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Title

MTF‑based power envelope restoration in noisy
reverberant environments

Author(s)Unoki, Masashi; Yamasaki, Yutaka; Akagi, Masato

Citation17th European Signal Processing Conference(EUSIPCO 2009): 228‑232

Issue Date

2009‑08‑25

Type

Conference Paper

Text version

publisher

URL

http://hdl.handle.net/10119/9979

RightsCopyright (C) 2009 EURASIP. Masashi Unoki, Yutaka
Yamasaki, and Masato Akagi, 17th European Signal
Processing Conference (EUSIPCO 2009), 2009, 228‑
232.

Description

Japan Advanced Institute of Science and Technology

17th European Signal Processing Conference (EUSIPCO 2009)

Glasgow, Scotland, August 24-28, 2009

MTF-BASED POWER ENVELOPE RESTORATION IN NOISY REVERBERANTENVIRONMENTS
Masashi Unoki, Yutaka Yamasaki, and Masato Akagi
School of Information Science, Japan Advanced Institute of Science and Technology
1-1 Asahidai, Nomi, Ishikawa, 923-1292 JAPANemail: {unoki, yutaka1017, akagi}@jaist.ac.jp

the enclosure on the intelligibility of speech in both noisy
and reverberant environments by using the modulation transfer function (MTF) [6]. The MTF concept enables noise andreverberation to be simultaneously suppressed.
We had already proposed the use of a power envelope
inverse filtering method that is based on the MTF concept[7, 8]. Using our method restored the power envelope ofthe reverberant speech, recovered 30% of the loss of intelligibility caused by the reverberation [9] and produced 30%
relative improvement in the error reduction rate in ASR due
to reverberation [10], under the only noise-less condition. If
we could extend this method as a noise suppression method
based on the MTF concept, we would be able to propose theuse of a way of using MTF to enhance speech, which suppresses noise and reverberation simultaneously. The goal of
our work is to propose a method of enhancing speech thatcan be used to reduce the effects of noise and reverberation.
As our first step, we proposed restoring the smeared MTF torestore the power envelopes of noisy reverberant speech.

ABSTRACT
Many speech enhancement methods had been proposed tosuppress the effects of noise or reverberation. Althoughmost of methods aimed to enhance only noisy or reverberant speech, these cannot simultaneously enhance noisy reverberant speech. This paper proposes a method for restoring the power envelope from the noisy reverberant speech.
This method is based on the MTF concept and does not require that the impulse response and noise conditions in theroom acoustics (noisy reverberant environments) be measured. The proposed method suppresses the effects of reverberation and noise on the power envelopes by restoring thesmeared MTF. We carried out 12,000 simulations of noisesuppression and dereverberation for noisy reverberant speech
to objectively evaluate the proposed method. The results
showed that the proposed method can simultaneously work
well in both noise-suppression and dereverberation.
1. INTRODUCTION
In real environments, significant features of speech aresmeared because of noise and reverberation. The quality ofsound and intelligibility of speech are significantly reduced.
We need to improve noisy reverberant speech (noise suppression and dereverberation) in various speech signal processing
systems, such as hearing aids and the preprocessing for automatic speech recognition (ASR).
There are several well-known suppression methods thatcan be used to remove the effects of noise or reverberationin either noisy or reverberant environments. For example,
the spectral subtraction method proposed by Boll [1], theKalman filtering method proposed by Paliwal and Basu [2],minimum-phase inverse filtering method proposed by Neelyand Allen [3], and the multiple input/output inverse theorem(MINT) method proposed by Miyoshi and Kaneda [4]. Although these methods can work well in either noisy (first two
methods) or reverberant environments (last two methods),
they cannot simultaneously work well these environments.
Recently, Kinoshita et al. have found a way to enhance speech recorded in noisy reverberant environments,
by considering two sequential processes: noise reduction using spectral subtraction for noisy reverberant speech and thendereverberation using linear prediction for noise-reduced reverberant speech [5]. Although this seems to be the simplest modeling of the effects of noise and reverberation, it isthought that a combination of different systems (representations and/or processing) cannot simultaneously deal with theeffects of additive noise and reverberation.
On the other hand, Houtgast and Steeneken have proposed a method of prediction that can assess the effects of© EURASIP, 2009

2. MTF CONCEPTThe MTF concept was proposed by Houtgast and Steeneken
to account for the relation between the degree of modulationof the envelopes of input and output signals and the characteristics of the enclosure and a way to predict the speechtransfer index, which is strongly related to intelligibility [6].
This concept was introduced as a measure in room acoustics for assessing the effect of the enclosure on intelligibility.
They defined input and output temporal power envelopes as
Input= Ii2 (1 + cos(2π f mt)),(1)

Output = Io2 {1 + m( fm ) cos(2π f m (t − τ ))} , (2)where Ii2 and Io2 are the input and output intensities, f m is
the modulation frequency, and τ is the phase information.
The modulation index of the power envelope is m( f m ) andreferred to as MTF. We will now explain the MTF in noisy
and/or reverberant environments.
2.1 Model concept based on the MTF
We assume the output, the input, the impulse response, andthe noise signals to be y(t), x(t), h(t), and n(t). These aremodeled based on the MTF [7, 8, 9] as follows:
y(t)
x(t)
h(t)
n(t)

228

= h(t) ∗ x(t) + n(t),= ex (t)cx (t),= eh (t)ch (t) = a exp(−6.9t/TR)ch (t),= en (t)cn (t),

(3)
(4)
(5)
(6)

SNR = 100 dB

1
R

0.909

0.8

SNR = 10 dB

SNR = 20 dB
SNR = 10 dB

T = 0.1 s

MTF

SNR = 5 dB

T = 0.3 s

0.6

R

0.402

0.4

0.365

R

TR = 1 s

0.2(a) mR(fm)0

TR = 0.5 s
SNR = 0 dB

T = 0.5 s

0

SNR = −5 dB

5

10

15

Modulation Frequency, fm (Hz)(c) m(f )=m (f )m (f ) TR = 0.5 s & SNR = 10 dB(b) m (f )TR = 2 s

N m

20 0

m

5

10

15

20 0

Modulation Frequency, f (Hz)
m

R m

N m

5

10

15

Modulation Frequency, f (Hz)20m

Figure 1: Theoretical representations of the MTFs, m( f m ), in (a) reverberant environment, (b) noisy environment, and (c) bothnoisy and reverberant environments. The bold solid lines indicate the MTF with T R = 0.5 s and SNR = 10 dB.
where ex (t), eh (t), and en (t) are the temporal envelopes ofx(t), h(t), and n(t). c x (t), ch (t), and cn (t) are carriers such as
random variable. Here, c l (t), cl (t − τ ) = δ (τ ) and · is an
ensemble average operation. TR is the reverberation time. In
this model, e2y (t) can be derived as
 2 
y (t)

 2
 

h (t) ∗ x2(t) + n2 (t) ,=e2y (t) = e2h (t) ∗ e2x (t) + e2n (t).

where SNR = 10 log10 (e2x /e2n ) in dB. This MTF is independent of f m and reduced as a function of SNR (Fig. 1(b)). In
the case of SNR of 10 dB, m( f m ) is 0.909.
2.4 MTF in noisy and reverberant environments

(7)
(8)

(see [7, 8] for a detailed derivation of Eq. (8)). We used
the relationship between temporal power envelopes to restore
e2x (t) from the observed e 2y (t).

In the reverberant condition, the input and output temporal
power envelopes, e 2x (t) and e2y (t), are represented ase2y (t) = e2x (t) ∗ e2h (t) =


e2x

α

m( fm ) ==2.2 MTF in reverberant environments

e2x (t) = e2x (1 + cos(2π f mt)),

The MTF in noisy reverberation environments calculated
from Eqs. (11) and (13), can be represented as(9){1 + mR( fm ) cos(2π f mt)} ,(10)

where α = 0∞ h2 (t)dt and β = 0∞ h2 (t) exp(− jωm t)dt. The
complex MTF in reverberant environments is defined as
  


β 
TR 2
(11)
mR ( fm ) =   = 1 + 2π fm
α13.8mR ( f m ) · mN ( f m )



TR 2
1 + 2π fm
13.8

1 + 10− 10

SNR

.(14)

The MTF in noisy reverberant environments depends on f m .
This means the low-pass characteristics resulting from reverberation as a function of TR and the constant attenuation resulting from noise as a function of SNR (Fig. 1(c)). In thecase of a TR of 0.5 s and SNR = 10 dB, m( f m ) at fm = 10 Hz
is 0.365 (= 0.402 × 0.909). Hence, the effect of noise andreverberation can be suppressed by using the inverse filteringof MTF in Eq. (14).
3. POWER ENVELOPE RESTORATION
3.1 Implementation

The MTF in reverberant environments depends on f m . Thismeans the low-pass characteristics as a function of TR (asshown in Fig. 1(a)). In the case of a TR of 0.5 s, m( f m ) at
fm = 10 Hz is 0.402.

We propose the use of the power envelope restoration based
the MTF concept. A block-diagram of the method is shownin Fig. 2. This method consists of (i) power envelope extraction, (ii) power envelope subtraction, and (iii) power envelope inverse filtering with parameter estimation. Here, theconstant bandwidth filterbank was used to analyze the signal.
The power envelopes from y(t) are extracted by2e2y (t) = LPF y(t) + jHilbert[y(t)] ,2.3 MTF in noisy environments(15)

Where there is additive noise, e 2y (t) is represented aswhere LPF[·] is a low-pass filtering and Hilbert[·] is theHilbert transform. This method is based on a calculation of
the instantaneous amplitude of the signal, and is used in lowpass filtering as post-processing to remove the higher frequency components in the power envelopes. We used LPF
with a cut-off frequency of 20 Hz [7, 8, 9].
Power envelope subtraction on the basis of the MTF concept is done to suppress the noise. The modulation index andthe averaged power in Eq. (13) are only affected by noise. To
restore the first term in Eq. (8) from the power envelope of{1 + mN ( fm ) cos(2π f mt)} ,(12)

where e2n = T1 0T e2n (t)dt. Here, e2n (t) is assumed to be constant in the time domain and T is the signal duration. The
complex MTF in noisy environments, is defined ase2y (t) = e2x (t) + e2n (t) =mN ( f m ) =e2x + e2n

e2x
1
=
,
−(SNR)/102
2
ex + en 1 + 10

(13)

229

#1

Power envelope
restoration.
.
.
Reverberant
noisy signal

Analysisblock(Filterbank)y(t)Recovered power envelope2^ex,1 (t).
.
.

Power envelope restoration#kPower envelope
Extraction.
.
.

Eq. (15)

Power envelope
subtraction
2e^y,k (t)Eq. (16)

Power envelope
Inverse-filtering
Parameter
Estimation

^ ^

a, TR
Eqs. (18)-(20)2^ex,k (t)Eq. (17)
.
.
.

2

#K

e^x,K (t)Power envelope
restoration

Figure 2: The power envelope restoration method.
noisy reverberant signal e 2y (t), mN ( fm ) is utilized as follows.
ê2x (t)
1 + mN ( fm ) cos(2π f mt) ×

=

e2x

=

e2y (t) − e2n.

1,
mN ( f m )(16)Here, the robust VAD method (e.g., [12]) is used to calculatee2n (N) and (e2x + e2n ) (SN) in Eq. (13) from the observed e 2y (t)in noise duration and signal+noise duration respectively.
On the basis of this result, e 2x (t) can be recovered by deconvoluting e 2y (t) = e2x (t) ∗ e2h (t) in Eq. (8) with e 2h (t). Here,the transmission functions of power envelopes E x (z), Eh (z),and Ey (z) are assumed to be the z-transforms of e 2x (t), e2h (t),and e2y (t). Thus, the Ex (z) can be determined from 
Ey (z)
13.8
Ex (z) = 2
1 − exp −z−1 ,aTR · fs(17)

where f s is the sampling frequency. The power envelope
e2x (t) can then be obtained from the inverse z-transform ofEx (z). Here, two parameters (TR and a) are obtained as [9]dTP (TR )T̂R =argmin,(18)dTR0≤TR ≤TR,max




2


TP (TR ) = min argmin êx,n,T (t) − θ , (19)tmin ≤t≤tmax


â =

 T

1/
0

R

exp(−13.8t/ T̂R)dt.

(20)

3.2 Example

and the right panels ((b), (d), (f), and (h)) show the corresponding signals. As shown in this figure, m( f m ) decreased
from 1.0 (in Fig. 3(a)) to 0.404 × 0.5 (the maximum deviation of the envelope between the dotted lines in Fig. 3(e)relative to that in Fig. 3(a) and the reduction in Fig. 3(g)).
The solid line in Fig. 3(g) shows the restored power envelope ê2x (t) obtained from the noisy reverberant power envelope e2y (t) (Fig. 3(g)) using Eqs. (16) and (17) with T R = 0.5
s and SNR = 3 dB. It is shown that using power envelope
restoration can precisely restore the power envelope from anoisy reverberant signal in terms of its shape and magnitude.
4. EVALUATION
We now describe how we carried out the following simulations to evaluate the proposed method. The speech signals were three Japanese sentences (/aikawarazu/, /shinbun/,/joudan/) uttered by ten speakers (five males and five females) from the ATR database [11]. We used 100 artificial
impulse responses h(t) and 100 white noise signals n(t). Tworeverberation times (TR = 0.5 and 2.0 s) were used. Signal
to noise ratios (SNRs) between x(t) and n(t) were fixed at 10
and 0 dB. All reverberant signals (6, 000 = 10 × 3 × 2 × 100)and all noisy signals (6, 000 = 10 × 3 × 2 × 100) were generated by convolving x(t) with h(t) and by adding n(t) tox(t). All noisy reverberant signals y(t) (12, 000 = 10 × 3 ×
2 × 100) were also used. The sampling frequency of signal
fs is 20 kHz. We used a filterbank for speech restoration, anddivided the signal into 100 channels (100 Hz bandwidth).
In this paper, to evaluate both the error and similarity between temporal power envelopes (with magnitude andshape), we then used correlation (Corr) and SNR as evaluation measures. Improvements in these measures, therefore,show the extent to which using our method improve accuracyof the restoration. These measures are defined as
T

An example of how the power envelope restoration is related
to the MTF concept is shown in Fig. 3. A sinusoidal powerenvelope as the original e 2x (t) (= 0.5(1 + sin(2π f mt))) andx(t) calculated from e 2x (t) and a white noise carrier c x (t) using Eq. (4) are shown in Figs. 3(a) and (b); f m was 10 Hz andm( fm ) was 1. Figures 3(c) and (d) show e 2h (t) with TR = 0.5
s and h(t) of Eq. (5). An e 2n (t) and an n(t) of Eq. (6) with an
SNR of 3 dB are shown in Figs. 3(e) and (f), and we showe2y (t) (= e2x (t) ∗ e2h (t) + e2n (t) and the observed noisy reverberant signal y(t) (=x(t) ∗ h(t) + n(t)) in Figs. 3(g) and (h). The
left panels ((a), (c), (e), and (g)) show the power envelopesê2x (t) − ê2x dt
 
,
T
T 2
2 (t) − e2 )dt
2 )dt
(e
(
ê
(t)
−
ê
x
x
x
x
0
0

Corr(e2x , ê2x ) = 0e2x (t) − e2xT 2(e (t))2 dt
SNR(e2x , ê2x ) = 10 log10  T 0 x,22
20 (ex (t) − êx (t)) dt

(21)
(22)

where e2x is the average value of e 2x (t), ê2x (t) is the restored
temporal power envelope. The improvements in Corr and
SNR are calculated from Corr(e 2x , ê2x ) − Corr(e2x , e2y ), and

230

2
h

h(t)

e (t)

0
−0.2
(f)

1

n(t)

0.5
0

4
2
0
−2
−4

y(t)

0.5
0

0.2

0.4

0.6

TR=0.3 (s)T =0.5 (s)
R

0
0

0.2
0.4
time (s)

0.6

0.2
0.1
0
0

20

40

60

80

30
20
10
0

(b2) T =2.0 s

50

R

40
30
20
10
0

100

0

20

40

60

80

100

Channel number(a1) SNR=10 dB

0.4
0.3
0.2
0.1
0
−0.1

T =1.0 (s)R

Improved Corr

^ ex(t)

2

(i)
1

R

0.3

60

R

40

Figure 4: Improvement in dereverberation accuracy for the
power envelope of speech on the filterbank: (a) improved
correlations and (b) improved SNRs. TR = 0.5 and 2.0 s.

4
2
0
−2
−4
0

2

0.4

−0.1

(h)

1

(a2) T =2.0 s(b1) T =0.5 s

50Channel number

(g)

2
y

SNR =3 (dB)

Improved Corr

2
n

e (t)

(e)

e (t)

Improved Corr

R

0.2

0

0
−0.1

(d) T =0.5 (s)

0.5

0.1

Improved SNR (dB)

(c)

0.2

Improved SNR (dB)

0

0.3

60

Figure 3: Example of relationship between power envelopesof system based on the MTF concept: (a) power envelope
e2x (t) of (b) original signal x(t), (c) power envelope e 2h (t) of(d) simulated room impulse response h(t) (TR = 0.5 s), (e)power envelope e 2n (t) of (f) noise signal n(t), (g) power envelope e2y (t) derived from e 2x (t) ∗ e2h (t) + e2n (t), (h) noisy reverberant signal y(t) derived from x(t) ∗ h(t) + n(t), and (i)restored power envelope ê 2x (t).

(a2) SNR=0 dB

0.4
0.3
0.2
0.1
0
−0.1

0

20

40

60

80

100

Improved SNR (dB)

0.5

4
2
0
−2
−4

(a1) TR=0.5 s

0.4

60

Improved SNR (dB)1

Improved Corr

(b)
x(t)

2
x

e (t)

(a)

60

(b1) SNR=10 dB

50
40
30
20
10
0

(b2) SNR=0 dB

50
40
30
20
10
0
0

20

Channel number

40

60

80

100

Channel number

Figure 5: Improvement in suppression accuracy for the
power envelope of speech on the filterbank: (a) improved
correlations and (b) improved SNRs. SNR = 10 and 0 dB.
posed method for Japanese sentence (/aikawarazu/) of a malespeaker (Mau) with TR = 0.5 s and SNR = 10 dB is shown in
Fig. 7. The power envelopes of only a quarter of all channels
are plotted in this figure (#1, #5, #9, and so on). These magnitudes were normalized in each channel to view matches between e2x (t)s and ê2x (t)s. We can see many matches between
e2x (t)s and the restored ê 2x (t)s in panel (d), but there are fewer
matches in panel (c). These results demonstrate that the proposed method can be used to adequately restore the powerenvelope from noisy reverberant speech y(t).

SNR(e2x , ê2x ) − SNR(e2x , e2y ). Note that the positive values indicate the temporal power envelope and waveform of speech
were restored from the noisy signal to a certain degree.
The improvement of Corr and SNR in each channel under
the reverberant and noisy conditions are shown in Figs. 4 and5. The height of bar shows the mean value. Although the error bar (standard deviation) was not plotted in here for clearlyviewing, note that the standard deviation at each condition
was not too much. The improvement in Corr was almost
zero in the noisy conditions while the improvement in Corr
was too much in the reverberant conditions. The improvements in the average SNR increased as the SNRs decreasedin the noisy conditions while the improvement in SNR was
almost constant in the reverberant conditions. These results
show that using the proposed method can improve the temporal power envelope of the input signal from the reverberantor noisy signal. In particular, the proposed method greatly
improved Corr in the reverberant conditions while the SNR
in the noisy conditions was also significantly improved.
The improvement in Corr and improved SNR in eachchannel under the noisy reverberant conditions are shown in
Fig. 6. These improvements show that the proposed method
can be used to improve the temporal power envelope fromthe noisy reverberant signals to an adequate level. Furthermore, doing this can simultaneously suppress the effects ofreverberation and noise.
An example of a restoration when we used the pro-

5. CONCLUSION
We have explained how the MTF concept helps to suppress
the effects of reverberation and noise for improving the intelligibility of speech. We then proposed a power envelope
restoration method that is based on the MTF concept. We
have carried out simulations to evaluate whether using the
proposed method can restore smearing of the temporal powerenvelope of speech signals in both noisy and reverberant environments. We found that using the proposed method can beused to simultaneously restore the temporal power envelopes
and to suppress the noise and reverberation effects.
In our future work, we will (1) reconsider an adaptive restoration method on the time-frequency divisions forrestoring noisy reverberant speech, (2) attempt to construct a
way of restoring carriers in the filterbank model to resynthesize the restored speech, and (3) test whether our approach
can suppress the reduction caused by reverberation and noise

231

0

Improved Corr

−0.1(a2) SNR=10 dB / T =2.0 s

0.4

R

0.3
0.2
0.1
0

Improved Corr

−0.1(a3) SNR=0 dB / TR=0.5 s

0.4
0.3
0.2
0.1
0

Improved Corr

−0.1(a4) SNR=0 dB / T =2.0 s

0.4

R

0.3
0.2
0.1
0
−0.1

0

20

40

60

80

100

60

60

x(t)

40

0

20

(a)
−2

0
60

4

x 10

2

(b2) SNR=10 dB / TR=2.0 s
40

y(t)

0.1

x 10

2

(b1) SNR=10 dB / TR=0.5 s

20

0

(b)

0

−2
(b3) SNR=0 dB / TR=0.5 s

50

0

0.5

1

1.5

1

1.5

100

40
30
20

Channel number

0.2

Improved SNR (dB) Improved SNR (dB)

0.3

Improved SNR (dB)

0.4

60

Improved SNR (dB)

Improved Corr(a1) SNR=10 dB / TR=0.5 s

100(b4) SNR=0 dB / T =2.0 s

50

R

40
30
20
10

80
60
40
20

(c)

0
0

Channel number

20

40

60

80

100

0
100

Channel number

Channel number

Figure 6: Improvement in restoration accuracy for the powerenvelope of speech on the filterbank: (a) improved Corrs and(b) improved SNRs. TR = 0.5 and 2.0 s. SNR = 10 and 0 dB.
to the intelligibility of speech.

80
60
40
20

(d)

Acknowledgements

0This work was supported by a Grant-in-Aid for Scientific Research (No. 18680017) from the Ministry of Education, Culture, Sports, Science, and Technology, Japan and the Strategic Information and COmmunications R&D Promotion ProgrammE (SCOPE) (071705001) of the Ministry of Internal
Affairs and Communications (MIC), Japan.

00.5Time (s)Figure 7: Example of the power envelope restoration: (a)original speech x(t), (b) noisy reverberant speech y(t) inthe case of TR = 0.5 s and SNR = 10 dB, (c) no processing (e2y (t)s; solid lines) and (d) restoration using proposed
method (ê 2x (t)s; solid lines). Dashed lines show e 2x (t)s.

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