PROCEEDINGS of the
23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Primary ambient extraction for random sign Hilbert filtering
decorrelation
Lu CHEN; Chuang SHI; Huiyong LI
University of Electronic Science and Technology of China, Chengdu, China
Corresponding email: shichuang@uestc.edu.cn

ABSTRACTThe primary ambient extraction (PAE) decomposes a stereo mixture into separated primary and ambient
components, providing a crucial step in spatial audio analysis and reproduction. The necessary spatial
assumptions of PAE include (i) uncorrelated balanced ambient components, (ii) uncorrelated ambient andprimary components, and (iii) primary components with the only difference in the panning factor. Hence,different PAE methods can be developed for different decorrelation processes that are used to produce theuncorrelated ambient components. This paper investigates a new decorrelation process, namely the random
sign Hilbert filtering decorrelation process. This decorrelation process ensures that the ambient components
consistently have ±90° phase difference between the left and right channels. The PAE method catering for the
random sign Hilbert filtering decorrelation process is called the uncorrelated-ambient PAE (UAPAE). This
paper expounds the UAPAE and demonstrate a comparison between the UAPAE and existing PAE methods.
Keywords: Primary ambient extraction, Decorrelation, Hilbert filtering

1. INTRODUCTION
Channel-based audio formats are widely used in consumer electronics, such as mobile phon es,
tablets and personal computers. Most of the channel-based audio files simply contain two channels
that can be directly played back with headphones. In order for an immersive listening environment tobe constructed with arbitrary playback systems, Goodwin and Jot proposed the idea of PAE that
intended to change the number of channels without losing the spatial information (1).
Considering the audio signal as a linear combination of the primary and ambient component s, there
is a high possibility that the PAE would face an underdetermined problem, resulting in a necessity forthree spatial assumptions (2). Firstly, the ambient components are assumed to be uncorrelated between
any two channels and have equal energy. Secondly, the ambient components are assum ed to be
uncorrelated with the primary components. Thirdly, the primary components are almost identical. The
only difference between any two primary components is just a panning factor.
When the primary components have higher energy than ambient components, principal component
analysis (PCA) is dedicated to find the common unit vector of the primary components that maximizes
the energy of the primary components (1). The result of PCA implies that the primary components arevertical to the ambient components. When ambient components are extracted from a stereo mixture,
one ambient component pans to the opposite direction of the other, which doesn’t obey with theassumptions that the ambient components are uncorrelated and balanced (3).
Ambient phase estimation with a sparsity constraint (APES) is suitable for the uncorrelated
ambient components produced by the random phase decorrelation process (4). Magnitudes of ambient
components are further assumed to be equal in every frequency bin. An additional sparse constraint isrequired to solve the underdetermined problem. APES achieves better accuracy when the primary
components are dominant in the stereo mixture (5). The optimization that minimizes the norm of the
primary components is non-convex in APES. Therefore, APES introduces an angle-by-angle searchalgorithm to find out the correct phases of ambient components. To reduce the computation complexityof APES, APEX has been proposed as a simplified algorithm with little loss in extraction accuracy (6).
Different PAE methods can be developed for different decorrelation processes that are used to
produce the uncorrelated ambient components. The random sign Hilbert filtering decorrelation processensures the ambient components have ±90° phase difference between the left and right channels.

7239

Correlation coefficients between the processed ambient components are constantly nearly 0. In
comparison, the random phase decorrelation process leads to correlation coefficients with morevariations. Thus, this paper investigates the random sign Hilbert filtering decorrelation process andproposed the UAPAE method.

2. RANDOM SIGN HILBERT FILTERING DECORRELATION PROCESS
Highly correlated audio signals often lead to unnatural listening experience. When they are playedback using headphones, listeners feel the sound artificially streaming inside of their heads (7, 8). Whenbroadcasted in a reverberating room, highly correlated audio signals cause the combing phenomenon,
which is destructive most of the time (9). The decorrelation process is a very important tool in audio
engineering that can eliminate those unnatural listening sensations and the combing phenomenon.
The random phase decorrelation process can be carried out in either the time domain or frequency
domain. Taking the frequency domain process as an example, the short time Fourier transform of the
input signal ‫ݕ‬ଵ ሺ‫ݐ‬ሻ is firstly calculated. Secondly, a random phase shift is added into every
time-frequency bin. Thirdly, the inverse Fourier transform is obtained to recover the output signal‫ݕ‬ଶ ሺ‫ݐ‬ሻ. The random sign Hilbert filtering decorrelation process is different from the random phasedecorrelation process only in the second step, where ൅ͻͲ° or െͻͲ° phase shift instead of the random
phase shift is added.
To evaluate the performance of decorrelation processes, the correlation coefficient ȳሺοሻ of two
signals ‫ݕ‬ଵ ሺ‫ݐ‬ሻ and ‫ݕ‬ଶ ሺ‫ݐ‬ሻ with equal energy is defined as
ͳ ା்
ͳ ା்
න ‫ݕ‬ଵ ሺ‫ݐ‬ሻ‫ݕ‬ଶ ሺ‫ ݐ‬൅ᇞ ‫ݐ‬ሻ݀‫ݐ‬቉൘ቈ න ‫ݕ‬ଵ ሺ‫ݐ‬ሻ‫ݕ‬ଵ ሺ‫ݐ‬ሻ݀‫ݐ‬቉்՜ஶ ʹܶ ି்்՜ஶ ʹܶ ି்

(1)

ͳ ା்
ͳ ା்
න ‫ݕ‬ଵ ሺ‫ݐ‬ሻ‫ݕ‬ଶ ሺ‫ ݐ‬൅ᇞ ‫ݐ‬ሻ݀‫ݐ‬቉൘ቈ න ‫ݕ‬ଶ ሺ‫ݐ‬ሻ‫ݕ‬ଶ ሺ‫ݐ‬ሻ݀‫ݐ‬቉ ǡ்՜ஶ ʹܶ ି்்՜ஶ ʹܶ ି்(2)ȳሺοሻ ൌ ቈ or equivalentlyȳሺοሻ ൌ ቈ 

where ο‫ ݐ‬represents a temporal offset.
Figure 1 presents correlation coefficients of the random sign Hilbert filtering and random phasedecorrelation processes. It shows that correlation coefficients of the random sign Hilbert filtering
decorrelation process are almost constantly 0, which are significantly smaller than those of the random
phase decorrelation process.
-3

6

x 10

random sign Hilbert filtering
random phase

Correlation Coefficient

4

2

0

-2

-4

-6
0

0.5

1

1.5

2

2.5

3

3.5

4

Temporal Offset(s)Figure 1 – Correlation coefficients of decorrelation processes
The combing phenomenon testing system is another approach to evaluate the effectiveness of
decorrelation processes. A block diagram of the combing phenomenon testing system is shown in
Figure 2.

7240

Monophonic
Input Signal

q

MonophonicOutput Signal

Decorrelationq
Attenuation

Delay
Decorrelation

Figure 2 – Combing phenomenon testing system

Magnitude

Magnitude

MagnitudeFirstly, the factor ‫ ݍ‬is set to 0. When there is no decorrelation process, the overall system behaves
like a comb filter. Setting the attenuation gain to 0.7 and the delay amount to 0.04s leads to the result
plotted in Figure 3(a). The magnitude response clearly demonstrates that the frequency interval
between neighboring troughs is reciprocal of the delay amount. Figures 3(b) and 3(c) shows the results
when the random sign Hilbert filtering and random phase decorrelation processes are taken into
account. There is no obvious pattern in both magnitude responses. This validates that the random sign
Hilbert filtering decorrelation process can make similar decorrelation effect as compared to therandom phase decorrelation process.
4

no decorrelation

2
0
-100

-50

0

50

100

Frequency (Hz)(a)

4random phase

2
0
-100

-50

0

50

100

Frequency (Hz)(b)

4random sign Hilbert filtering

2
0
-100

-50

0

50

100

Frequency (Hz)(c)

Figure 3 – Magnitude response of the combing phenomenon testing system when ‫ ݍ‬ൌ Ͳ and (a) no
decorrelation; (b) the random phase decorrelation process; (c) the random sign Hilbert filter is carried out
Furthermore, setting ‫ ݍ‬to 0.25, 0.5 and 1, the magnitude response when the random sign Hilbert
filtering decorrelation process is considered are plotted in Figure 4. As ‫ ݍ‬increases, the combing
phenomena gradually recovers. The effect of the random sign Hilbert filtering decorrelation process iscontrollable by the factor ‫ ݍ‬in the combing phenomenon testing system (4, 10).

3. UNCORRELATED-AMBIENT PAE
3.1 Description
In PAE, a stereo mixture is considered as a linear combination of primary and ambient components,
which are written as(3)‫ݔ‬௅ ሺ‫ݐ‬ሻ ൌ ‫݌‬௅ ሺ‫ݐ‬ሻ ൅ ܽ௅ ሺ‫ݐ‬ሻand‫ݔ‬ோ ሺ‫ݐ‬ሻ ൌ ‫݌‬ோ ሺ‫ݐ‬ሻ ൅ ܽோ ሺ‫ݐ‬ሻ,
(4)

7241

Magnitude

q=0.25

5
0

0

50

100

150

200

Magnitude

Frequency (Hz)
(a)
q=0.5

5
0

0

50

100

150

200

Magnitude

Frequency (Hz)
(b)
q=1

5
0

0

50

100

150

200

Frequency (Hz)(c)

Figure 4 – Magnitude response of the combing phenomenon testing system when the random sign Hilbert
filter is carried out and (a) ‫ ݍ‬ൌ ͲǤʹͷ; (b) ‫ ݍ‬ൌ ͲǤͷ; (c) ‫ ݍ‬ൌ ͳ, respectively
where ‫ݔ‬௅ and ‫ݔ‬ோ are the left and right channels of the stereo mixture. The primary components ‫݌‬௅and ‫݌‬ோ are correlated and different only in a panning factor ݇ as ‫݌‬ோ ൌ ݇‫݌‬௅ . The ambient components
ܽ௅ and ܽோ are uncorrelated and have equal power. They are also uncorrelated with the primary
components. These spatial assumptions are crucial in PAE.
After the short-time Fourier transform, equations (3) and (4) are rewritten as(5)ܺ௅ ሾ݉ǡ ݂ሿ ൌ ܲ௅ ሾ݉ǡ ݂ሿ ൅ ‫ܣ‬௅ ሾ݉ǡ ݂ሿ
andܺோ ሾ݉ǡ ݂ሿ ൌ ܲோ ሾ݉ǡ ݂ሿ ൅ ‫ܣ‬ோ ሾ݉ǡ ݂ሿ,(6)
where ݉ is the frame index and ݂ is the index of the frequency bin. PAE is thus carried out in every
time-frequency bin. In the latter part of this paper, the notation ሾ݉ǡ ݂ሿ is abbreviated unless necessary.
As shown in Figure 5, ܺ௅ , ܺோ , ܲ௅ , ܲோ , ‫ܣ‬௅ , and ‫ܣ‬ோ are all complex and can be represented as
vectors in the complex plane. Denote the coordinate of ܺ௅ , ܺோ , ‫ܣ‬௅ , and ‫ܣ‬ோ as ሺ‫ݔ‬ଵ ǡ ଵ ሻ, ሺ‫ݔ‬ଶ ǡ ଶ ሻ,ሺܽଵ ǡ ܾଵ ሻ and ሺܽଶ ǡ ܾଶ ሻ, respectively. The random sign Hilbert filtering decorrelation process suggeststhat ‫ܣ‬௅ ٣ ‫ܣ‬ோ and ȁ‫ܣ‬௅ ȁ ൌ ȁ‫ܣ‬ோ ȁ, i.e.
(7)ܽଵ ܽଶ ൅ ܾଵ ܾଶ ൌ Ͳ
and(8)
ܽଵଶ ൅ ܾଵଶ ൌ ܽଶଶ ൅ ܾଶଶ.
Apparently, ܽଶ ൌ ‫ܾט‬ଵ and ܽଵ ൌ േܾଶ . The sign is associated with the random sign in the decorrelation
process, which represent either ‫ܣ‬௅ is behind‫ܣ‬ோ in phase by 90° or ‫ܣ‬௅ is ahead‫ܣ‬ோ in phase by 90°
Im

XR

XL
PL

O (0,0)

AL

PR

Re

AR


Figure 5 – PAE in one time-frequency bin illustrated on the complex plane

7242

Since ܲோ ൌ ݇ܲ௅ , knowing thatܲ௅ ൌ ܺ௅ െ ‫ܣ‬௅ ൌ ሺ‫ݔ‬ଵ െ ܽଵ ǡ ‫ݕ‬ଵ െ ܾଵ ሻandܲோ ൌ ܺோ െ ‫ܣ‬ோ ൌ ሺ‫ݔ‬ଶ െ ܽଶ ǡ ‫ݕ‬ଶ െ ܾଶ ሻ
yieldsሺ‫ݔ‬ଶ െ ܽଶ ǡ ଶ െ ܾଶ ሻ ൌ ݇ሺ‫ݔ‬ଵ െ ܽଵ ǡ ‫ݕ‬ଵ െ ܾଵ ሻ.
Given that ܽଶ ൌ െܾଵ and ܽଵ ൌ ܾଶ , equation (11) determines the ambient components byଶଶ‫ܽۓ‬ଵ  ൌ ሺെ݇‫ݕ‬ଵ ൅ ݇ ‫ݔ‬ଵ െ ݇‫ݔ‬ଶ ൅ ‫ݕ‬ଶ ሻΤሺ݇ ൅ ͳሻۖ ܾଵ  ൌ ሺ݇ ଶ ‫ݕ‬ଵ ൅ ݇‫ݔ‬ଵ െ ݇‫ݔ‬ଶ ൅ ‫ݔ‬ଶ ሻΤሺ݇ ଶ ൅ ͳሻ.
ଶଶ‫ܽ۔‬ଶ  ൌ െሺ݇ ‫ݕ‬ଵ ൅ ݇‫ݔ‬ଵ െ ݇‫ݕ‬ଶ െ ‫ݔ‬ଶ ሻΤሺ݇ ൅ ͳሻۖܾ  ൌ ሺെ݇‫ ݕ‬൅ ݇ ଶ‫ ݔ‬െ ݇‫ ݔ‬൅ ‫ ݕ‬ሻΤሺ݇ ଶ ൅ ͳሻ
ଵ
ଵ
ଶ
ଶ
‫ ە‬ଶ

(9)
(10)
(11)

(12)

Alternatively, given that ܽଶ ൌ ܾଵ and ܽଵ ൌ െܾଶ , equation (11) determines the ambient components byଶଶ‫ܽ ۓ‬ଵ  ൌ ሺ݇‫ݕ‬ଵ ൅ ݇ ‫ݔ‬ଵ െ ݇‫ݔ‬ଶ െ ‫ݕ‬ଶ ሻΤሺ݇ ൅ ͳሻۖ ܾଵ  ൌ ሺ݇ ଶ ‫ݕ‬ଵ െ ݇‫ݔ‬ଵ െ ݇‫ݕ‬ଶ ൅ ‫ݔ‬ଶ ሻΤሺ݇ ଶ ൅ ͳሻ.
ଶଶ‫ܽ۔‬ଶ  ൌ ሺ݇ ‫ݕ‬ଵ െ ݇‫ݔ‬ଵ െ ݇‫ݕ‬ଶ ൅ ‫ݔ‬ଶ ሻΤሺ݇ ൅ ͳሻۖܾ  ൌ െ ሺ݇‫ ݕ‬൅ ݇ ଶ ‫ ݔ‬െ ݇‫ ݔ‬െ ‫ ݕ‬ሻΤሺ݇ ଶ ൅ ͳሻ
ଵ
ଵ
ଶ
ଶ
‫ ە‬ଶ

(13)

After ambient components are determined, primary components are readily obtained by equations (9)and (10).
The panning factor ݇ of a stereo mixture is estimated by
ு
ு
ு
ு
ு
ଶ
݇ ൌ ሺ࢞ுோ ࢞ோ െ ࢞௅ ࢞௅ ሻൗሺʹ࢞௅ ࢞ோ ሻ ൅ ටሾሺ࢞ோ ࢞ோ െ ࢞௅ ࢞௅ ሻΤሺʹ࢞௅ ࢞ோ ሻሿ ൅ ͳ(14)࢞௅ ൌ ሾ‫ݔ‬௅ ሺ‫ݐ‬଴ ሻ‫ݔ‬௅ ሺ‫ݐ‬ଵ ሻ‫ݔ‬௅ ሺ‫ݐ‬ଶሻ‫ݔ ڮ‬௅ ሺ‫ݐ‬ே ሻሿ

(15)

where
and
(16)
࢞ோ ൌ ሾ‫ݔ‬ோ ሺ‫ݐ‬଴ሻ‫ݔ‬ோ ሺ‫ݐ‬ଵ ሻ‫ݔ‬ோ ሺ‫ݐ‬ଶ ሻ‫ݔ ڮ‬ோ ሺ‫ݐ‬ே ሻሿ
are segments of the left and right channels.
However, there are two different solutions as provided by equations (12) and (13) in every
time-frequency bin. It is necessary to select one of them. The rule of thumb used in the APES method
is considered, i.e. the solution with the minimum magnitude or energy of ܲ෠௅ is selected. The flow of
the UAPAE method is depicted in Figure 6
Estimate k using equation (14)Take the short-time Fourier transform toconverse xL(t) and xR(t) into frequency domain
Compute PL,PR,AL,AR in every timefrequency bin using equations (12) and (13)
Selet the solution with theminimum magnitude or energy of PˆL
Take the inverse short-time Fourier transformto converse the signal into time domain

Figure 6 – Flow chart of the UAPAE method7243

3.2 Experimental Results
In this experiment, a monophonic male speech is used as the primary component of the left channel.
The panning factor ݇ is set to 2, in order for the primary component of the right channel to begenerated. A wave lapping sound recorded at the beach is selected as the ambient component of the leftchannel, which is also used as the input of the random sign Hilbert filtering decorrelation process togenerate the ambient component of the right channel. When the primary and ambient components are
mixed up, the power ratio of the primary components to the stereo mixture (abbreviated as PPR) is a
useful measure to describe the relative energy of the primary and ambient components in the time
domain. The audio files of the male speech and the wave lapping sound are extracted from (6).
The primary extraction error between the estimate of the primary component and the ground truth iscomputed by݁‫ݎݎ‬௣ ൌ ԡ‫݌‬௅ െ ‫݌‬Ƹ ௅ ԡଶଶΤʹԡ‫݌‬௅ ԡଶଶ ൅ ԡ‫݌‬ோ െ ‫݌‬Ƹ ோ ԡଶଶΤʹԡ‫݌‬ோ ԡଶଶ.
(17)
Similarly, the ambient extraction error between the estimate of the ambient component and the groundtruth is computed by(18)݁‫ݎݎ‬௔ ൌ ԡܽ௅ െ ܽො௅ ԡଶଶΤʹԡܽ௅ ԡଶଶ ൅ ԡܽோ െ ܽොோ ԡଶଶΤʹԡܽோ ԡଶଶ.
The primary and ambient extraction errors are plotted with respect to PPR in Figure 7, where the
UAPAE method is compared with the APES, APEX, and PCA methods.
10

PCA
APES
APEX
UAPAE

30
20

Error of the Arimary Components (dB)

Error of the Primary Components (dB)

40

10
0
-10
-20
-30
-40
0

0.5

PPR

1

PCA
APES
APEX
UAPAE

5
0
-5
-10
-15
-20
-25
-30
-35
0

0.5

1

PPR

Figure 7 – Extraction error of various PAE methods with respect to PPR
Figure 7 shows that the primary extraction error decreases with PPR for every PAE methods andthe ambient extraction error increases with PPR except for the PCA method. The UAPAE method
achieves the lowest extraction error for both the primary and ambient components when the random
sign Hilbert filtering decorrelation process has been taken.
Besides the extraction error, the time-domain segmental SNR (SNRseg),the frequency-weighted
segmental SNR (fwSNRseg), the log likelihood ratio (LLR), perceptual evaluation of speech quality(PESQ) and perceptual evaluation of audio quality (PEAQ) are also calculated for comparison (11,12).
The SNRseg is defined asெିଵ ൌே௠ାேିଵ
ே௠ାேିଵ
ͳͲሾ‫ݔ‬ሺ݊ሻ െ ‫ݔ‬ොሺ݊ሻሿଶ ǡ‫ ݔ‬ଶ ሺ݊ሻ൨൘෍෍ ଵ଴ ൤෍
‫ܯ‬
௡ୀே௠
௡ୀே௠
௠ୀ଴

(19)

where ‫ݔ‬ሺ݊ሻ is the ground truth of the primary or ambient components; ‫ݔ‬ොሺ݊ሻ is the estimate
provided by PAE; ܰ is the frame size and ‫ ܯ‬is the number of frames. The frame size is set to 1323
in this experiment.
The fwSNRseg is defined as

7244

ெିଵ

௅

௅

ሼܺሾ݉ǡ ݂ሿሽଶͳͲ ൌ෍ ቐ෍ ‫ݓ‬ሾ݉ǡ ݂ሿ ଵ଴ଶ ቑ൙቎෍ ܹሾ݉ǡ ݂ሿ቏ ǡ‫ܯ‬൛ܺሾ݉ǡ ݂ሿ െ ܺ෠ሾ݉ǡ ݂ሿൟ௠ୀ଴ ௙ୀଵ
௙ୀଵ

(20)

where ܺሾ݉ǡ ݂ሿand ܺ෠ሾ݉ǡ ݂ሿ are the ground truth and estimate of the primary or ambient componen ts;‫ ܮ‬ൌ ʹͷ is the number of critical bands; ܹሾ݉ǡ ݂ሿ is the energy of ground truth in the ݂-th criticalband.
The linear predictive coding (LPC) represent the spectral envelope of a speech or an audio signal.
By using LPC, LLR measures the spectral envelope difference between the ground truth and estimateof the primary or ambient components. It is defined as݀௅௅ோ ൌ ൣሺࢇ௣ ࡾ௖ ࢇ்௣ ሻΤሺࢇ௖ ࡾ௖ ࢇ்௖ ሻ൧(21)
where ࢇ௣ is the LPC vector of the estimate; ࢇ௖ and ࡾ௖ are the LPC vector and the autocorrelation
matrix of the ground truth, respectively. LLR of a clip is calculated frame by frame and boundedwithin 0 to 2. Only the lowest 95% LLR values are averaged to result in a single value.
The PESQ and PEAQ imitate the auditory system of human ear and predict the subjective score ofa stimulus (13, 14).The range of PESQ is generally between 1 and 4.5 and a higher score represents
better speech quality. The PEAQ uses the subjective difference grade (SDG) to represent audio quality.
Although the value of SDG is from -4 to 4, only negative SDG values are obtained when the reference
audio and the testing audio are distinguishable. In this experiment, PESQ is used to evaluate extracted
primary components and PEAQ is used to score extracted ambient components.
When PPR is set to 0.8, evaluation results of various PAE methods are listed in Table 1. The best
result in each category is in bold. The UAPAE method achieves the best performance, while the PCA
method is worse than the other PAE methods.
Table 1 – Objective scores of primary and ambient components extracted with different PAE methods
SNRseg (dB) FwSNRseg (dB)‫݌‬Ƹ ௅

‫݌‬Ƹ ோ

ܽො௅

ܽොோ

LLR

PESQ

PEAQ

PCA

4.9855

6.41701.27662.0308\APEX

5.450911.19960.31482.5319\APES

5.5786

11.45840.28732.6277\UAPAE

8.394116.40090.20092.9283\PCA

4.98866.24811.27312.0255\APEX

5.754511.3184

0.32612.5519\APES

6.049212.3706

0.30392.6617\UAPAE

9.175516.9130

0.19682.9388\PCA

6.955618.49030.0602\-3.412APEX

12.211024.35200.0517\-2.593APES

12.8904

24.78440.0495\-2.551

UAPAE

16.1388

30.3395

0.0289\-1.094PCA

0.970912.7951

0.1561\-3.713APEX

8.217822.17530.0456\-3.536APES

8.679722.68390.0464\-3.514UAPAE

10.7547

27.1677

0.0185\-2.367

4. CONCLUSIONSPAE decomposes a stereo mixture into separated primary and ambient components and forms anunderdetermined problem that always incur errors in the solution. Based on spatial assumption of PAE
that the ambient components are uncorrelated, the random sign Hilbert filtering decorrelation process
is investigated in this paper. It is relatively easy to implement and achieves similar decorrelation

7245

performance as compared to the random phase decorrelation process. To further support the random
sign Hilbert filtering decorrelation process, this paper proposes the UAPAE method, which has been
proved to outperform the other PAE methods in the experiment. The computation complexity of the
UAPAE method is much lower than the APES method and with similar level of the frequency domain
PCA and APEX methods.

ACKNOWLEDGEMENTS
This work is jointly supported by the National Science Foundation of China (Grant No. 61671137
and Grant No. 61701090) and Sichuan Science and Technology Program (Project No. 2018JY0218 and2019YJ0182).

REFERENCES
1. Goodwin M, Jot JM. Primary-ambient signal decomposition and vector-based localization for spatial
audio coding and enhancement. Proc ICASSP; 15-20 April 2007; Honolulu, HI, USA. p. 9–12.
2. Avendano C, Jot JM. A frequency-domain approach to multichannel upmix. J Audio Eng Soc. 2004;
52(7): 740-749.
3. He J, Gan WS, Tan EL. A study on the frequency-domain Primary-ambient extraction for stereo audio
signals. Proc ICASSP; 04-09, May, 2014; Florence, Italy 2014.
4. Kendall G. The decorrelation of audio signals and its impact on spatial imagery. Computer Music
Journal. 1995; 19(4): 71–87.
5. He J, Gan WS, Tan EL. Primary-ambient extraction using ambient phase estimation with a sparsity
constraint. IEEE Sig Process Letters. 2015; 22(8):1127-1131.
6. He J. Spatial audio reproduction with primary ambient extraction. Singapore: Springer Publishing
Company; 2016.
7. Xie BS. Head related transfer function and virtual auditory. Guangzhou, China: National Defense
Industry Press; 2008.
8. Blauert J, Butler RA. Spatial hearing: The psychophysics of human sound localization by Jens Blauert.
J Acoust Soc Am. 1985; 77(1): 334-335.
9. Bilsen FA. On the interaction of a sound with its repetitions. Waltman. 1968.
10. Xiang N, Xie B, Shi B. Decorrelating audio signals for stereophonic and surround sound using codedand maximum-length-class sequences. US Patent No. 9025776. 2015.
11. Hu Y, Loizou PC. Evaluation of objective quality measures for speech enhancement. IEEE Trans Audio
Speech Lang Process. 2008;16(1): 229-238.
12. Ma J, Hu Y, Loizou PC. Objective measures for predicting speech intelligibility in noisy conditions
based on new band-importance functions. J Acoust Soc Am. 2009; 125(5): 3387-3405.
13. Beerends JG, Hekstra AP, Rix AW, et al. Perceptual evaluation of speech quality (PESQ) - The new
ITU standard for end-to-end speech quality assessment - Part II - Psychoacoust model. J Audio Eng
Soc. 2002; 50(10): 765-778.
14. ITU-R Recommendation BS.1387-1. Method for objective measurements of perceived audio quality.
2001.

7246