Study on the Reproducton of Vocal Fluctuations using Box-Mullermethod for Artificial Synthesis
Tomohisa OKAWA1 , Takaaki KONDO1 , Shun KADOI1 , Kyouhei KAMIYAMA1 , and Hiroyuki KAMATA211Graduate School of Science and Technology, Meiji University, Japan2
School of Science and Technology, Meiji University, Japan

Introduction

The human voice contains the ﬂuctuations of fundamental frequency and human speech waveform. According toa study, these ﬂuctuations are producing the naturalnessof human voice.[1] Today, text-to-speech synthesis has become mainstream in speech synthesis. This technology,
however, requires a large amount of data to make highquality speech synthesis. For this reason, it is impossible to create a synthesized voice of many people. In thisstudy, we aim to create a synthesized speech by focusing
on ﬂuctuation of the vocal cords. By using the Box-Mullermethod, we try to reproduce the ﬂuctuations of the vocalcords. In the Box-Muller method, the average and variancevalues of the Gaussian function is used. In this paper, weextract the fundamental frequency and frequency variancevalue from the human voice. We expect that this result
will be an indicator of reproduction of vocal ﬂuctuations
by the Box-Muller method.

2

Fluctuation of vocal cords

At ﬁrst sight, the human speech waveform seems to bea series of similar shape. However, this form is changing
slightly for each shape. Cycle width is also changing aswell. The diﬀerence in width of the period is called theﬂuctuation of the vocal cords.[2]3Derivation of the fluctuation of the vocal cords

In this chapter, we describe the method of reproducing the ﬂuctuation of vocal cords. In this study, we try
to reproduce the ﬂuctuation of vocal cords by using theBox-Mueller method. This method uses the statistical
distribution of the ﬂuctuation of vocal cords of humanvoice. Therefore, we calculate the fundamental frequency
and variance value in order to the statistical distribution.
Fundamental frequency f is calculate from the average frequency of the waveform of period 300, the variance value
σ 2 is calculated by the following equation.
1∑(fi − f )2nnσ2 =(1)i=1Here, fi is the frequency of each cycle. Using this result,
we generate a random number according to the normal distribution created by Box-Muller method. How to generaterandom numbers Z1 ,Z2 by Box-Mueller method is shownbelow.
√Z1 = σ −2 × ln x cos(2πy)√Z2 = σ −2 × ln x sin(2πy)

(2)
(3)

Here, x and y are mutually independent random variables, which are subject to the uniform distribution on(0,1).
4Result

We show the result of relationship between the fundamental frequency and variance value from a human voice.
According to Fig. 2, the variance value is somewhat highwhen the fundamental frequency is low. and the variance value become lower with increasing fundamental frequency. Considering the relationship between fundamental
frequency and variance value, we made a synthesis of theﬂuctuation of vocal cords by using the Box-Muller method.

Fig. 1. The vocal ﬂuctuations

References[1] Naohumi AOKI, Tohru IFUKUBE, Frequency Characteristics of Amplitude and Period Fluctuations in SustainedVowels and Their Psychoacoustic Eﬀects, IEICE A, 82,649–657, 1999
[2] Yuuki
NANIWA,Takaaki
KONDO,
Kyouhei
KAMIYAMA, Hiroyuki KAMATA, Study on theArtiﬁcial Synthesis of Human Voice using Radial Basis
Function Networks, IEICE technical report NC, 110,199–204, 2011

Fig. 2. Relationship between the fundamental frequency
and variance value

Next, we show the result of the synthesis of the ﬂuctuation of vocal cords by using Box-Muller method.

Fig. 3. The synthesized ﬂuctuations(fundamental frequency =108[Hz], variance value = 2,71[Hz])5Conclusion

In this study, in order to reconstruct the speech synthesis with highly naturalness, we focused on the ﬂuctuationsof vocal cords in a real voice signal /a/. In this result using
the Box-Muller method, some diﬀerent were observed between the reproduced frequency and the frequency of thereal voice. Major diﬀerence is that real voice has small ﬂuctuations in adjacent frequency, however the ﬂuctuations of
the reproduced frequency sometimes becomes large. By
this result, in order to reproduce the frequency of the ﬂuctuations of vocal cords, it is necessary to consider the frequency of the previous cycle, not only to generate a normal
random.
In future, we plan to a comparison of real speech andsynthetic speech with this result.