Physica A 442 (2016) 343–349
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Physica A
journal homepage: www.elsevier.com/locate/physa
Analysis of speech signals’ characteristics based on MF-DFA
with moving overlapping windows
Huan Zhao
a
, Shaofang He
a,b,∗
a
School of Information Science and Engineering, Hunan University, Changsha, 410082, China
b
College of Science, Hunan Agricultural University, Changsha, 410128, China
h i g h l i g h t s
• Analysis of speech signals’ characteristics based on MF-DFA is given.
• Using a window-shift parameter, MF-DFA with moving overlapping windows is proposed.
• The characteristics based on AMF-DFA outperform MF-DFA and MF-DMA.
a r t i c l e i n f o
Article history:
Received 8 April 2015
Received in revised form 4 September 2015
Available online 25 September 2015
Keywords:
MF-DFA
Speech signals
Multi-fractal characteristics
a b s t r a c t
In this paper, multi-fractal characteristics of speech signals are analyzed based on MF-DFA,
and it is found that the multi-fractal features are influenced greatly by frame length and
noise, besides, there is a little difference between them among speech frames. Secondly,
motivated by framing and using frame shift to ensure the continuity and smooth transition
of speech in speech signals processing, an advanced MF-DFA (MF-DFA with forward mov-
ing overlapping windows) is proposed. The length of moving overlapping windows is deter-
mined by parameter θ . Given the value of time scale s, we have MF-DFA with the maximum
moving overlapping windows and MF-DFA with half overlapping windows when θ = 1/s
and θ = 1/2 respectively. Moreover, when θ = 1 we exactly have MF-DFA. Numerical ex-
periments and analysis illustrate that the multi-fractal characteristics based on AMF-DFA
outperform MF-DFA and MF-DMA in stability, noise immunity and discrimination.
© 2015 Elsevier B.V. All rights reserved.
1. Introduction
Speech is composed of chaotic natural phonemes, which signals waveform is extremely complex and irregular, and
cannot be described accurately by traditional geometric language. Yet many details of waveform have self-similarity, and
fractal may be good for modeling chaotic natural phonemes [1]. As a reflection of ‘geometric’ feature information of speech
signals, fractal is a measure of strong degree and irregularity of different speaker’s voice signals, and has been currently
applied in speaker recognition as a characteristic component of speech signals, which has got a certain achievements.
However, single fractal dimension is just a scaling exponent, and it only describes signal quantitatively from the perspective
of the overall or average, but did not consider the fluctuation of different levels. It needs two or more target speech signals’
fractal dimensions to describe the internal characteristics fully and completely, which leads to the generation of multi-
fractal method for studying speech signals. The multi-fractal-based method was used to characterize the consonants [2].
∗
Corresponding author at: College of Science, Hunan Agricultural University, Changsha, 410128, China. Tel.: +86 073184618071.
E-mail address: wxdyzp@sina.com (S. He).
http://dx.doi.org/10.1016/j.physa.2015.09.033
0378-4371/© 2015 Elsevier B.V. All rights reserved.