This document proposes a novel approach to decorrelating stereo acoustic signals for acoustic echo cancellation based on the psychoacoustic phenomenon of the "missing fundamental". The approach tracks and removes the pitch from one channel of the stereo signal using an adaptive notch filter, which greatly reduces inter-channel coherence in the lower spectrum without affecting signal quality. Experimental results show the proposed approach provides significant coherence reduction and faster convergence speed of adaptive filters compared to a masked noise injection method, while better preserving the stereo quality.

1. A NOVEL APPROACH TO CHANNEL
DECORRELATION FOR STEREO ACOUSTIC ECHO
CANCELLATION BASED ON MISSING
FUNDAMENTAL THEORY
L. Romoli, S. Cecchi, L. Palestini, P. Peretti and F. Piazza
A3Lab - DIBET - Università Politecnica delle Marche
Via Brecce Bianche 1, 60131 Ancona Italy
www.a3lab.dibet.univpm.it
Decorrelation is a well known issue in the context of
Stereophonic Acoustic Echo Cancellation: it is related to the
problem of uniquely identifying each pair of room acoustic
paths, due to high inter-channel coherence. In this paper, a
novel approach to decorrelate a stereo signal based on the
missing fundamental phenomenon is proposed. An adaptive
algorithm is employed to track the behavior of one of the two
channels, ensuring a continuous decorrelation without affecting
the stereo quality. Several results are presented comparing our
approach with Masked Noise injection method in terms of
Magnitude Square Coherence, Itakura Saito measure and
Convergence Speed of adaptive filters in order to confirm the
validity of the proposed approach.
Abstract
Stereophonic Acoustic Echo Cancellers:
1. Introduction
used in teleconferencing systems with several participants
to give spatial information for identifying speakers positions.
Non uniqueness problem:
a linear relation between the two channels of the stereo
signal exists. Therefore, a method to decorrelate the input
channels must be introduced in order to obtain a suitable
signal for echo cancellation [1, 2, 3, 4, 5, 6, 7, 8, 9].
Objective of this work
Starting from the psychoacoustic effect of the missing
fundamental, a new approach is derived iteratively modifying
one of the two channel, obtaining a great decorrelation in the
lower part of the spectrum without affecting the signal quality.
The novelty of the approach is the great inter-channel
coherence reduction obtained in a frequency band, where signal
alteration tipically causes a degradation of the signal quality.
2. Missing fundamental theory
The missing fundamental effect is a well known psychoacoustic
phenomenon based on the perception of a pitch (i.e. the
fundamental frequency) without the corresponding frequency
actually being contained in the signal (Fig. 1) [10].
This effect is usually employed to enhance low frequency sound
reproduction (e.g. in case of small loudspeakers characterized
by a limited frequency extension [11]).
Otherwise, our approach exploits it to weaken the relation
between the two channels, especially in the lower part of the
spectrum.
3. Proposed algorithm
The proposed approach is based on an adaptive algorithm able
to estimate and remove the pitch, using an adaptive notch filter
[12]. The algorithm is applied only on one channel of the stereo
signal, in order to decrease the inter-channel coherence.
Figure 2: Overall scheme of
the proposed approach.
Figure 3: Structure of the
adaptive notch filter.
Fig. 2 shows a block diagram of the entire proposed algorithm,
which can be summarized as follows:
1. low-pass filter, in order to act just on the desired frequency
range;
2. down-sampling by a factor M, in order to increase spectral
resolution;
3. pitch estimation and removal using the adaptive notch filter
(given by a second order lattice form [13]):
21
0
21
0
)1(1
21
)( 




zzk
zzk
zH

4. up-sampling by a factor M;
5. sum of the up-sampled signal and the delayed high-pass
filtered signal.
Adaptive coefficient k0 (related to the tracked frequency):
where λ is a forgetting factor close to 1 and y(n) is the all-pole
filtered version of the input signal x(n) as shown in Fig. 3.
 
))((cos
2
1
)(
)()1()()(
)2()()1(2)1()(
)1(4)1()(
)(
)(
)(
0
1
0
000
2
0
nknf
nknknk
nynynynCnC
nynDnD
nD
nC
nk










Figure 1: Intermodulation effect of the human ear.
Estimated frequency:
where fs is the sampling frequency.
))((cos
2
1
)( 0
1
0 nk
M
f
f
M
f
nf ss
est  


2. 4. Experimental results
Conclusions
References
New approach proposed for stereophonic
decorrelation, based on the psychoacoustic
effect of the missing fundamental.
Decorrelation performed by tracking and
removing the pitch of just one of the two
channels.
Method applied only on [0:500] Hz band,
where the pitch is typically contained.
Good reduction of the MSC obtained only on
the band around the estimated pitch, while
the spectrum out of this band is equal to
the original one.
Increased convergence speed clearly visible
in [0:500] Hz band.
Stereo perception preserved.
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Evaluation parameters:
• Magnitude Squared Coherence (MSC) as measure of inter-
channel coherence;
• Itakura Saito Measure (ISM) as index of signal quality [14];
• Misalignment as measure of convergence speed.
Fig. 4 shows how the coherence reduction increases when the
contraction factor α is reduced (a great value for α corresponds
to a narrow filter's bandwidth).
Tab. 1 shows how the ISM decreases, i.e. the audio signal
quality is better, when the contraction factor α is increased (the
ISM has been calculated for the channel of the stereo signal on
which the proposed method has been applied).
α ISMband ISM
0.1 0.5528 0.2749
0.3 0.4704 0.2288
0.6 0.3136 0.1546
0.9 0.2114 0.0688
Figure 4: Zoom of the MSC in the
band [0:500] Hz for different
values of contraction factor α.
Table 1: ISM for different
values of contraction
factor α.
Test setup conditions:
• speech with fs=16 kHz (high initial inter-channel coherence);
• injection of spectrally shaped noise [9] on each channel in
[0:500] Hz band (in order to make consistent comparisons
with the proposed approach).
As it can be seen from Fig. 4, the MSC reduction of the masked
noise approach is greater but localized in the frequencies band
of [0:100] Hz. On the other hand, our approach shows a MSC
reduction comparable with the other technique and more
spread on the frequencies range of interest.
The obtained values for ISM (ISMband=0.1127 and
ISM=0.0168, calculated for one of the two channels as for the
proposed approach), in comparison with Tab. 1, show a
reduction of the distortion introduced by this technique with
respect to our approach, confirming its effectiveness for a small
frequency range.
Test setup conditions:
• transmission room not considered (the stereophonic signal has
been applied directly to SAEC);
• simulated impulse responses (IRs) at the receiving room with
a reverberation time of about 128 ms (RT60);
• adaptive filters of the same length as the IRs (2048 samples);
• improved Normalized Least Mean Square (NLMS) algorithm
[14];
• misalignment calculated only for [0:500] Hz band, to better
underline the achieved results for the band of interest.
Fig.5 shows an increase of the convergence speed for both
techniques, but a greater improvement of our approach is
clearly visible: about 10 dB after 20 sec up to more than 15 dB
after 40 sec. For the sake of brevity, the Echo Return Loss
Enhancement (ERLE) has not been reported even if some tests
have been done: as expected, its behaviour reflects
misalingment performances.
Figure 5: Misalignment for different values of contraction factor
α and for masked noise approach in [0:500] Hz.
We also performed some informal listening tests by playing the
original and the modified stereo signals.
The stereo perception is preserved; it is possible to perceive
just a fine variation of the pitch that does not influence
stereophonic reproduction.
Test setup conditions:
• speech with fs=16 kHz (high initial inter-channel coherence);
• proposed approach applied on the first channel in [0:500] Hz
band (where the pitch is tipically contained);
• filtering with a pair of complementary low-pass and high-pass
filters with fcut-off=500 Hz;
• decimation factor M=16;
• λ=0.9 and ρ=0.5 [12, 13].
4.1 MSC and ISM evaluation of the proposed approach
4.2 Comparison with masked noise approach
4.3 Convergence speed evaluation
4.4 Informal listening tests
Future works oriented towards a subband
structure to combine the proposed approach
for low frequencies with other techniques.