Voice conversion (VC) aims to convert speaker characteristics from source speaker to target speaker. It is an enabling technique for many applications, such as text-to-speech synthesis [1, 2] and emotional voice conversion [3, 4].
In this paper, we focus on cross-lingual voice conversion , where the source and target speakers speak different languages. Cross-lingual voice conversion is more challenging than mono-lingual voice conversion  because source and target speakers speak in two different phonetic systems and prosodic styles, furthermore, parallel training data is not easily available [7, 8, 9]. The comparison between cross-lingual and mono-lingual voice conversion is illustrated in Fig. 1(a). and Fig. 1(b). In the training phase, cross-lingual voice conversion is trained with non-parallel speech from the source and target speaker speaking with different languages, whereas mono-lingual voice conversion can be trained with parallel/non-parallel speech from source and target speaker speaking with the same language [10, 11, 12, 13].
Previous studies on mono-lingual voice conversion mainly focus on finding a mapping function between the source and target through parallel training data, which includes Gaussian mixture model (GMM), non-negative matrix factorization (NMF) based sparse representation [15, 16], and group sparse representation 17]
and generative adversarial network (GAN), have greatly improved conversion quality.
One way of cross-lingual voice conversion is to rely on multilingual speakers to provide same-speaker, cross-lingual training data. Some statistical approaches for spectral mapping include codebook mapping  and Gaussian mixture model (GMM) 
, that show comparable performance with that of mono-lingual voice conversion. However, collecting such data from a bilingual speaker can be expensive and time-consuming. Besides, system performance also depends largely on the speaker’s proficiency in the language pair. To circumvent the need for bilingual data, hidden Markov model (HMM), unit selection [21, 22] and the iterative frame alignment [23, 24] were proposed to find source-target frame pairs from non-parallel utterances.
and variational autoencoding wasserstein generative adversarial networks (VAW-GAN) have achieved high-quality mono-lingual voice conversion with non-parallel data. GAN-based methods for cross-lingual voice conversion  have shown similar results with monolingual voice conversion without the need for parallel training data, nor external modules (such as ASR).
Unfortunately, prosody conversion for cross-lingual voice conversion has not been well studied. The differences between two languages lie not only in phonetic systems, but also in linguistic prosody and speaking style, that are characterized by the F0 contour of speech. Motivated by the success of CycleGAN in spectral conversion, we would like to study the conversion of both spectrum and prosody in this paper. In the context of cross-lingual voice conversion, the source speaker is a native speaker of the language, therefore, the source linguistic prosody, such as sentence-level pitch trajectory, should be carried over to the target as much as possible, while the conversion is expected to handle speaker-dependent prosody elements such as pitch level, phoneme-level pitch patterns etc.
It is well known that speaker characteristics are usually related to: 1) prosodic factors which are concerned with syllables and larger units of speech instead of individual phonetic segments (vowels and consonants); and 2) segmental factors that involve short time spectrum. As an essential prosodic factor, fundamental frequency (F0) represents the variation of the vocal pitch over the whole time domains . Some cross-lingual voice conversion methods  use a simple linear transformation to convert F0. Since F0 is hierarchical in nature and affected by short-term as well as long-term dependencies, we believe that a simple linear transformation is insufficient to model the variations of F0 in different temporal scales [30, 3]. Therefore, we propose to use CWT decomposition to analyse F0 in different time scales, and find a mapping for each time scale. The CWT decomposition describes a frame-based F0 value with a set of CWT coefficients, that represent prosodic features. We note that this is the first study of F0 modeling for cross-lingual voice conversion.
In this paper, we propose a cross-lingual voice conversion framework based on CycleGAN, that can learn the mappings of spectrum and prosody between the speakers speaking with different languages. We also use CWT to decompose F0 into 10 different temporal scales to describe the prosody from the phone level to the utterance level. It is noted that our proposed framework does not rely on any training data from bilingual speakers or any other external modules such as speech recognition or time alignment procedures.
The main contributions of this paper include: 1) we propose a cross-lingual voice conversion framework based on CycleGAN to convert the spectrum and prosody; 2) we propose to analyze F0 in different time resolutions with CWT; and 3) we explored the effect of prosody conversion in cross-lingual voice conversion. To our best knowledge, this paper reports the first attempt to incorporate generative models and CWT-based prosody analysis for cross-lingual voice conversion.
The rest of this paper is organized as follows: In Section II, we provide the motivation and related work to set the stage for this study. In Section III, we propose a spectro-prosodic cross-lingual voice conversion framework. In Section VI, the experiment results are presented. Section V concludes the discussion.
2 Related Work
2.1 Prosody Modelling with CWT
Generally speaking, speech can be characterized by spectral and prosodic features in general [31, 32]. Prosody is supra-segmental and hierarchical in nature, hence prosody modeling is not as straghtforward as frame-based spectral modeling in voice conversion.
Continuous wavelet transform (CWT) has shown to be effective in simultaneous analysis and visualization of various time scales of a signal . It provides a way to describe F0 in different time scales. We also note that CWT has been successfully applied in analysis and modelling of F0 in speech synthesis[33, 34, 35] and mono-lingual voice conversion [36, 30]. In this paper, we further this idea and decompose F0 into 10 temporal scales.
Given a continuous input signal , its continuous wavelet transform can be written as:
where is the Mexican hat mother wavelet. The original signal can be recovered from the wavelet representation by inverse transform using the following formula:
where and . These time scales were originally proposed in .
Given 10 wavelet components, , that are the converted version of CWT components for target speaker, we can recompose signal by the following formula :
As can be observed in Fig. LABEL:fig:SF2 and LABEL:fig:TF2 where two speakers read the same text, high scale (e.g. scale 9 and 10) coefficients are similar between speakers, and low scale (e.g. scale 1 and 2) coefficients are speaker-dependent .
With the multi-scale CWT decomposition, we can now represent a F0 sequence using a sequence of CWT coefficient frames, in parallel to spectral frames of an utterance. We expect to train a prosody mapping function to learn the mapping between individual CWT coefficients, in particular to reflect, the speaker style transfer. Fig. LABEL:fig:cwt_english and 4 show an example of English-Chinese training pair from two different speakers. We will study the prosody mapping in Section III.
2.2 CycleGAN for Style Transfer
Generative adversarial networks (GANs) [39, 40, 41] provide a way of representing and modelling the high-dimensional distribution of data. GANs learn deep representation and generate many different acceptable answers by implicitly modeling the high-dimensional distribution of data . GANs consist of two neural networks, a generator and a discriminator, which compete with each other. The generator creates samples following the same distribution of the training set to fool the discriminator while the discriminator distinguishes whether they are real samples from training set or fake generated samples [43, 44]. GANs have shown remarkable performance in the fields of computer version [45, 46, 47, 48]49, 50], speech synthesis [51, 27, 52] and voice conversion [26, 9, 18].
CycleGAN, a successful implementation of GANs, was first proposed for unpaired image-to-image translation, and then applied to other non-parallel style transfer tasks, such as speech synthesis and mono-lingual voice conversion [25, 53, 54]. CycleGAN has also been used for spectrum mapping in cross-lingual voice conversion . In this paper, we extend the idea and formulate a CycleGAN that learns prosody mapping of CWT coefficients without the need of parallel or bilingual data. Despite different languages, as shown in Fig. 3(c) and Fig. 4, the low scale CWT coefficients of F0 between the two utterances could be very different, but the high scale CWT coefficients of F0 are similar. We expect that CycleGAN is able to learn the differentiated mapping relationship between low and high scale coefficients.
3 CycleGAN based cross-lingual voice conversion
In this section, we propose a CycleGAN-based cross-lingual voice conversion framework that effectively learns a mapping between source and target speakers from two different languages. We also use CWT to decompose F0 into 10 different time scales for both source and target languages, ranging from the micro-prosody level to the whole utterance level, with the aim to describe the prosody in different time resolutions.
3.1 Training of Spectrum and Prosody Conversion with CycleGANs
We first use WORLD vocoder to extract spectral features and fundamental frequency (F0) from source and target waveform. It is noted that the extracted F0 features are discontinuous due to the voiced/unvoiced activities in an utterance, as shown in Fig. LABEL:fig:original_F0. Since CWT is sensitive to the gaps in the extracted F0 contour [29, 36], the following pre-processing steps are necessary [30, 6]
: 1) linear interpolation over unvoiced regions; 2) transformation of F0 from linear to a logarithmic scale; and 3) normalizing the resulting F0 to zero mean and unit variance. The continuous F0 signals after pre-processing is shown in Fig.LABEL:fig:continuous_F0. After the pre-processing, we obtain the 10-scale CWT-F0 coefficients, or a 10-dimensional prosody frame.
For spectrum conversion, we extract 24-dimensional Mel-cepstral coefficients (MCEPs) features for spectral CycleGAN model, denoted as Spectrum-CycleGAN. As for prosody conversion, we use 10-dimensional CWT-F0 coefficients as prosodic features for prosodic CycleGAN model, and denoted as Prosody-CycleGAN. The same training procedure applies to the training of both models.
During training, CycleGAN is capable of learning the forward and inverse mappings simultaneously through the non-parallel training data and trying to find an optimal pseudo pair for the spectrum and prosody conversion. The training phase of the proposed framework is shown in Fig. 5, that includes a spectrum and a prosody modeling pipeline. Previous study on emotional voice conversion  has shown that separate training of the spectrum and prosody can achieve better performance than joint training. Therefore, we train the two CycleGANs separately.
We assume that source and target speaker speak two different languages: English and Chinese respectively, which are denoted as and . The goal of CycleGAN is to learn a mapping between the source and the target
. CycleGAN is incorporated with three main loss functions: adversarial loss, cycle-consistency loss, and identity-mapping loss.
An adversarial loss measures how distinguishable between the data distribution of converted data and source or target data. For the forward mapping, it is defined as:
Since the adversarial loss only restricts to follow the target distribution, a cycle-consistency loss is proposed in order to guarantee the consistency of the contexture information between input and output. It is defined as:
Cycle-consistency loss encourages the forward mapping and the inverse mapping to find an optimal pseudo pair of through circular conversion.
In order to preserve linguistic information without any external processes, identity mapping loss is defined as:
With these three loss, we expect CycleGAN to learn a bi-directional mapping between the spectrum and prosody distributions in different languages, from source and target speakers.
3.2 Run-time Conversion
The conversion phase of the proposed framework is illustrated in Fig. 6. Similar to that of training phase, WORLD vocoder is used to extract spectral features, F0 and aperiodicities (APs) of source speech. We then encode 24-dimensional MCEPs spectral features, and decompose F0 into 10-scales, denoted as CWT-F0 coefficients. The 24-dimensional MCEPs and 10-dimensional CWT-F0 coefficients are converted by the trained Spectrum-CycleGAN and Prosody-CycleGAN respectively. We reconstruct F0 from the converted 10-dimensional CWT-F0 coefficients through CWT synthesis given in Fig. 6, using Eq. 4.
At run-time, we present the combined results of spectrum conversion and prosody conversion to the vocoder for reconstruction of speech waveform. Therefore, we call the proposed framework Spectrum-Prosody-CycleGAN. It is noted that APs are directly copied from source to that of target speaker without any modification .
In this section, we conduct experiments to assess the performance of our proposed CycleGAN-based cross-lingual voice conversion framework for spectrum and prosody. We use VCC 2016 dataset  and Blizzard Challenge 2010 database , which consists of English and Chinese speech data respectively. We choose four English speakers and one Chinese speaker for experiments. We conduct cross-lingual voice conversion both from English to Chinese, denoted as ; and from Chinese to English, denoted as , respectively. We note that bilingual data are required for MCD calculation in cross-lingual VC [9, 7], hence we only conduct subjective experiments to show the effectiveness of our proposed framework.
We build two systems for a comparative study, the proposed Spectrum-Prosody-CycleGAN, and the Spectrum-CycleGAN baseline , where spectrum is converted with CycleGAN and fundamental frequency (F0) is converted through the logarithm Gaussian (LG) normalized transformation . In Spectrum-Prosody-CycleGAN, we perform CWT to decompose F0 into 10 different time scales and train two CycleGAN networks using non-parallel data with two different languages to learn the mappings of spectral and prosody features between source and target speaker.
4.1 Experimental Setup
To evaluate the systems under the condition of non-parallel and limited amount of data, we use 81 non-parallel utterances from source and target speakers with English and Chinese for training, and 54 utterances for evaluation. It is noted that our proposed cross-lingual VC method is trained under the disadvantageous condition (non-parallel and limited amount of data).
The speech data is downsampled to 16kHz, and 24-dimensional Mel-cepstral coefficients (MCEPs), fundamental frequency (F0), and aperiodicity (APs) are then extracted every 5 ms using WORLD vocoder . For both frameworks, we extract 24-dimensional MCEPs and one-dimensional F0 features for each frame. We further obtain 10-dimensional CWT-based F0 features from one-dimensional F0 features with CWT analysis in our proposed framework. It is noted that APs are directly copied from the source to target without any modification.
In both systems, the generator uses a one-dimensional (1D) CNN to capture the relationship among the overall features while preserving the temporal structure. The 1D CNN is incorporated with down-sampling, residual,and up-sampling layers. We design the discriminator using a 2D CNN to focus on a 2D spectral texture. In the training phase, we set =10. and only use for the first iterations. The Adam optimizer  with a batch size of 1 is used to train the networks. The initial learning rate for the generators is set to 0.0002 while that of discriminators are set to 0.0001. The learning rate keeps the same for the first iterations, and linearly decays over the second iterations. The momentum term is set to 0.5.
We conduct two listening tests to assess system performance of in terms of voice quality and speaker similarity. For each test, we conduct cross-lingual VC from English to Chinese and from Chinese to English respectively, which denoted as and . 15 bilingual native Chinese speakers participated in all the listening tests and listened to 90 converted utterances in total.
4.2.1 Mean Opinion Score Tests
To evaluate the converted speech quality, we first conduct mean opinion score (MOS) test between the baseline and our proposed method. 15 sentences are randomly selected from the evaluation set. In MOS test, each subject are asked to score each sample in a five-point-scale (5: excellent, 4: good, 3: fair, 2: poor, 1: bad). As shown in Table 1, our proposed method achieves comparable results with the baseline for both and .
|Framework||Mean Opinion Score (MOS)|
|Spectrum-CycleGAN & LG ||2.91 0.33||3.30 0.27|
|Spectrum-Prosody-CycleGAN||2.92 0.27||3.34 0.29|
4.2.2 Similarity Listening Tests
We consider that how similar the converted speech is to the target speech reflects the effect of prosody conversion. Therefore, we conduct XAB preference test between our proposed framework and the baseline framework in terms of speaker similarity. The subjects are asked to listen to the reference target samples and the converted samples of the baseline and our proposed framework, and choose the one which sounds closer to the target sample. We expect that the proposed prosody conversion approach will remarkably improve the speaker similarity, as prosody contains the information of speaking style.
As shown in Fig. 7, we observe that our proposed method clearly outperforms the baseline framework in both experiments English to Chinese (), and Chinese to English () experiments. The results suggest that CWT is an effective way of prosody modeling for cross-lingual voice conversion, and through CycleGAN we can learn a prosody mapping between source and target that speak different languages. The results also validate our idea to use CycleGAN to learn the differentiated mapping relationship among low and high scale coefficients of F0.
In this paper, we propose a novel parallel-data-free cross-lingual voice conversion framework. We convert the spectrum and prosody based on CycleGAN with non-parallel and limited amount of training data. Moreover, We also provide a non-linear method which uses CWT to describe the prosody in different time scales for cross-lingual voice conversion. Experimental results show the effectiveness of our proposed framework in terms of voice quality and speaker similarity.
This work is supported by National Research Founda- tion Singapore under the AI Singapore Programme (Award Number: AISG-100E-2018-006 , AISG-GC-2019-002 ), under the National Robotics Programme (Grant Number: 192 25 00054), and Programmatic Grant No. A18A2b0046 (Human Robot Collaborative AI for AME) and A1687b0033 (Neuro- morphic Computing) from the Singapore Government’s Re- search, Innovation and Enterprise 2020 plan in the Advanced Manufacturing and Engineering domain.
This work is also supported by SUTD Start-up Grant Artificial Intelligence for Human Voice Conversion (SRG ISTD 2020 158) and SUTD AI Grant titled ’The Understanding and Synthesis of Expressive Speech by AI’ (PIE-SGP-AI-2020-02).
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