LIFTER TRAINING AND SUB-BAND MODELING FOR COMPUTATIONALLY EFFICIENTAND HIGH-QUALITY VOICE CONVERSION USING SPECTRAL DIFFERENTIALS
Takaaki Saeki, Yuki Saito, Shinnosuke Takamichi, and Hiroshi Saruwatari
Graduate School of Information Science and Technology, The University of Tokyo, Japan.
{takaaki saeki, shinnosuke takamichi}@ipc.i.u-tokyo.ac.jp

ABSTRACTIn this paper, we propose computationally efficient and high-quality
methods for statistical voice conversion (VC) with direct waveform modification based on spectral differentials. The conventional
method with a minimum-phase filter achieves high-quality conversion but requires heavy computation in filtering. This is because theminimum phase using a fixed lifter of the Hilbert transform often results in a long-tap filter. One of our methods is a data-driven method
for lifter training. Since this method takes filter truncation into
account in training, it can shorten the tap length of the filter while
preserving conversion accuracy. Our other method is sub-band processing for extending the conventional method from narrow-band(16 kHz) to full-band (48 kHz) VC, which can convert a full-band
waveform with higher converted-speech quality. Experimental results indicate that 1) the proposed lifter-training method for narrowband VC can shorten the tap length to 1/16 without degrading theconverted-speech quality and 2) the proposed sub-band-processing
method for full-band VC can improve the converted-speech quality
than the conventional method.
Index Terms— Voice conversion, spectral differentials, deepneural network, minimum-phase filter, sub-band processing
1. INTRODUCTION
Voice conversion (VC) is a method for converting the characteristics of a source speech into those of a target speech, while keeping the linguistic information unchanged [1]. VC has the potential
to achieve speech communication beyond the physical constraintsof the human vocal organs [2]. The most common VC method
is statistical VC, which constructs an acoustic model that converts
speech features of a source speaker into those of a target speaker.
Deep neural network (DNN)-based VC [3, 4] has been widely studied, and many models for achieving higher-converted-speech quality
have been proposed. From a practical point of view, real-time VC
methods based on a Gaussian mixture model [5] and DNN [6] havealso been studied. They achieve online high-quality conversion of
narrow-band (16 kHz) speech using a single CPU on a laptop PC.
However, their computational cost is still high, and we need to reduce this cost towards portable (e.g., VC using a low-power CPU ona smart phone) or full-band (48 kHz) VC.
VC consists of three steps: feature analysis, feature conversion,
and waveform synthesis. We particularly focus on the last step anduse a spectral-differential VC [7] that performs VC in the waveformdomain by applying a spectral differential filter to the source speech
waveform. This 1) achieves high-quality conversion by avoiding
vocoder errors and 2) incurs less computational cost than neuralvocoders [8, 9, 10] that use large DNNs and require sample-bysample heavy computation. The spectral-differential VC originallyused a mel-log spectrum approximation (MLSA) filter [11] to filter aConventional method
Source speech

Filtering⊗

Minimumphase
Real-cepstrum
conversion

Results in long-tap filter= heavy computation

Proposed lifter-training method
Source speech

Filtering⊗

Data-driven
phase
Real-cepstrum
conversion

Target speech

Target speech

Shorten tap length= light computation

Fig. 1. Comparison of conventional and proposed lifter-training
methods
source speech, but Suda et al. found that using a minimum-phase filter achieved higher converted-speech quality than using the MLSA
filter [12]. In the case of the minimum-phase filter, an acoustic model(e.g., DNN) outputs a real cepstrum of the converted speech, and theHilbert transform using a lifter with fixed parameters determines thephases of the filter from the real cepstrum. These processes are suitable for our aim because their computational costs (i.e., filter design)are very small. However, since the minimum-phase filter is not guaranteed to have a short tap length (i.e., the number of samples of thefilter), it increases the computational cost of filtering. The practical
way to reduce the cost is to truncate the filter in the time domain [13],e.g., using the first half taps instead of full taps. However, such filter
truncation degrades converted-speech quality.
Therefore, we propose a lifter-training method for reducing
computational cost without degrading converted-speech quality.
Our method jointly trains not only a DNN-based acoustic model
but also a lifter with trainable parameters. Since parameters of the
DNNs and the lifter are optimized to maximize conversion accuracy with the consideration of a truncated (i.e., short-tap) filter, ourmethod can reduce the computational cost while preserving conversion accuracy. The main difference between our method anda conventional one using a minimum-phase filter is with the lifter
to determine the phase of the filter, as shown in Fig. 1. Whereas
the lifter of the minimum-phase filter is fixed, that of our method istrained from speech data to determine the phases of a truncated filter.
Furthermore, in this paper we extend the conventional method fromnarrow-band (16 kHz) to full-band (48 kHz) VC. Since fluctuations
in wider-band voices are difficult to model with statistical models,
the quality of the converted speech is relatively bad. Thus, we also
propose a sub-band-processing method for improving the convertedspeech quality. This method is designed to statistically convert thelower frequency band and preserve the higher frequency band. We
conducted objective and subjective evaluations to investigate theeffectiveness of the two proposed methods. Experimental results
indicate that 1) the proposed lifter-training method for narrow-band
VC can shorten the tap length to 1/16 without degrading convertedspeech quality and 2) the proposed sub-band-processing method forfull-band VC can improve the converted-speech quality.

STFT

2. CONVENTIONAL SPECTRAL-DIFFERENTIAL VC
WITH MINIMUM-PHASE FILTER

DNN

This section describes the training and conversion processes of theconventional spectral-differential VC with a minimum-phase filter.
2.1. Training process(X)

Target speech STFT &Cepstrum calc.

Source speech

HilberttransformReal
cepstrum

DFT

Truncation

IDFT

Lifter
Minimized to train

Fig. 2. Procedure of proposed lifter-training method(X) > >
(X) >
(X) >
]
, ..., F T[F 1, ..., F t

be a complex freLet F=
quency spectrum sequence obtained by applying the short-time
Fourier transform (STFT) to an input speech waveform, where t represents the frame index and T is the total number of frames. For thesimplicity, we now focus on the frame t. A low-order real cepstrum(X)(X)
C t can be extracted from F t [14]. The DNNs then estimate a(X)(D)
real cepstrum of differential filter C t from C t . The loss func(Y)
(Y)
(Y)
(Y)
− Ĉ t )> (C t − Ĉ t ),(Y)
where Ĉ t
is a real cepstrum of converted speech given as
(Y)
(Y)
(D)
(X)
Ĉ t
= C t + C t , and C t is a real cepstrum of the tar-tion for t is calculated as Lt = (C t

get speech. The DNNs are trained to minimize the loss function for
all time frames represented as follows:
T

L=

1 X
Lt .
T t=1

(1)

2.2. Conversion process(D)

C t is estimated with the DNNs. After the high-order components(D)of the cepstrum are padded with zeros, C t is multiplied by a timeindependent lifter umin for a minimum-phase filter. The complex(D)frequency spectrum of differential filter F t can be obtained bytaking the inverse discrete Fourier transform (IDFT) of the liftered
cepstrum. The lifter umin is represented as follows [15]:1 (n = 0, n = N/2)
(2)
umin (n) = 2 (0 < n < N/2) ,0 (n > N/2)
where N is the number of frequency bins of the DFT. A differential(D)
filter in the time domain f t is obtained by applying the IDFT to(D)(D)
F t . The tap length of f t is equal to N . To reduce the com(D)putational cost of convolution operation, we can truncate f t witha fixed tap length l (l < N ). We define the l-tap truncated filter as(l)f t . Although filter truncation can efficiently reduce the computa(l)tional cost, f t degrades converted-speech quality.
3. PROPOSED METHODS
We present the proposed methods for lifter training with filter truncation for computational-cost reduction and sub-band processing for
improving the full-band converted-speech quality.

where c is the dimension of the real cepstrum. The filter-truncation
process with l is integrated into training as shown in Fig. 2.
(D)
As we described in Section 2.1, the DNNs estimate C t from(X)
(D)
C t . Then C t is multiplied by the trainable lifter u, and the(D)complex frequency spectrum of the differential filter F t is ob(D)tained from the IDFT of C t and exponential calculation. The(D)
differential filter in the time domain f t is obtained by applying
(D)
(D)
(l)
the IDFT to F t . f t is truncated to f t by applying a windowfunction w given as Eq. (3):
ft

(l)

=

w

=

(D)

f t · w,>(l−1)th lth(N −1)th0th
1 ,··· , 1 , 0 ,··· ,
0
.

(3)
(4)

By using the DFT again, a complex spectrum of the l-tap truncated(l)differential filter F t can be obtained. A complex spectrum of con(Y)(X)(l)
by F t , and the(Y)(Y)
real cepstrum of converted speech Ĉ t is extracted from F̂ t . The

verted speech F̂ t

is obtained by multiplying F tparameters of the DNNs and the lifter are jointly trained to minimize
the same loss function as Eq. (1). Since all processes of this method
are differentiable, the training can be done by back-propagation [16].
3.2. Conversion process
In the conversion process, the trained DNNs and lifter estimate
(D)
(D)
(D)
(l)
F t . f t is obtained by applying the IDFT to F t , and f t is
obtained by truncating with l. We can obtain the converted speech(l)waveform by applying f t to the source speech waveform.
3.3. Sub-band processing for full-band VC
We now describe our sub-band processing method for full-band
extension of the conventional method. When the bandwidth ofspectral-differential VC is extended to 48 kHz, conversion cannot
be performed well due to the large fluctuations in the wider-band
components. To avoid errors in the high-frequency components,
our method involves sub-band processing for filtering separately foreach frequency band. We apply the differential filter in a frequency
region lower than 8 kHz, and do not apply it to a frequency region
higher than 8 kHz. In practice, conversion of only the low-frequency
band is possible by 1) subtracting 1.0 from the absolute value of(D)
F t , 2) applying the sigmoid function that transitions 1 to 0 at
around 8 kHz, and 3) adding 1.0 again.

3.1. Lifter training with filter truncation
Our lifter-training method trains not only DNNs but also a lifter toavoid converted-speech quality degradation caused by filter truncation. Let u = [u1 , ..., uc ]> be a time-independent trainable lifter,

3.4. Discussion
With the conventional method, the cepstrum is multiplied by thelifter coefficient to determine the shape of the filter so that the phaseCum ulat ive power

1.0

4. EXPERIMENTAL EVALUATIONS

0.8

4.1. experimental condition

0.6
0.4
Convent ional
Proposed

0.2
0.0

0

20

40
60
Tap lengt h

80

100

Coefficient difference (x 0.01)

Fig. 3. Cumulative power distributions of the differential filter
0.0
− 0.2
− 0.4
− 0.6

Convent ional
Proposed

− 0.8
0

5

10
15
20
25
30
Real-cepst rum index

3540

Fig. 4. Difference between lifter trained with the proposed liftertrained method (l = 64) and that for minimum phasing
is minimized. Although the shape of the differential filter changes
due to truncation, it is transformed to compensate for the effect of thetruncation by applying the Hilbert transform using the lifter trainedwith the proposed lifter-training method. As a result, our liftertraining method can reduce the calculation amount while suppressing converted-speech quality degradation caused by the filter truncation. Figure 3 shows the cumulative power distribution of the differential filter with the conventional method (l = 512) and proposed
lifter-training method (l = 32). The values on the vertical axis arenormalized with the cumulative total. The power is concentrated in
the region of tap length 0 to 100. Figure 4 also shows the difference
between the lifter trained with the proposed method (l = 64) andthat for minimum phasing.
As explained in Section 1, liftering-based phase estimation requires only small computation. Since our lifter-training method
adopts the same estimation as the conventional method, there is no
increase in computational cost of phase estimation.
We applied our lifter-training method to VC, i.e., speaker conversion. We expect that this method can be applied to other tasks
processed by filtering, e.g., source separation and speech enhancement.
We also discuss our sub-band processing method. Since thecharacteristics of a speech waveform vary significantly from bandto band, it is effective to process the waveform separately for eachband. In sub-band WaveNet [17], the speech waveform is divided
into several bands and down-sampled, and the waveform in eachband is processed separately. In our proposed sub-band processing method using full-band speech, the waveform of each frequency
band is not down-sampled. In implementing real-time conversion,
the computational cost of filtering can be reduced to 1/3 by dividing the frequency domain into three bands and down-sampling the
waveform of each band.

We built two intra-gender VC: for female-to-female (f2f) and maleto-male (m2m) conversion. The source and target speakers infemale-to-female conversion were stored in the JSUT corpus [18]and Voice Actress Corpus [19], respectively. Those in male-to-maleconversion were stored in the JVS corpus [20]. We used 100 utterances (approx. 12 min.) of each speaker, and the numbers ofutterances for training, validation, and test data were 80, 10, 10,
respectively.
We used narrow-band speech (16 kHz) and full-band speech(48 kHz) for the evaluation. In the narrow-band case, the window
length was 25 ms, frame shift was 5 ms, the fast Fourier transform (FFT) length was 512 samples, and number of dimensionsof the cepstrum was 40 (0th-through-39th). In the full-band case,the window length and frame shift were the same as those in the
narrow-band case, but the FFT length was 2048 samples, and number of dimensions of the cepstrum was 120 (0th-through-119th). For
pre-processing, the silent intervals of training and validation data
were removed, and the lengths of the source and target speech werealigned by dynamic time warping.
The DNN architecture of the acoustic model was multi-layer
perceptron consisting of two hidden layers. The numbers of eachhidden unit were 280 and 100 in the narrow-band case, and 840 and
300 in the full-band case. The DNNs consisted of a gated linear
unit [21] including the sigmoid activation layer and tanh activation
layer, and batch normalization [22] was carried out before applying each activation function. Adam [23] was used as the optimization method. During training, the cepstrum of the source and target
speech was normalized to have zero mean and unit variance. The
batch size and number of epochs were set to 1,000 and 100, respectively. The model parameters of the DNNs used with the proposed
lifter-training method were initialized with the conventional method.
The initial value of the lifter coefficient was set to that of the lifter
for minimum phasing. In the narrow-band case, the learning rates
for the conventional and proposed lifter-training methods were set to
0.0005 and 0.00001, respectively. In the full-band case, the learning
rates for the conventional and proposed lifter-training methods were
set to 0.0001 and 0.000005, respectively.
The proposed lifter-training method was evaluated using bothnarrow-band (16 kHz) and full-band (48 kHz) speech. The truncatedtap length l for the narrow-band case was 128, 64, 48, and 32, andthat for the full-band case was 224 and 192. On the other hand, theproposed sub-band processing method was evaluated using only thefull-band speech.

4.2. Objective evaluation
We compared root mean squared error (RMSE) with the proposed
lifter-training and conventional methods when changing l. The
RMSE is obtained by taking the squared root of Eq. (1). Figure 5
shows a plot of the RMSEs in male-to-male and female-to-female
VC using narrow-band speech (16 kHz). The proposed lifter-training
method achieved higher-precision conversion than the conventional
method for all l. The differences in the RMSEs between the proposed and conventional methods also tended to become more significant when l is smaller. This result indicates that the proposed
lifter-training method can reduce the effect of filter truncation.

RMSE

1.20
1.15
1.10
1.05
1.00
0.95
0.90
20

Conventional (f2f)
Proposed (f2f)
Conventional (m2m)
Proposed (m2m)40

60
80 100
truncated tap length l

Table 2. Preference scores with proposed lifter-training and conventional methods in full-band case (48 kHz)(a) Speaker similarity
Proposedl = 192 (m2m)
l = 192 (f2f)l = 224 (m2m)l = 224 (f2f)

Score
0.431 vs. 0.569
0.519 vs. 0.481
0.474 vs. 0.526
0.519 vs. 0.481

Proposedl = 192 (m2m)
l = 192 (f2f)l = 224 (m2m)l = 224 (f2f)

Score
0.529 vs. 0.471
0.447 vs. 0.553
0.513 vs. 0.487
0.517 vs. 0.483

120

Fig. 5. RMSEs at each l in narrow-band case (16 kHz)
Table 1. Preference scores with proposed lifter-training and conventional methods in narrow-band case (16 kHz)p-value
4.9 × 10−4
3.4 × 10−1
2.0 × 10−1
3.4 × 10−1

Conventionall = 2048 (m2m)l = 2048 (f2f)l = 2048 (m2m)l = 2048 (f2f)(b) Speech quality
p-value
2.3 × 10−1
8.9 × 10−3
5.2 × 10−1
4.2 × 10−1

Conventionall = 2048 (m2m)l = 2048 (f2f)l = 2048 (m2m)l = 2048 (f2f)(a) Speaker similarity
Proposedl = 32 (m2m)l = 32 (m2m)l = 32 (f2f)l = 32 (f2f)
l = 48 (m2m)
l = 48 (m2m)
l = 48 (f2f)
l = 48 (f2f)

Score
0.587 vs. 0.413
0.463 vs. 0.537
0.642 vs. 0.358
0.543 vs. 0.457
0.533 vs. 0.467
0.550 vs. 0.450
0.613 vs. 0.387
0.548 vs. 0.452

p-value
1.3 × 10−5
7.3 × 10−2
< 10−10
3.4 × 10−2
1.0 × 10−1
1.4 × 10−2
1.3 × 10−8
2.0 × 10−2

Conventionall = 32 (m2m)
l = 512 (m2m)l = 32 (f2f)l = 512 (f2f)
l = 48 (m2m)
l = 512 (m2m)
l = 48 (f2f)l = 512 (f2f)(b) Speech quality
Proposedl = 32 (m2m)l = 32 (m2m)l = 32 (f2f)l = 32 (f2f)
l = 48 (m2m)
l = 48 (m2m)
l = 48 (f2f)
l = 48 (f2f)

Score
0.687 vs. 0.313
0.529 vs. 0.471
0.807 vs. 0.193
0.742 vs. 0.258
0.606 vs. 0.394
0.523 vs. 0.477
0.581 vs. 0.419
0.513 vs. 0.487

p-value< 10−10
2.3 × 10−1
< 10−10< 10−10
8.7 × 10−8
2.6 × 10−1
5.5 × 10−5
5.1 × 10−1

Conventionall = 32 (m2m)
l = 512 (m2m)l = 32 (f2f)l = 512 (f2f)
l = 48 (m2m)
l = 512 (m2m)
l = 48 (f2f)l = 512 (f2f)

Table 3. Preference scores with proposed sub-band processing andconventional methods in full-band case (48 kHz)(a) Speaker similarity
Proposed (sub-band)
Score
p-value
Conventional
m2m
0.519 vs. 0.481 3.4 × 10−1
m2m
f2f
0.603 vs. 0.397 5.0 × 10−7f2f(b) Speech quality
Proposed (sub-band)
Score
p-value
Conventional
m2m
0.721 vs. 0.279 < 10−10m2m
f2f
0.700 vs. 0.300 < 10−10
f2f

but the proposed lifter-training method with l = 192 degradedspeaker similarity and speech quality. Therefore, the proposed
lifter-training method can significantly reduce the tap length in the
full-band case, though not as much as the narrow-band case.
4.3.2. The evaluation of sub-band processing

4.3. Subjective evaluations
4.3.1. The evaluation of lifter training
To investigate the effectiveness of the proposed methods, we conducted a series of preference AB tests on speech quality and XAB
tests on speaker similarity of converted speech. Thirty listeners participated in each of the evaluations through our crowd-sourced evaluation systems, and each listener evaluated ten speech samples. The
target speaker’s natural speech was used as the reference X in thepreference XAB tests.
We compared several settings of the conventional and proposed
lifter-training methods. Table 1 lists the results for the narrow-band(16 kHz) case. Compared to the truncated conventional method(“Conventional (l = 32, 48)”), we can see that the proposed liftertraining method significantly outperformed the conventional one interms of speaker similarity and speech quality. Also, compared to
the non-truncated conventional method (“Conventional (l = 512)”),the proposed lifter-training method (“Proposed (l = 32, 48)”) had
the same or higher quality. These results indicate that the proposed
lifter-training method can reduce the tap length to 1/16 without
degrading converted-speech quality whereas the truncated conventional method significantly degrades converted-speech quality. The
same tendency can be seen in the full-band (48 kHz) case, as shownin Table 2. The proposed method with l = 224 had the same
converted-speech quality as the non-truncated conventional method,

We also compared our proposed sub-band-processing method withthe conventional method. The AB tests on speech quality and XAB
tests on speaker similarity were conducted in the same manneras those mentioned in Section 4.3.1. Table 4.2 lists the results.
Note that, lifter training and filter truncation were not used forboth conventional and proposed methods. The proposed sub-bandprocessing method achieved a higher score than the conventional
method excluding the speaker similarity of the male-to-male VC,
demonstrating the effectiveness of this method.
5. CONCLUSION
We presented a lifter-training and sub-band-processing methods forcomputationally efficient and high-quality voice conversion based on
spectral differentials. The lifter was trained considering filter truncation. The sub-band-processing method efficiently converted thelower frequency band of a full-band voice. The experimental results
indicate the superiority of our methods in terms of computational
efficiency, converted-speech quality compared to the conventional
method. For future work, we will implement real-time VC using the
proposed methods and evaluate its effectiveness in converted-speech
quality and latency.
Acknowledgements: Part of this work was supported by the
MIC/SCOPE #182103104.

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