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https://dspace.jaist.ac.jp/Title

Investigation of a Method of Speech Signal
Analysis Using Empirical Mode Decomposition andIts Applications

Author(s)Sawaguchi, Tomoki; Unoki, Masashi

Citation

Journal of Signal Processing, 14(4): 273‑276

Issue Date

2010‑07

Type

Journal Article

Text version

author

URL

http://hdl.handle.net/10119/9509

RightsCopyright (C) 2010 Research Institute of Signal
Processing Japan. Tomoki Sawaguchi and Masashi
Unoki, Journal of Signal Processing, 14(4), 2010,273‑276.

Description

Japan Advanced Institute of Science and Technology

Investigation of a Method of Speech Signal Analysis Using Empirical Mode Decompositionand Its Applications
Tomoki Sawaguchi and Masashi Unoki
School of Information Science, Japan Advanced Institute of Science and Technology
1-1 Asahidai, Nomi, Ishikawa 923–1292 Japan
Phone/FAX:+81-761-51-1391/+81-761-51-1149
E-mail: {tomoki-s, unoki}@jaist.ac.jp

Abstract
In recent years, a number of noise reduction methods basedon empirical mode decomposition (EMD) have been proposed in the field of speech signal processing. However, thesemethods cannot effectively reduce noise components fromnoisy speech they lack useful prior knowledge related to thenoise characteristics. Moreover, because they reduce only thehigher frequency components of noise, the overall effect onnoise reduction seems to be insufficient. Our aim was to develope a speech signal analysis method that can adequately
analyze non-stationary speech signals in time-frequency domains. We investigated the properties of an analysis method
for non-stationary signals based on EMD and the characteristics of AM-FM representations in the intrinsic mode function(IMF) and have subsequently developed a method of noise
reduction based on our investigations. Simulations were conducted to determine whether or not the proposed method caneffectively reduce noise components from noisy speech. Results demonstrate that it can do so adequately.

speech representation based on EMD seems to be moresuitable that conventional methods in terms of representing
speech features such as non-stationary fluctuations. However, it is unclear how or if noisy speech can be represented
as suitable forms (separately speech and noise), and it is also
unclear whether these speech and noise components can becompletely separated in the representations. Because thesepreviously proposed methods [2, 3] use particular IMFs corresponding to noise components in speech in which the noise
is to be reduced, they can remove IMFs of non-stationary
speech by reducing the noise components on these representations.
We investigated the properties of the analysis method fornon-stationary signals using EMD and the characteristics ofthe decomposed intrinsic mode function (IMF). We then examined the possibility of using EMD to reduce the noise innoisy speech signals.
2. Empirical Mode Decomposition (EMD)
2.1. Signal representation using EMD

1. Introduction
Currently, the Fourier transform and the wavelet transform
are the standard techniques used to analyze signals in timefrequency analysis. These methods can analyze the temporal spectral fluctuations of the signal in the time-frequency
domains, but only if the analytical signal is assumed tobe stationary. Realistic signals (i.e., electroencephalogram(EEG) signals, seismic waves, speech signals, etc.) are nonstationary signals so these methods cannot precisely analyze
the non-stationary fluctuations of the instantaneous amplitude
and the instantaneous phase of the signal.
In recent years, the empirical mode decomposition (EMD)
technique [1], originally proposed by Huang et al., has beenused for analyzing non-stationary signals. This technique cananalyze EEG signals and explore the source of seismic waves,and it is currently being applied to speech signal processing.
In particular, EMD-based noise reduction methods have been
proposed to reduce musical noise [2] from restored speech
and to classify robust voiced/unvoiced signals in noisy environments [3].
Because speech signals are generally non-stationary,

EMD decomposes signal x(t) into IMFs, c k (t), and negligible residue r(t). x(t) is represented as follows.
x(t) =K

ck (t) + r(t)

(1)

k=1

where k represents the channel number and K represents thenumber of IMFs. Here, the IMF must satisfy two conditions:(1) in the entire data set, the number of extrema and the number of zero crossings must either equal or differ at most byone, and (2) at any point, the mean value of the envelope defined by the local maxima and the envelope defined by thelocal minima is zero. K depends on the characteristics of theanalytical signal so all signals may not have the same K.
Figure 1 shows the problem analysis diagram (PAD) of
the EMD algorithm. In this algorithm, upper envelope u(t)and lower envelope l(t) are obtained from local maxima andlocal minima, respectively, by using cubic spline interpolation. Next, the mean value between u(t) and l(t) is subtracted
from the original signal while mean value is not zero. Finally,while the IMF satisfies the two constraints, the original signal

c1 (t)10c2 (t)-1
10c3 (t)-1
10Figure 1: PAD of the empirical mode decompositionc4 (t)-11

10-1

00.2x(t)

0.5
00.8

1

Figure 3: Decomposition of y(t) (IMFs, c k (t))
1x̂(t)-1
10.5n(t)0.6Time [s]-0.500-1-0.51n̂(t)-1
10.5y(t)0.400-1-0.5-100.2

0.4

0.6

0.8

1Time [s]Figure 2: Mixed signal y(t) composed of non-stationary signal x(t) and stationary signal n(t)is decomposed into IMFs by repeating these subtractions, as
shown in Fig. 1.
2.2. Properties of EMD
In this section, we investigate the properties of EMD andthe characteristics of the decomposed IMFs. First, we study
how the IMFs are derived by the EMD algorithm. The meanvalue between the upper and lower envelopes is subtracted
from the signal to derive the first IMF. This step is repeated
while the mean value is not zero to derive the kth IMF. It canthus be understood that the decomposed IMFs are obtainedwith the intent of grouping them in a common envelope. In
this case, the IMF can be matched to slow or fast fluctuationsin the envelope.
Next, we investigate the characteristics of the decomposed
IMFs. The first constraint indicated that IMFs must be a signal that alternates the extreme value and zero crossing in turn.
This suggests that the IMFs are represented as an FM-signals
without any band-limitation because there is no limitationof the pair-frequency of the extreme value and zero crossing. The second constraint indicated that the IMFs must havethe same upper and lower envelopes. This suggests that theIMFs are common AM-signals. In summary, the decomposed

00.2

0.4

Time [s]0.60.8

1Figure 4: Resynthesized signals x̂(t) and n̂(t)IMFs can be regarded as AM-FM signals based on commonenvelope decomposition.
2.3. Example of signal analysis using the EMD
We examined an example of signal analysis using EMD forthe following mixture: y(t) is composed of non-stationary
signal x(t) and stationary signal n(t), as shown in Fig. 2.
The decomposed IMFs of y(t), c 1 (t), c2 (t), · · ·, and c4 (t),are shown in Fig. 3. Based on our investigations in Sec.
2.2, c1 (t) can be regarded as a stationary signal with a constant envelope while the other IMFs c 2 (t), c3 (t), and c4 (t)can be regarded as non-stationary signals. This means thatthe first IMF, c1 (t), seems to be n̂(t) and the summed IMF,c2 (t) + c3 (t) + c4 (t), seems to be x̂(t), as shown in Fig. 4.
This result demonstrates that the essence of signal analysisbased on EMD is to separate non-stationary signals from stationary signals during the signal representation procedure bya common-envelope-based decomposition.
3. EMD-Based Noise Reduction Method
We next consider the applicability of sound analysis basedon EMD. In the previous section, we showed that EMD caneasily separate stationary and non-stationary signals on thedecomposed IMFs. With this advantage, we consider a sepa-1Speech IMF
Noise IMF

0.9
0.8

Figure 5: Proposed method

Modulation Index

0.7
0.6
0.5
0.4
0.3
0.2
0.1005101520

Modulation frequency [Hz]Figure 7: Modulation index of speech and noise IMFs

ration of non-stationary speech signals and stationary white
noise as an application. An EMD-based noise reduction
method has already proposed by Molla & Hirose [3]. In thismethod, they focus on energy distribution of noise in the decomposed IMFs as prior knowledge to remove noise IMFs,
and they then mandatorily remove the first two IMFs (c 1 (t)and c2 (t)) to reduce the noise components. This method results in the reduction of only higher frequency components ofthe noise and therefore seems to be insufficient.
We propose another approach to noise reduction based on
EMD, as shown in Fig. 5. In our method, the channel selection of speech-IMFs and noise-IMFs, as shown in Fig. 6,
is combined with the conventional method to separate noise
IMFs from the decomposed IMFs. First, noisy speech y(t)is decomposed by EMD. Next, temporal envelope e k (t) isextracted from decomposed IMF c k (t), by the Hilbert transform and low-pass filtering where the cut-off frequency is 20
Hz because modulation index (MI) of lower than 20 Hz is important for speech perception. Next, a modulation filterbank(with a constant bandwidth filterbank) is used to analyze themodulation characteristics of the IMF’s temporal envelope
ek,m (t). The MI of decomposed IMF M k,m is determined
as10Improved SNR, I, [dB]

Figure 6: Channel selection of IMFs

0-10
Proposed
Molla & Hirose (2008)-20-505101520

SNR [dB]

Figure 8: Evaluation result: improved SNR [dB]between the modulation spectrum of speech and that of noise.
It is well known that the dominant modulation frequency on
the speech MI is roughly between 2 and 8 [Hz] [4], and weclassify the decomposed IMFs of noisy speech in relation tothese characteristics. The MIs of the speech IMF and noise
IMF are shown in Fig. 7. In the proposed method, speech
IMFs are defined as if the MI peak position is in a region
between 2 and 8 Hz and the MI peak value is over 0.25.
4. Evaluation

We conducted simulations to determine the effectivenessof the proposed method compared with Molla & Hirose’s
method [3]. Thirty speech signals (each comprised of threewords from five males and five females) from the ATR
database a-set [5] were used in these simulations. White noise
max(ek ,m (t )) − min(ek ,m (t ))Mk,m =(2) was added to original speech signals to obtain noisy speechmax(ek ,m (t )) + ek ,m (t )signals with SNRs of −5, 0, 5, 10, 15, and 20 [dB]. An improved SNR, I, was used to evaluate the amplitude informaChannel selection (Fig. 6) is used to clarify the decomposed tion as well as the signal’s phase information. Here, I is deIMFs into speech IMFs and noise IMFs based on the modula- fined astion characteristics in Eq. (2). Finally, the proposed method
 2
 2x̂ (t)dt
x (t)dt
resynthesizes restored speech x̂(t) as follows.
I = 10 log10  2− 10 log10  2(4)n̂ (t)dt
n (t)dtx̂(t) =ck (t)(3)
The proposed method and Molla & Hirose’s method werek∈Sapplied to 30 noisy speech signals. Improved SNRs for bothmethods were calculated by using Eq. (4). The results arewhere S is a set of speech IMFs.
We examine the differences between the characteristics of shown in Fig. 8. In a low SNR condition, the noise reducthe speech and noise IMFs. Here, we focus on the difference tion was more effective in the proposed method than in Molla11x̂(t)x(t)

0.500-0.5-1n(t)

-1
10

0.2

0.4

0.6

0.8

1

1.2

0.5

Time [s]0Figure 11: Restored signal x̂(t)

1.4

-0.5
-1
15. Conclusiony(t)0.50-0.5
-10

0.2

0.4

0.6

0.8

11.2

1.4

Time [s]c1 (t)

Figure 9: Noisy speech y(t) composed of original speech x(t)and Gaussian noise n(t) (SNR = 0 [dB])
10c2 (t)-1
10c3 (t)-110Acknowledgments

c4 (t)-1
10

This work was supported by the Strategic Information andCOmmunications R&D Promotion ProgrammE (SCOPE)(071705001) of the Ministry of Internal Affairs and Communications (MIC), Japan.

c5 (t)-1
10-1

c6 (t)

We investigated the properties of an analysis method basedon EMD for non-stationary signals and found that the essenceof this method is to represent non-stationary signals as an
AM-FM decomposition based on a common temporal envelope. We then investigated the characteristics of the decomposed IMFs from the noisy speech signal and found that EMD
decomposes noisy speech into two separate IMFs, speech andnoise. We used these findings to develope a noise reduction method based on EMD and then conducted simulations
to evaluate its effectiveness in reducing noise components innoisy speech. Results demonstrate that non-stationary speechand stationary noise can effectively be separated by using ourproposed method.

10-1

00.2

0.4

0.6

0.8

11.2

1.4

References

Time [s]Figure 10: Decomposition of noisy speech y(t) (the first six
IMFs: c1 (t), c2 (t), · · ·, and c6 (t))& Hirose’s method. In a high SNR condition, Molla & Hirose’s method exhibited a speech signal that was over-filtered,
which resulted in a restored signal that was corrupted due toover-subtraction. In the same condition, the proposed method
reduced the noise components from noisy speech without
distortion, because it uses channel selection to reduce only
noise-IMFs in the decomposed IMFs.
We illustrate an example of noise reduction using the proposed method. A noisy speech y(t) with a SNR of 0 dB isshown in Fig. 9. The noisy speech is decomposed by EMD
and the decomposed IMFs (the first six) are then obtained,as shown in Fig. 10. These results demonstrated how EMD
decomposes noisy speech into stationary noise IMFs and nonstationary speech IMFs. The proposed method reduced noisecomponents in the decomposed IMFs and then restored thesignal, as shown in Fig. 11.

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