子网络组成。虽然我们在这里不考虑音视频输入，但该模型相对简单，可以对幅度和相位进行显式估计，这对我们的实验至关重要。与视频流相关的部分被忽略，模型进行了相应的调整。结果网络如图2所示，如下所述
图2：所提出的网络架构概述，基于[12]的视听模型，尽管仅使用带噪语音信号作为输入
基本卷积块如图3所示。请注意，相位子网络的输入由估计幅度以及噪声相位的余弦和正弦组成，为了简单起见，这里显示为单个输入
这两个子网络都使用沿时间轴的一维深度可分离卷积层[32]实现卷积神经网络(在这种设置中，输入端的不同频点被视为通道)。两个网络都由多个相同的残差块组成；基本构建块由预激活(ReLU)、批量归一化层和卷积层组成，卷积层的输出被添加到块的输入中(见图3)。
图3 基本残差卷积块，由ReLU预激活、批量归一化层和一维深度可分离卷积层组成
3.1 幅度子网络
幅度子网络采用带噪幅度谱$|X|$输出一个实数掩模，该掩模应用于带噪STFT幅度谱以产生幅度估计(注意，来自[12]的原始网络使用梅尔尺度的频谱以及视频特征作为输入)。噪声幅度谱通过15个卷积块的链进行，每个卷积块有1536个输入/输出通道。输入和输出的线性层有助于对频率间关系建模，并将数据投影到正确的维度。将sigmoid激活函数应用于输出，得到一个值在[0,1]内的实数掩码。实数的掩模与输入相乘，得到一个幅度估计$|\hat{S}|$。
3.2 相位子网络
相位子网络的输入是沿频率轴的$|\hat{S}|$， $cos(\phi X)$和$sin(\phi X)$的级联。它被输入到一个线性输入层，随后通过6个具有1024个通道的卷积块和一个线性输出层。线性层的输出被视为相位残差的余弦和正弦的级联，它们被添加到各自的输入。对得到的估计进行$L_2$归一化，以确保余弦和正弦输出彼此一致(即它们表示复平面上的一个单位向量)。
3.3 训练过程
与[12]中提出的多阶段学习方法相比，我们只是在由不同信噪比(SNR)的带噪和纯净语音样本对组成的整个训练集上训练网络(更多细节请参见第4.1节)。本文采用了一种时域损失函数，即负尺度不变信号失真比(negative scale invariant signal to distortion ratio, SI-SDR)[33]，而不是[12]中提出的频域损失函数。当幅度谱和相位谱都被估计时，SISDR损失已经被证明可以产生优越的结果[26]。
4 实验
我们进行的主要实验是比较该模型在不同STFT帧长$M$的性能，在感知和客观测量方面。由于我们考虑的模型包括相位和幅度的显式估计，我们还能够分析和量化幅度和相位估计的相对贡献，再次作为帧长的函数。这种分析的方式与[4]、[28]、[29]中的感知实验类似，尽管这里我们使用纯净语音幅度和相位的估计，而不是纯净或噪声时域信号。对于每个帧长，我们产生三个纯净语音信号的估计：网络的实际输出以及两个由估计幅度和噪声相位组成的合成信号，反之亦然：
$$公式4：\hat{s} =iSTFT\{|\widehat{S}| \mathrm{e}^{\mathrm{j} \widehat{\phi}_S}\}$$
$$公式5：\widehat{s}_{\mathrm{mag}} =iSTFT\{|\widehat{S}| \mathrm{e}^{\mathrm{j} \phi_X}\}$$
$$公式6：\widehat{s}_{\mathrm{ph}} =iSTFT\{|X| \mathrm{e}^{\mathrm{j} \widehat{\phi}_S}\}$$
为了进行公平的比较，我们必须保持DNN参数的数量恒定。在我们考虑的网络架构的情况下，参数的数量取决于频点数量$K$。因此，我们在应用DFT之前对帧进行零补全，使得K = 257，这对应于$f_s$ = 16kHz时我们考虑的最长帧($M_t$ = 32 ms)。在所有实验中，我们使用平方根Hann窗，重叠比R = 50%。同样的窗口用于正向和逆STFT。
4.1 数据及训练明细
在训练中，我们使用2020年深度噪声抑制(DNS)数据集[34]的纯净语音和噪声，SNR$\in ${- 5,0，…, 10} dB。每个语音长度为2 s，数据集总共包含100 h的语音，其中80%用于训练，剩余20%用于验证。使用Adam优化器训练所有模型，batch size大小为32，学习率为$10^{-4}$。如果10个迭代周期内验证损失没有减少，则停止训练。
在两个测试集上进行评估：DNS合成无混响测试集，包含150个节选语音，每个语音10 s，信噪比$\in ${0,1，…， 20}dB，另一个自定义测试集，由来自WSJ语料库[35]的纯净语音和来自CHiME3数据集[36]的噪声组成，混合信噪比$\in ${−10，−5，…, 20} dB。该测试集共包含672个摘要。所有训练和评估数据都以$f_s$ = 16kHz采样。
5 结果和讨论
表1：DNS测试集上的评估结果
对于每个重构信号(如公式(4)到(6)展示了各种帧长下POLQA和ESTOI的改进(对带噪输入信号的w.r.t.)
每列中最好的结果和接近的秒数以粗体显示
在DNS测试集上的评估结果如表1所示。虽然可理解性(在ESTOI方面)受帧长选择的影响不大，但我们看到了对语音质量(POLQA)的显著影响，它受益于减少帧长，直到在$M_t$ = 4 ms达到最大值，之后开始下降，但对于1 ms到2 ms的非常短的帧仍然达到相对较高的值。对于POLQA和ESTOI，基于幅度和基于相位的估计(分别为$\hat{s}_{mag}$和$\hat{s}_{ph}$)显示了一幅有趣的图像：在$M_t$ = 32 ms时，$\hat{s}_{mag}$达到了与$\hat{s}$相似的值，而基于相位的估计$\hat{s}_{ph}$与噪声输入相比几乎没有改善。随着帧长的减少，这种情况逐渐发生变化：基于幅度的估计失去了质量和可理解性，而基于相位的估计则相反。
图4：WSJ/CHiME测试集的评估结果(见章节4.1)。
图中显示了POLQA, ESTOI和SI-SDR在所有信噪比下的平均改进随帧长的变化。
误差带表示95%的置信区间。短帧有利于POLQA测量的语音估计质量。
此外，基于相位和基于幅度的重建的不同度量显示出一种互补的行为，这让人想起在之前的oracle实验中观察到的行为(参见图1)。
如图4所示，对更大的WSJ/CHiME数据集的评估在POLQA、ESTOI和SI-SDR方面显示出类似的趋势。虽然ESTOI和SI-SDR在帧长上几乎保持不变，但POLQA显然从较短的帧中受益。同样，可以看到基于幅度和基于相位的估计的互补行为。这种行为非常类似于早期基于oracle的研究[28]，[29]。实际上，∆ESTOI结果与图1之间有惊人的相似之处，尽管基于相位的估计变得更好的点略有偏移。
POLQA的改进在Mt = 4 ms时达到最大，其中基于相位的估计也达到最大。当帧数更短时，所有三个指标的性能都会下降。总的来说，ESTOI和SI-SDR的改进似乎并不强烈依赖于帧长，尽管上述互补行为也可以清楚地观察到。然而，在这种相位感知设置中，随着帧变短，语音质量(POLQA)确实呈现上升趋势。我们将这种依赖性归因于相位和幅度谱的相对贡献以及它们之间的相互作用。虽然基于幅值的估计显示短帧的质量下降，但相位谱的贡献提高了整体性能，导致了优越的结果。
由于图4中的结果是在所有信噪比下的平均结果，我们在图5中通过显示两个选定帧长(4 ms, 16 ms)在不同信噪比下的POLQA改进来提供进一步的了解。除了较短帧的整体性能较好和较长帧的相位估计不重要之外(cf. Fig. 4)，基于幅度和相位估计的质量对信噪比的依赖性更强。特别是，在低信噪比(≤0 dB)下，基于相位的估计实际上超过了基于幅度的估计，这表明相位估计在困难的噪声条件下尤其有益，根据先前的感知研究[37]。这也转化为联合估计的情况(即$\hat{s}$)，其中帧长之的∆POLQA差异在低信噪比下更明显。
图5：M_t$\in ${4,16}ms WSJ/CHiME测试集上的平均POLQA改进，显示为输入信噪比的函数
6 结论
在这项工作中，我们提出了一项关于帧长对基于DNNs的STFT相位感知语音增强的影响的研究。结果表明，通过使用相对较短的帧(4 ms)，与通常在基于STFT的处理中使用的较长帧相比，性能有了显著提高。此外，通过显式估计相位和幅度，我们能够表明这种性能提升与幅度和相位估计的单独贡献有关，这高度依赖于帧长。这反映了以前在oracle数据上的实验得出的见解，同时首次表明，可以利用这一现象来改善语音增强结果。
7 贡献
这项工作得到了德意志Forschungsgemeinschaft (DFG，德国研究基金会)的资助-项目编号247465126。我们要感谢J. Berger和Rohde&Schwarz swiss squal AG对POLQA的支持。
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