PERFORMANCE EVALUATION OF A MODIFIED SUBBAND
NOISE CANCELLATION SYSTEM IN A NOISY ENVIRONMENT
Ali O. Abid Noor, Salina Abdul Samad and Aini Hussain
Department of Electrical, Electronic and System Engineering, Faculty of Engineering and Built Environment
University Kebangsaan Malaysia – UKM, Malaysia
Keywords: Noise Cancellation, Adaptive Filtering, Filter Banks.
Abstract: This paper presents a subband noise canceller with reduced residual noise. The canceller is developed by
modifying and optimizing an existing multirate filter bank that is used to improve the performance of a
conventional full-band adaptive filtering. The proposed system is aimed to overcome problems of slow
asymptotic convergence and high residual noise incorporating with the use of oversampled filter banks for
acoustic noise cancellation applications. Analysis and synthesis filters are optimized for minimum
amplitude distortion. The proposed scheme offers a simplified structure that without employing cross
adaptive filters or stop band filters reduces the effect of coloured components near the band edges in the
frequency response of the analysis filters. Issues of increasing convergence speed and decreasing the
residual noise at the system output are addressed. Performance under white and coloured environments is
evaluated in terms of mean square error MSE performance. Fast initial convergence was obtained with this
modification. Also a decrease in the amount of residual noise by approximately 10dB compared to an
equivalent subband model without modification was reachable under actual speech and background noise.
1 INTRODUCTION
Subband adaptive filtering using multirate filter
banks has been proposed in recent years to speed up
the convergence rate of the least mean square LMS
adaptive filter and to reduce the computational
expenses in acoustic environments (Petraglia and
Batalheiro, 2008). In this approach, multirate filter
banks are used to split the input signal into a number
of frequency bands, each serving as an input to a
separate adaptive filter. The subband decomposition
greatly reduces the update rate of the adaptive filters,
resulting in a much lower computational complexity.
Furthermore, subband signals are often
downsampled in a subband adaptive filter system,
this leads to a whitening effect of the input signals
and hence an improved convergence behavior.
In critically sampled filter banks, where the
number of subbands equals to the downsampling
factor, the presence of aliasing distortions requires
the use of adaptive cross filters between subbands
(Petraglia et al., 2000). However systems with cross
adaptive filters generally converge slowly and have
high computational cost, while gap filter banks
produce spectral holes which in turn lead to
significant signal distortion. Problems incorporating
with subband splitting have been treated in literature
regarding issues of increasing convergence rate (Lee
and Gan, 2004), lowering computational complexity
(Schüldt et al., 2000) and reducing input/output
delay (Ohno and Sakai, 1999).
Oversampled filter banks has been proposed as
the most appropriate solution to avoid aliasing
distortion associated with the use of critically
sampled filter banks (Cedric et al., 2006) . However
this solution implies higher computational
requirements than critically sampled one. In
addition, it has been demonstrated in literature that
oversampled filter banks themselves color the input
signal, which leads to under modelling (Sheikhzaheh
et al., 2003). These problems can be traced back to
the fact that oversampled subband input will likely
generate an ill-conditioned correlation matrix
(Deleon and Etter, 1995). In this case, the small
eigenvalues are generated by the roll off of the
subband input power spectrum. A pre-emphasis
filter for each subband is suggested by (Tam et al.,
2002) as a remedy for this slow asymptotic
convergence. An alternative approach to remove the
band edge components might be the use of a
238
Abid Noor A., Abdul Samad S. and Hussain A. (2009).
PERFORMANCE EVALUATION OF A MODIFIED SUBBAND NOISE CANCELLATION SYSTEM IN A NOISY ENVIRONMENT.
In Proceedings of the 6th International Conference on Informatics in Control, Automation and Robotics - Signal Processing, Systems Modeling and
Control, pages 238-243
DOI: 10.5220/0002222902380243
Copyright
c
 SciTePress

bandstop filters. But this has the undesirable effect
of introducing spectral gaps in the reconstructed full
band signal. Furthermore it was proved by
(Sheikhzaheh et al., 2003) that the introduction of
pre-emphasis filters has no considerable effects on
the convergence behaviour of a subband noise
canceller.
In this paper an alternative procedure is adopted
to improve the performance of a noise cancellation
system aimed to remove background noise from
speech signals. Different prototype filters are used in
the analysis and synthesis filter banks. The analysis
prototype filter is modified so that the coloured
components near the band edges are removed by
synthesis filtering, and then the analysis/synthesis
filter bank is optimized in the input/output
relationship to achieve minimum amplitude
distortion. Compared to literature designs (Deleon
and Etter, 1995) and (Cedric et al., 2006 ), this paper
bears three differences: first, different methods used
for the design of analysis and synthesis filter banks,
second, optimization is performed to reduce
amplitude distortion with negligible aliasing error
due to the use of highly oversampled filter banks and
third, the resulting design is implemented efficiently
for the removal of background noise from speech
signals.
The proposed modified oversampled subband
noise canceller offers a simplified structure that
without employing cross-filters or gap filter banks
decreases the residual noise at the system output.
Issues of increasing convergence rate and reducing
residual noise on steady state are addressed.
Performance under white and coloured environments
is evaluated in terms of mean square error MSE
convergence. Comparison is made with a
conventional full band scheme as well as with a
similar system with no modification. The paper is
organized as follows: in addition to this section,
section 2, formulates the subband noise cancellation
problem, section 3 describes the optimum
analysis/synthesis filters design, section 4 presents
simulation results with discusses the main aspects of
the results and section 5 warps up the paper with
concluding remarks.
2 SUBBAND NOISE CANCELLER
The original noise cancellation model described in
(Sayed, 2008) is extended to subband configuration
by the insertion of analysis/synthesis filter banks in
signal paths, as depicted by Figure 1.
Figure 1: The subband noise canceller.
Assigning uppercase letters for z-transform
representation of variables and processors, the noisy
speech and the background noise are split into
subbands by two sets of analysis filters. The subband
analysis filters is expressed in z-domain as
∑
−
=
−
=
1
0
)()(
L
m
m
kk
zmhzH
(1)
for k=0,1,2,….M-1.
Where k is the decomposition index, h(m) is the
impulse response of a finite impulse response filter
FIR , m is a time index, M is the number of
subbands and L is the filter length. Now, consider
the adaptation process in each individual branch
according to Figure 1, and let us define e(m) as the
error signal, y(m) is the output of the adaptive filter
calculated at the downsampled rate, ŵ(m) is the filter
coefficient vector at mth iteration, μ is the adaptation
step-size factor , α is proportional to the inverse of
the power input to the adaptive filter, and m is a time
index, then we have
)()(
ˆ
)( mmmy
k
k
T
k
xw= (2)
)()()( mymvme
kkk
−
=
(3)
)()()(
ˆ
)1(
ˆ
mmemm
kkkkkk
xww
α
μ
+
=
+
(4)
Relation (4) represents the subband normalized
LMS update of the branch adaptive filters. In z-
domain, relation (3) can be expressed as
)()()( zYzVzE
kkk
−
=
(5)
PERFORMANCE EVALUATION OF A MODIFIED SUBBAND NOISE CANCELLATION SYSTEM IN A NOISY
ENVIRONMENT
239

Where represents the downsample
subband noisy signal, and is the output of the
subband adaptive filter. The aim of the adaptive
process is to surpress the noisy component in
by equating it to leaving the subband input
undistorted. Each subband error signal is then
interpolated by upsampling and synthesis filtering.
The final output can be expressed as
)(zV
k
Y
)(zY
k
)(zV
k
)(z
k
)(zS
k
)()()(S
ˆ
1
0
zUzGz
kK
M
k
k
∑
−
=
=
(6)
Where represents the upsampled version
of the subband error signals .We assume a
highly oversampled filter bank, say two fold , the
aliasing components in (6) can be considered to be
very small and therefore neglected, hence the final
system equation can be represented as
)(zU
k
)(zE
k
)()()()(S
ˆ
1
0
zHzGzSz
kK
M
k
k
∑
−
=
=
(7)
If we constrain the analysis and synthesis filters
and respectively to be linear phase
finite impulse response FIR filters, then the term
in equation (7) describes the
amplitude distortion function of the system.
)(zH
k
1
0
G
K
M
k
∑
−
=
)(zG
k
)(z
k
)( Hz
The branch filters and can be
derived from single prototype filters
according to and
, where
W
.
),(zH
K
)(
k
zH =
M
),(zG
K
),(
0
zH
)(
k
M
zW
Mj
e
/2 π −
),(
0
zG
0
H
=
)()(
0
k
Mk
zWGzG =
This way, a uniform discrete Fourier transform
DFT filter banks are created. Let A(z) be the
distortion function ,in frequency domain, A(z) can be
represented as
)()()(
1
0
ωωω j
k
j
k
M
k
j
eGeHeA
∑
−
=
=
(8)
The objective is to find prototype filters
and to minimize A
d
(z) according
to
)(
0
ω j
eH
)(
0
ω j
eG
))(1(A
d
ω j
eA−=
(9)
Ideally should be zero i.e. a perfect
reconstruction filter bank. Relaxing the perfect
reconstruction property, we can tolerate small
amplitude distortion; and then we can have
frequency selective filters in a near perfect
reconstruction NPR filter bank.
d
A
3 ANALYSIS/SYNTHESIS
PROTOTYPE FILTER DESIGN
The aim of the prototype filter design is to build a
complementary analysis and syntheses filter banks,
so that the reconstructed output signal has a very low
distortion. Different prototype filters for analysis and
synthesis filter banks are designed. The analysis and
synthesis prototype filters are selected as in Figure 2.
The cut off frequency of the analysis prototype
filter is given by
c
f
2/)(
sapa
c
fff
+
=
(10)
provided that .
sspa
ff >
Where f
pa
is the end of the passband of the
analysis filter, f
sa
is the beginning of the stopband of
the analysis filter; f
ss
is the beginning of the stopband
of the synthesis filter.
f
pa
Magnitude
Synthesis
Analysis
f
p
f
s
f
s
Frequenc
y
Figure 2: Analysis/Synthesis filters design.
The 3dB down of the prototype synthesis filter
(normalized) (1 /2 M ) is determined by the number
of subbands M, whereas the analysis filter
bandwidth is larger and only limited by the
decimation factor D according to
sapa
ff
D
+
≤
2
(11)
where D is the largest integer less than or equal to
the right hand side term of (11), f
pa
and f
pa
are
normalized to the sampling frequency. Values for D
ICINCO 2009 - 6th International Conference on Informatics in Control, Automation and Robotics
240

such that the ratio
M/D =2 i.e. two fold over
sampled found to be the best in terms of alias
cancellation.
The design algorithm starts by designing cut off
frequencies for an arbitrary analysis and synthesis
prototype filters. The analysis prototype filter is
optimized using Parks McClellan algorithm to meet
requirements in (10). With analysis prototype filter
fixed, the synthesis prototype filter is optimized by
minimizing the distortion function given by (9) over
the frequency grid in the band [0-π].Figure 3 depicts
steps the design procedure and Figure 4 shows a
reconstruction error comparison between the
modified oversampled filter bank and an equivalent
conventional oversampled filter bank.
Figure 3: Steps of design algorithm.
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
-15.5
-15
-14.5
-14
-13.5
-13
-12.5
-12
Reconstruction Error
Normalized Frequency
A
d
(e
j
ω
) [dB]
MOSFB
OSFB
Figure 4: Reconstruction error comparison of the modified
filter bank MOSFB and an equivalent conventional
oversampled filter bank OSFB.
Analysis and synthesis filter banks can be
implemented efficiently using polyphase
representation of a single prototype filter followed
by fast Fourier transforms FFT.
4 RESULTS AND DISCUSSION
The noise path used in these tests is an
approximation of a small room impulse response
modelled by a FIR processor of 256 taps. The
number of subbands M=8, downsampling factor
D=4, prototype filters order is 128.To measure the
convergence of the subband noise canceller, a
variable frequency sinusoid was corrupted with
white Gaussian noise that was passed through a
transfer function representing the acoustic path. The
corrupted signal was then applied to the primary
input of the noise canceller; regarding zero mean,
white Gaussian noise is applied to the reference
input. A subband power normalized version of the
LMS algorithm is used for adaptation. Mean square
error MSE convergence is used as a measure of
performance. Plots of MSE were produced and
smoothed with a suitable moving average filter. A
comparison is made with a conventional fullband
system as well as with an oversampled system
without modification. The unmodified oversampled
subband noise canceller is denoted with OSSNC and
the modified system is denoted with MOSSNC.
Results are depicted in Figures 5 and 6.
To test the behaviour under real environmental
conditions, a speech signal is then applied to the
primary input of the proposed noise canceller. The
speech is a Malay utterance “Kosong, Satu, Dua,
Tiga” spoken by a woman, sampled at 16 kHz.
Different types of background interference were
used to corrupt the aforementioned speech. MSE
plots are produced for two cases: Figure 7 for the
case of machinery noise as background interference
and in Figure 8 for the case of a cocktail party i.e.
disturbance by another speech.
Apart from the fast initial convergence, it is clear
from Figure 5, that the mean square error (MSE)
plot of the oversampled subband system OSSNC
levels off quickly before the MSE plot of the
fullband system. This is obviously due to the
inability to properly model the presence of coloured
components near the band edges of the filter bank.
During initial convergence the subband system
performs better than the fullband system but is less
effective afterward. On the other hand, the MSE
convergence of the modified system MOSNC
outperforms that of the fullband system during initial
convergence and exhibits comparable steady state
performance as shown by Figure 6. It is obvious that
while the MSE of the fullband system converging in
slow asymptotic way, the MOSNC system reaches a
steady in 2000 iterations. The fullband system needs
more than 6000 iterations to reach the same noise
PERFORMANCE EVALUATION OF A MODIFIED SUBBAND NOISE CANCELLATION SYSTEM IN A NOISY
ENVIRONMENT
241

cancellation level. The main difference between
Figure 5 and Figure 6 is in the amount of residual
noise which has been g reduced with the MOSSNC.
Results obtained for actual speech and background
noise (Figures 7 and 8) prove that the fullband
system cannot model properly with coloured noise
as the input to the adaptive filters, and the residual
error can be sever when the environment noise is
highly coloured. Tests performed in this part of the
experiment proved that the MOSSNC does have
improved performance compared to OSSNC and the
full-band model. Depending on the type of the
interference, the improvement in reducing resedual
noise n varies from 15-20 dB better than full-band
case.
2000 4000 6000 8000 10000 12000
-35
-30
-25
-20
-15
-10
-5
0
iteration
MSE dB
Fullband system
OSSNC
1
2
1
2
Figure 5: MSE convergence behaviour of OSSNC under
white Gaussian noise.
2000 4000 6000 8000 10000 12000
-35
-30
-25
-20
-15
-10
-5
0
iteration
MSE dB
Fullband system
MOSSNC
1
2
1
2
Figure 6: MSE convergence behaviour of MOSSNC under
white Gaussian noise.
0.5 1 1.5 2 2.5
x10
4
-40
-35
-30
-25
-20
-15
-10
-5
0
iteration
MSE dB
1
1
2
3
3
2
MOSSNC
Fullband system
OSSNC
Figure 7: Performance comparison under actual speech
and machinery noise.
0.5 1 1.5 2 2.5 3
x 10
4
-50
-45
-40
-35
-30
-25
-20
-15
-10
-5
0
iteration
MSE dB
MOSSNC
Fullband system
OSSNC
1
2
3
3
1
2
Figure 8: Performance comparison under actual speech
disturbed by another speech.
5 CONCLUSIONS
In this work, an oversampled subband noise
canceller with modified filter bank is developed to
overcome the problem of slowly converging
components associated with the usual oversampled
subband scheme. An efficient optimized DFT filter
bank is used in the canceller. The analysis filter bank
is modified to remove slowly converging
components near band edges, while the synthesis
filter bank is optimized to minimize input/output
distortion.The modified system has shown improved
performance compared to a similar scheme with
conventional oversampled filter bank. The
convergence behaviour under white and coloured
ICINCO 2009 - 6th International Conference on Informatics in Control, Automation and Robotics
242

environments is greatly improved. The amount of
residual noise is reduced by 15-10dB under actual
speech and background noise. The next logical step
is to realize this system on a suitable DSP processor
such as the Texas C6000 to prove the validity of the
method for noise cancellation. Also, other types of
filter banks and transforms can be investigated and
used for the same purpose.
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