A Combined Voice Activity Detector Based On Singular Value Decomposition and Fourier Transform

A. Afzalian, M. R. Karami mollaei & J. Ghasemi
Signal Processing: An International Journal (SPIJ), Volume(4): Issue(1) 54
A Combined Voice Activity Detector Based On Singular Value
Decomposition and Fourier Transform
Amard Afzalian a.afzalian@gmail.com
Islamic Azad University, Science
and Research,Tehran, IRAN.
Mohammad Reze Karami Mollaei mkarami@nit.ac.ir
Faculty of Electrical and Computer Engineering,
Babol Noshirvani University of Technology
Babol, P.O. Box 47135-484, IRAN
Jamal Ghasemi jghasemi@stu.nit.ac.ir
Faculty of Electrical and Computer Engineering,
Signal Processing Laboratory
Babol Noshirvani University of Technology,
Babol, P.O. Box 47135-484, IRAN
Abstract
Voice activity detector (VAD) is used to separate the speech data included parts
from silence parts of the signal. In this paper a new VAD algorithm is represented
on the basis of singular value decomposition. There are two sections to perform
the feature vector extraction. In first section voiced frames are separated from
unvoiced and silence frames. In second section unvoiced frames are silence
frames. To perform the above sections, first, windowing the noisy signal then
Hankel’s matrix is formed for each frame. The basis of statistical feature
extraction of purposed system is slope of singular value curve related to each
frame by using linear regression. It is shown that the slope of singular values
curve per different SNRs in voiced frames is more than the other types and this
property can be to achieve the goal the first part can be used. High similarity
between feature vector of unvoiced and silence frame caused to approach for
separation of the two categories above cannot be used. So in the second part,
the frequency characteristics for identification of unvoiced frames from silent
frames have been used. Simulation results show that high speed and accuracy
are the advantages of the proposed system.
Keywords: Speech, Voice Activity Detector, Singular Value.
1. INTRODUCTION
Voice activity detection is an important step in some speech processing systems, such as speech
recognition, speech enhancement, noise estimation, speech compression ... etc. In speech
recognition when a word or utterance begins or ends (the end points) must be specified [1]. Also
VAD is used to disable speech recognition for silence segments. Some speech transition systems
transmits active segments in high rate of bits and transmits silence in low rate of bits, by this
method they improve the band-width [2]. In some speech enhancement algorithm for example

spectral subtraction method, a VAD method is required to know when to update the noise
reference [3,20,21]. Conversational speech is a sequence of consecutive segments of silence
and speech. In noisy signal silence regions are noisy. Voice sound contain more energy than
unvoiced sound, while unvoiced sounds are more noise-like, so in noisy condition activity
detection is harder In unvoiced regions. Feature extraction is the most important section in VAD
system that elicits required parameters from desired frame. To achieve an accurate algorithm, the
system parameters must be selected until by them can be able to separate from each other
areas. After proper feature election, threshold is applied to the extracted parameters and the
decisions are made. To achieving good detection level threshold can be adapted to the change of
the noise conditions. Many of the algorithms assume that the first frames are silence [5, 6, and 7],
so we can initialize noise reference from these frames. Common features used in VAD's are short
term Fourier transform and zero crossing rate [4, 6, 11, and 12]. Another important and widely
used parameter in this regard is Cepstral Coefficient [7, 9]. In this method the Cepstral
coefficients are calculated within frames and then by calculating the difference between this
vector and the value assigned to the noise signal and then comparing the result with the basic
threshold value, the frame identity could be determined. LPC method is also another major
applicable method for VAD implementation [13]. Generally in LPC based algorithms a series of
mean coefficients are experimentally considered for voice, unvoiced and silent modes. In the next
step the LPC coefficients of suspicious frame and their relative difference with mean indices are
calculated and the frame identity is recognized based on these values. The other parameters for
implementing VAD in combined algorithms are LTSE (long term Spectral Estimation)[5], wavelet
coefficient [8,10], the ratio of signal to noise in sub-band [14], LSPE(Least Square Periodicity
Estimator)[11] and AMDF(Average Magnitude Difference Function)[15]. One of most important
cases in VAD system is speed of system performance beside proper accuracy. In this paper is to
present a new algorithm of VAD based on single value decomposition and frequency features,
specifications accuracy and speed simultaneously be fulfilled. Based on this, paper organization
as follows that in Section 2 single values decomposition (SVD) will be explained. In Section 3 the
proposed method with the system block diagram is given. In Section 4 simulation results in terms
of quantitative and qualitative criteria is evaluated. Finally, the article concludes with Section 5
ends.
2. Singular Value Decomposition
The singular value composition is one of the main tools in digital signal processing and statistical
data. By doing SVD on a matrix with dimensions of M×N, we have:
(1)T
X U V= Σ
On above relation U and V matrixes are singular vectors matrix with dimensions of M×M and
N×N, respectively. Also, ∑ with r order of a diagonal matrix M×N is included singular values so
that components on the main dial gauge are not zero and other components are zero. The
elements on main dial gauge areas 11 22 ... 0rrσ σ σ> > > > And are the values of X matrix. For
exercising SVD to one dimensional matrix, the vector of signal samples must map to subspace
with more dimensions, on the other hand must be changed to a matrix in certain way. Different
ways have indicated for one dimensional signal transformation to a matrix that in this article
(here) have used Hankel’s way [16,19].
3. Purposed algorithm
The main question on sound discovery is the classification of listening signal characteristic to
diagnosis sound parts. Thus, listening signal are classified to sound classes: silence, voiced, and
unvoiced. For classifying, suitable characteristics must elicit from the speech signal parts (frame).
Before studying the details of purposed system, general block diagram are showed in figure 1.

One Frame of Noisy signal
Windowing
SVD
VAD Output
VAD Decision
FFT & Gaussian
Approximation
Feature Extraction BlockInput Signal
Figure (1) block diagram of propositional method for indicator system of voice activity.
As shown on figure 1, feature vector extraction done in two parts. In first part, voiced frames are
separated from unvoiced and silence frame as for statistical characteristics of singular values
matrix. In second part, unvoiced frames are separated from silence frames that this separation is
based on its frequency spectrum and Gaussian rate in each frame. At the end, one value accrues
to voiced and unvoiced frames that including voice information, and zeros one to silence frames.
3.1. Voiced frames separation from the other parts
In suggested system to separate the voiced parts from two parts of unvoiced and silence ones, it
is used on slop of singular value curve in related part. For doing atop stages, first noisy signal
divide to 16ms frames. According to relation (2), Hankel matrix makes for every frame.
(2)
0 1 1
1 2
0 1 1
1 1
...
...
[ , ,..., ]
...
M
M
k n k
L L N
x x x
x x x
X x x x H
x x x
−
−
− −
 
 
 = → =
 
 
 
M M M M
Where kX is the vector of exist samples in K frame in input signal and kH is the isomorphic
Hankel matrix of L×M dimensions with kX . The percent of sample overlapping in matrix and the
conditions of kH dimensions are brought on (3) and (4) relations.
(3)1
% 100
L
overlapping
L
−
= ×
(4)1,M L N L M+ = + ≥
For gaining full primitive pattern of kX frame, the number of added zeros must lessen in M
column of kH matrix that its results have brought on (5) relation.
(5)- mod( , ) [ ] 1, -[ ]
2 2
N N
ZeroPadding L N L L M N= ⇒ = + =
Gained values of L, M in (5) relation get kH semi rectangular matrix with maximum sample
overlapping. The singular values of each frame are got by Hankel matrix of existed frame and
using SVD map on related singular values.
(6)T
k k k kH U V= ∑
In (6) relation kU and kV the singular vectors of diagonal matrix and also k∑ are isomorphic
singular values matrix with kH (part 2). Figure (2), singular values vectors show the every voiced
frames in 16 millisecond length and SNR=10db with white Gaussian noise.

0 20 40 60 80 100 120 140
0
2
4
6
8
10
12
Singular Values of Voice Frame
0 20 40 60 80 100 120 140
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Singular Values of Unvoice Frame
0 20 40 60 80 100 120 140
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Singular Values of Silence Frame
Figure (2) singular values vectors of voiced, unvoiced
and silence frame in SNR=10db (voice signal from
housewives_16.wav on TIMIT database)
According as seeing on figure (2) the slop of curve in singular values between voiced frames are
different from the other parts. In fact, singular values of voiced frames have more slop than
singular values of unvoiced and silence frames. The base of statistical feature extraction for
separating voiced frames is the slop of singular values curve related to each frame by using linear
regression. Table 1 shows the values of this slop in different SNRs on three certain frames that
have chosen from voiced, unvoiced and silence parts.
Table (1):
slope of singular values curve in linear regression related to species of frame on different SNRs
(voice signal from housewives_16.wav on TIMIT database)
Mean amount of singular values curve slope on 10 times repeat for each SNR
Silence frameUnvoiced
frame
Voiced
frame
SNR
0.09490.09870.14980db
0.05280.05660.12325db
0.03050.03380.117010db
0.01760.02320.114315db
0.00980.01750.113920db
Results of table (1) are support on this thesis that the slop of singular values curve on different
SNRs in voiced frames are more than the others and by using this trait we can achieve the goal
of first section that was the feature vector extraction in voiced frames from related singular values
matrix.

2.3. Separating the voiced and silence frames
By studying figure (2) and table (1) are deduced that according to approximation through slop of
singular values curves related to voiced and silence frames, it can't divide these two type frames
from each other. Because of this in purposed system have used the other trait to separate these
two parts. In this part, frequency trait has used for recognition unvoiced frames from silence ones.
The base of comparison is the curve of Gaussian function, (7) relation.
(7)
2
2
( )
2
( ; , )
x c
f x c e γ
γ
− −
=
Atop relation C is mean and γ is variance of curve. By doing study, we see the discrete Fourier
transform of unvoiced frames in meddle frequency are similar to the curve of Gaussian functions
to some extent. Figure (3) and (4) show the smooth frequency spectrum related to unvoiced and
silence frames and their comparison with the curve of Gaussian function. (Voice signal from
TIMIT database with SNR=15db)
0 20 40 60 80 100 120
0
1
2
3
4
5
6
x 10
-3 Unvoice Frame in FFT Domain & Gaussian function
Figure (3) frequency spectrum of Unvoice frame in
SNR=15db and the curve of Gaussian function ( 0.6γ = )
0 20 40 60 80 100 120 140
0
1
2
3
4
5
6
x 10
-3 Silence Frame in FFT Domain & Gaussian function
Figure (4) frequency spectrum of Silence frame in
SNR=15db and the curve of Gaussian function ( 0.6γ = )
According as atop figures are seen, frequency spectrum of voiced frame is more similar to
Gaussian curve than silence frame noise in meddle frequency. Also by different examinations, the
optimal values of γ parameter in varying SNRs are as 0.2 with a view of minimizing the
difference between Gaussian pattern and frequency spectrum of silence frame pattern.
4. SIMULATION RESULTS
In this section, the operation of purposed system study and compare considered as accuracy and
speed. Sx114.wav voice signal from TIMIT database including 166 of 16 millisecond frames with
sampling rate is 16 kHz that each frame has 256 samples. Figure (5) shows the noisy signal with
SNR=10db and the indicator systems output of voice activity.

(a)
(b)
(c)
0 0.5 1 1.5 2 2.5 3 3.5 4
x 10
4
-0.1
0
0.1
time
Amplitude
original signal
0 20 40 60 80 100 120 140 160
-1
0
1
2
Output Of Ideal VAD
0 20 40 60 80 100 120 140 160
-1
0
1
2
Output Of VAD Based on Wavelet
0 20 40 60 80 100 120 140 160
-1
0
1
2
Output Of Perposed VAD
(d)
Figure(5).Simulation Results: (a)TIMIT Signal, (b) Output of ideal VAD, (c) Output of VAD
based on Wavelet, (d) Output of Purposed VAD
According as seeing, suggested method has more efficiency to keep the parts of signals that the
activity signal is weak. In figure (5) and dashed line-drawn area, one unvoiced letter has omitted
in VAD system as wavelet (figure 5-c ) that it has kept on VAD output propositional system (figure
5-d ). In table (2) the accuracy rate of VAD propositional system is shown as wavelet transform
[17] about voice signal sx114.wav for different SNRs.
Table (2): percent of VAD system error comparison by using purposed algorithm and wavelet based
algorithm in different SNRs
Wavelet based algorithm
Purposed
algorithm
SNR
36%25%0db
20%18%5db
14%15%10db
12%13%15db
10%8%20db
One of the strength points of the purposed algorithm is its speed. In table (3), speed of two
algorithms has compared with each other in processing the sx114.wav sound file (CPU Intel
Core2Duo 2.5 GHz, 4 M Cache 733 MB RAM)
Table (3):
Speed comparison of VAD system by using purposed algorithm and wavelet based algorithm
Consumed time in wavelet based algorithmConsumed time in purposed algorithm
12 second4 second
In this part by using two VAD systems as preprocessing block has brought the results of hearing
test for a speech signal rich-making system that accuracy of VAD operation system be proved in
keeping unvoiced areas. In table 4 the standards has come that is used in evaluation of speech
with hearing factor.

Table (4)
Five-Point adjectival scales for quality and impairment, and associated scores
ImpairmentScore
Imperceptible5 (Excellent)
(Just) Perceptible but not Annoying4 (Good)
(Perceptible and) Slightly Annoying3 (Fair)
Annoying (but not Objectionable)2 (Poor)
Very Annoying (Objectionable)1 (Bad)
In table 5, results of using two said VAD algorithms have shown as preprocessing block for
enhancement method of multi band spectral subtraction. Specifications of this test are in [3].
Table (5)
Results of MOS test;
17 clean speech signal from TIMIT database; Noise Type: White Gaussian Noise.
Input SNR
10db5db0db
Used Algorithm
2.82.31.6Wavelet Based
3.32.71.8Purposed
Studying the results of table (5) are shown the reform efficiency of speech enhancement by using
of propositional VAD algorithm to wavelet transform way.
5. CONCLUSION
In this paper a new method for Voice activity detector based on Singular Value Decomposition
and discrete Fourier transform was proposed. The proposed method is evaluated by using
various criteria. By using the mentioned criteria, it is presented that this method can compete with
other methods. Also, the aim of indicator systems of voice activity is control of destruction
unvoiced signal sites in rich-making operation that observantly to results of hearing test, the
propositional algorithm have proper power in compare with wavelet transform way. The
propositional system has manifold speed than usual method that is one of the obvious characters
in practical usage and hardware implementation.
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