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Title

Study on a method of suppressing noise based on
the MTF concept

Author(s)Yamasaki, Yutaka; Unoki, Masashi

Citation

Journal of Signal Processing, 13(4): 335‑338

Issue Date

2009‑07

Type

Journal Article

Text version

publisher

URL

http://hdl.handle.net/10119/9183

RightsCopyright (C) 2009 信号処理学会. Yutaka Yamasaki
and Masashi Unoki, Journal of Signal Processing,13(4), 2009, 335‑338.

Description

Japan Advanced Institute of Science and Technology

Journal of Signal Processing. Vol. 13. No.4. pp. 335-338 . .Iuly 2009

SELECTED PAPER

Study on a Method of Suppressing Noise Based on the MTF Concept
Yutaka Yamasaki and Masashi Unoki
School of Infonnation Science, Japan Advanced Institute of Science and Technology
I-I Asahidai, Nomi, Ishikawa 923-1292, Japan
PhoneIFAX:+81-761-51-1699 (Ex. 1391) 1+81-761-51-1149
E-mail: {yutakaI017.unoki}@jaist.ac.jp

Abstract
Many methods of enhancing speech have recently been proposed to suppress the effects of noise or reverberation. Although most of these have aimed to only enhance noisy
speech or reverberant speech, they have not simultaneously
been able to enhance noisy reverberant speech. As MTF canbe used to predict the loss of speech intelligibility due to noiseand reverberation, it may be possible to simultaneously suppress the effects of deterioration due to noise and reverberation, by utilizing MTF-based processing. No methods of suppressing noise based on the MTF concept have yet been considered while a method of dereverberation based on the MTF
concept has already been proposed. We propose a method ofrestoring temporal power envelopes from noisy speech basedon MTF. The proposed method suppresses noise by restoring smeared MTF. We carried out simulations on suppressing
noise in noisy speech to objectively evaluate the model we
propose. The results obtained from evaluating the method
demonstrated that the proposed approach could effectively
suppress noise.

ear prediction for noise-reduced reverberant speech [5]. However, Kinoshita's modeling seems to be too complex. We
thought that the best solution would be able to simultaneously
deal with both additive noise and reverberant effects.
However, Houtgast and Steeneken proposed a method ofprediction that could assess the effects of an enclosure on
speech intelligibility in both noisy and reverberant environments by using the modulation transfer function (MTF) [6].
The MTF concept made it possible to simultaneously suppress both noise and reverberation.
Unoki et al. proposed a method of inverse filtering for temporal power envelopes based on the MTF concept [7, 8, 9].
Their method assumed environments that had reverberationand it improved speech intelligibility in these by about 30%.
We propose a method of speech enhancement based on MTF
that can simultaneously suppress noise and reverberation, sothat it can improve speech intelligibility lost through additivenoise and reverberation.
Our goal was to propose a method of speech enhancement
to reduce noise and dereverberation. This paper proposes amethod of suppressing noise by restoring smeared MTF.

1. Introduction

2. MTF Concept

Significant features of speech are smeared in real environments due to noise and reverberation so that the sound quality
and intelligibility of observed speech are drastically reduced.
Noisy reverberant speech (noise suppression and dereverberation) therefore needs to be enhanced in various speech-signal
processes, such as those in hearing-aid systems and preprocessing in automatic speech recognition systems.
There are several well-known methods of suppression thatcan be used to remove the effects of noise or reverberation ineither noisy or reverberant environments. There have been,for example, the spectral subtraction proposed by Boll [I],the Kalman filtering proposed by Paliwal and Basu [2], theminimum-phase inverse filtering method proposed by Neelyand Allen [3], and the multiple input/output inverse theorem(MINT) proposed by Miyoshi and Kaneda [4]. Althoughthese methods can work well in either noisy or reverberant
environments, they cannot work simultaneously in both noisy
and reverberant environments. Kinoshita et al. recently studied a strategy of enhancing speech in noisy reverberant environments, by taking into consideration two sequential processes, i.e., noise reduction using spectral subtraction fornoisy reverberant speech and then dereverberation using lin-

The MTF concept was proposed by Houtgast andSteeneken to account for the relation between the degree ofmodulation in the envelopes of input and output signals andthe characteristics of the enclosure. This concept was introduced as a measure in room acoustics to assess what effect theenclosure had on speech intelligibility. The input and output
temporal power envelopes in their concept are defined as

Journal of Signal Processing, Vol. 13, No.4, July 2009

Input
Output1;(1 + cos(2rrfmt))(I)

I; {1 + mUm) cos(2rrfm(t - T))} (2)where 12 and I; are the input and output intensities, f m is themodulation frequency, and T is the phase infonnation. Here,mUm) is the modulation index of the modulation frequency
and is referred as to MTF.

2.1 MTF in noisy environments
This section explains MTF in noisy environments. The input temporal power envelope, e; (t), is defined ase;(t) = e;(1 + cos(2rrfmt))

(3)

335

(a)
x(t)

----t---~·GI----+t·Cfl------t---..·.

y(t)

n(t)

(b)

e~(t) -----t-----i{~f----+l.Cfl------+-----.

€r(t)

e~(t)

Figure 2: Diagram of transfer function: (a) is for signal, and(b) is for temporal power envelope.

~L-~--~~6--~8--~10--~12--~14--~16--~18~~20
Modulation Frequency. 1m (Hz)Figure 1: Theoretical representation ofMTF, m(f m), in noisy
and reverberant environments

Hence, noise and reverberant can be suppressed when using
the inverse filtering of the MTF in Eq. (7).
3. Method of Suppressing Noise

Under additive noise conditions, the output temporal powerenvelope, e~(t), is defined ase~(t)e~ {I + cos( 27r f m t)} + e~ (t)(e~ + e~) {I + mUm) cos(27r Im t )}(4)

where e~ (t) is the temporal power envelope of the noise signal. e~ = 1. JoT e~ (t) dt because e~ (t) is assumed to be constant over the time. Here T is the duration of the signal. The
complex MTF in noisy environments is defined ase2

1m(fm) = e 2 : e 2 = 1 + 10-(SNR)/10
x

n

(5)

noise
the ~ignal toration (SNR) equals
1010g10(e~/e~) in dB in decibels. This MTF is in dependent of modulation frequency f m· With an SNR of 5 dB,m(fm) is about 0.76 (as plotted in Fig. 1).

where

2.2 MTF in noisy and reverberant environments

The MTF in reverberant environments, m(f m), can be represented as [6, 7, 8,9]
(6)
where TR is the reverberation time. The MTF in reverberant
environments depends on f m. This equation indicates lowpass characteristics. The MTF in noisy and reverberation environments calculated from Eqs. (I), (2), (5), and (6) can be
represented asm(fm) =TR )[1 + (27r 1m 13.8

2]-1/2X (13.1

Model concept based on MTF

The output signal, the input signal, the impulse response,
and the noise signal have been assumed to correspond to y(t),x(t), h(t), and n(t) in this paper, as outlined in Fig. 2(a).
These four were modeled based on the MTF concept as

y(t)
h(t)
x(t)
n(t)

h(t) * x(t) + n(t)eh(t)ch(t)ex(t)cx(t)en (t)cn(t)(Cl (t), Cl (t - T)) = <5 ( T )

(8)
(9)
(10)
(11)
(12)

where ex(t), eh(t), and en(t) are the temporal envelopes ofx(t), h(t), and n(t). cx(t), Ch(t), and cn(t) are carriers suchas random variables. (.) is an ensemble average operation. In
this model, e~ (t) can be derived as<h 2 (t) * x 2(t)) + <n 2 (t) )e~(t) * e;(t) + e~(t)

(13)
(14)

(see [7, 8, 9] for a detailed derivation of Eq. (13).) The relation of temporal power envelopes was used in our study.
However, only noisy environments have been considered inthis paper for our proposed method of suppressing MTFbased noise.

3.2 Extraction of temporal power envelopes
Temporal power envelopes are extracted from y(t) by

e~(t) = LPF [Iy(t) + )Hilbert{y(t)} 12](15)+ 1O-(SNR)/10) -1 where LPF[·] is low-pass filtering. Hilbert(·) is the Hilberttransform. This method is based on calculating the instanta-(7) neous amplitude of the signal, and low-pass filtering is used

336

Journal of Signal Processing~ Vol. 13, No.4, July 2009

as post-processing to remove the higher frequency components in the power envelopes. We used LPF with a cut-off
frequency of 20 Hz. Unoki et al. 's method was adopted to
extract the temporal power envelopes [7,8,9].

3 2 . - . - - - - . - - - - - . - - - . , -_ _--,-_ _ _-,-,

3.3 Implementation
This section explains the method of suppressing noisebased on the MTF concept. The modulation index and theaveraged power in Eq. (4) are affected by noise. We restore
the averaged power levels to suppress the noise effects. Eq.
(16) is the offset value of the averaged power given by2"

OV = _e x _
e~ +

e;

( 16)
-5

10

e~

+ e~ . mUm) . cos(27rlmt)(17)

By multiplying the second term of Eg. (17) by l/m(f m) to
restore the modulation index, we can obtain
2
ex(t)

1
e~ + (e~·mUm) . cos 27r Jmt ) x m(fm)

-

e~(l

+ cos(27iJmt))

15

20

SNR (dB)

By substituting Eq. (16) into Eq. (4), we can obtain(18)

Figure 3: Mean improvement in restoration accuracy (LSD):
Error bars represent standard deviation.
The correlation (Corr), SNR, and log spectrum distance(LSD) were used as measures in these simulations to evaluate improvements in the accuracy of restoration achieved with
our method, These measures are defined asCorr( e~, e~)This obtains the noise-suppressed temporal power envelope,e~(t). This algorithm is the method of suppressing noisebased on the MTF concept.
(e~(t) - e~(t))dt}(e~(t) - e~(t))dt}
The proposed approach is equal to the method of sub(19)tracting the average value of noise temporal power envelopes
from the output temporal power envelope. Since, the proJ'T( 2 ( ))2dt
posed method is based on the MTF concept, it should be'
SNR( e 2 , e2 ) = 10 log,0 ex t,(20)
able to deal with not only additive noise but also reverberxx10(e;(t) _ ei(t))2dt
ation. Therefore, if the proposed approach is incorporated
into MTF-based dereverberation, the combined method cansimultaneously suppress both noise and reverberation.
g lO :LSD(S"Sx) =.
(21)
e; and e~ are needed to calculate the MTF in Eq. (5). e~
is estimated from the non-speech sections. e; is estimated
where e~ is the average value of e~(t), and e;(t) is theby subtracting e~ from e~. The MTF in Eq. (18) can be restored temporal power envelope. W is the upper frecalculated by using this SNR.
quency (here, it is 10 kHz), and Sx(w) and Sx(w) are
the amplitude spectra of x(t) and y(t) or x(t). The improvements in Corr, SNR, and LSD are calculated from
4. Evaluation

{JoT

{JoT

JoT

t

~ (2010 t~:~:r

We carried out the following simulations to evaluate theproposed model. The speech signals were three Japanese
sentences (laikawarazul, Ishinbunl, Ijoudanl) uttered by ten
speakers (five males and five females) from the ATR database[10]. We used 100 white noise signals, n(t). TheSNRs
were fixed at 20, 10, 5, 0, and -5 dB. All noisy signals(15,000 = 10 x 3 x 5 x 100) were generated by adding
x(t) to n(t). The sampling frequency of the signal was 20
kHz. We used a filterbank for speech restoration, and divided
the signal into 100 bands. The bandwidth of all channels was
set to 100 Hz.

Journal of Signal Processing, Vol. 13, No.4, July 2009

Corr(e;, e;) - Corr(e;, e~), SNR(e;, e;) - SNR(e;, e~),and LSD(Sx(w), Sy(w)) - LSD(Sx(w), Sx(w)). Note that

positive values indicate the temporal power envelopes andwaveforms of speech were restored from noisy signals to acertain degree.
Figure 3 plots the improvement in LSD. The maximum
improvement in LSD was about 30 dB. Figure 4 shows the
improvement in Corr and the improvement SNR in all channels. The heights of the bars and error bars correspond to themean and standard deviation. The improvement in Corr wasconstant. The improvements in SNR increased as SNRs decreased. These results indicate that the proposed method can337

: : :=

70

80

90

100

Figure 4: Improved accuracy for temporal power envelopes of speech in filterbank
improve temporal power envelopes and the waveforms of the
input signals from the noisy signals.

5. Conclusion and Future Perspectives
We introduced the MTF concept and proposed a methodof suppressing noise based on the MTF concept by restoringsmeared MTF. We carried out simulations in which the proposed approach was applied to temporal power envelopes torestore 15, 000 noisy speech signals. We found that the proposed method could be used to adequately restore the temporal power envelopes and to suppress the noise effects of noisy
signals.
We intend to further improve the method, consider carrier restoration, and carry out SUbjective evaluations in future
work. We further intend to propose a method of suppressing noise and reverberation by restoring the smeared MTF in
noisy and reverberant environments using the inverse filteringofMTF in Eq. (7).

Acknowledgements
This work was supported by a Grant-in-Aid for Scientific Research(No. 18680017) made available by the Ministry of Education, Culture, Sports, Science, and Technology, Japan. It was also partially
supported by the Strategic Information and COmmunications R&D
Promotion ProgrammE (SCOPE) (071705001) of the Ministry ofInternal Affairs and Communications (MIC), Japan.

338

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[2] K. K. Paliwal, A. Basu: A speech enhancement method basedon Kalman filtering, ICASSP'87, Vol. I, pp. 177-180, 1987.
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[4] M. Miyoshi, Y. Kaneda: Inverse filtering of room acoustics,
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Journal of Signal Processing, Vol. 13, No.4, July 2009