‫‪ELIMINATING THE EFFECT OF STUDIO WALL‬‬
‫‪RESONANCE AND THE COINCIDENCE‬‬
‫‪PHENOMENA FOR NOISY SPEECH‬‬
‫‪RECORDING‬‬
‫إزالة تأثير الضوضاء عند التردد الرنيني للحوائط و عند ظاهرة التطابق‬
‫داخل استوديوهات تسجيل الصوت‬
‫‪ABDALLA, MAHMOUD IBRAHIM‬‬
‫‪Electronics & Comm.dept., Faculty of Eng. ZagazigUniv.‬‬
‫الملخص العربي‪:‬‬
‫ه ذ اا حث ذذدا تذذيةاجتي ذذلاعيلذذيااحوديحعذذلا ذذج يل هيتاج ذذعلاا حت ذ ت‪-‬ا حجذذتاجيلذذيا ذذج ي و ياه ذ اا ذذية‪-‬ا ا حذذباثيقةتذذلا‬
‫قجتيي لاغلقاوكلفذلانذطايقةذسا ذج ي ةاويتذتاققوذت‪.‬اإطا حدذي ا حتذ جتاحوثذييتاا و ذج يل هيتا كذ طا ذد فيانيذيا حج اذقييا‬
‫اااا ا تذيةا حث ذداجتذو ةاحوق ذ ا‪ Coincidence phenomena‬حقيليذتاح ذ اا‬
‫ذج يل ا اكذ حبانيذيا ذيهقاا اااااااا‬
‫ققو ذذتا اءي ذذينفا اجيفلذ ذ فاعا ح ذذباحوديحع ذذلاو ذذكللا حد ذذي ا حتذ ذ جتاا ذذتا و ذذج يل هيتا اج ذذةا جث ذذيقاهذ ذ فا حجتي ذذلاا ذذتا عذ ذ يا‬
‫ح‬
‫ينا يقجا‬
‫ج يل ا اجةاإنيياا ويعا حج علاا حت جتاء‬
‫حا جذةا حذج لماوذطا ح‬
‫ذينا ا حذباءذي طا ذج ي ةا‬
‫أياوديحعيتات ج لاحأل ج يل ا‪.‬ا اه اا حجتي لاويي ثلاااتا يحلاج ةذاا حتينذيتا حذتاأوذيسطاج ذعلااثدذياءيي ذيابدون هددو ه‬
‫أنهتغيرهمناوهالبناءهانهاستخوا همناوهصنتيةهنهاختصارهأألجراءاتهالرنتينية‪.‬‬
‫‪ABSTRACT‬‬
‫‪This work introduces an economic solution for the problems of sound insulation of speech recording studios.‬‬
‫‪Sound insulation at wall resonance frequency is weak. Instead of acoustical treatment, a digital filter is used to‬‬
‫‪eliminate the effects of wall resonance and coincidence phenomena on recording of speech. Pole /zero placement‬‬
‫‪technique is used to calculate the IIR filter coefficients. The digital filter is designed, simulated, tested and‬‬
implemented. The proposed system is used to treat these problems and it is shown to be effective in recording
the noisy speech.
1. INTRODUCTION
Active noise control (ANC)
techniques have attracted much
research attention because they
provide numerous advantages over
conventional passive method [1-3].
The maximum external noise
spectrum must be reduced to the
background noise goal within the
space
(the
studio)
by
the
transmission loss of the walls,
window, ...etc. For insulating against
outside airborne sounds, general rule
is the heavier the wall, the better
insulation. The more massive the
wall, the more difficult it is for
sound waves in air to move in it to
and fro. The sound insulation of the
studio is weak at the resonance
frequency of the wall. To solve this
problem at speech recording studio,
acoustical treatment must be used. In
this work digital signal processing is
used instead of the acoustic
treatment to eliminate the effect of
noise at the studio wall resonance.
Another problem at speech recording
studio can be affected by the
external noise at the coincidence
frequency [4]. When coincidence
occurs it gives rise to a more
efficient transfer of energy from the
air to the wall to the air on the other
side of the wall of the studio. Thus
the effective insulation of the wall is
lowered producing” coincidence
dip” in the insulation curve [4].
Coincidence dip occurs in the
frequency range from 1.0 kHz to 4.0
kHz which includes important
speech frequencies. In this work
digital filter is designed to eliminate
the
effects
of
coincidence
phenomena on speech recording
environments. This technique is
cheap and effective in canceling the
noise at the desired frequencies.
2. DIGITAL FILTER DESIGN
A filter is essentially a system or
network that selectively changes the
wave-shape. Digital filters can be
used to separate signals that have
been combined, such as a musical
recording and noise added during the
recording process or to separate
signals into their constituent
frequencies. Analog filters can be
used to accomplish these tasks but
digital filters offer greater flexibility
and accuracy than analog filters.
Analog filters can be cheaper, faster
and have greater dynamic range;
digital filters are more flexible than
analog filters [5]. The ability to
create filters that have arbitrary
shape frequency response curve, and
filters that meet performance
constraints such as bandpass width
and transition region width, is well
beyond that of analog filters. Digital
filters are broadly divided into two
classes, namely infinite impulse
response (IIR) and finite impulse
response (FIR) filters. The IIR filter
equation can be expressed in a
recursive form as:

m
k 0
k 1
Y (n)   ak x(n  k )   bk y (n  k )
(1)
Where the ak and bk are the
coefficients of the filter. Equation
(1) can be written in the form of
transfer function as:
a0  a1 z 1  a2 z 2  ....  an z  n
(2)
H ( z) 
1  b1 z 1  b2 z 2  .....  bm z m
It is clear that the current output
sample Y(n) is a function of past
outputs as well as present and past
input. The choice between FIR and
IIR filters depends largely on the
relative advantages for the filter
types[5]. FIR filter requires more
coefficients for sharp cutoff filters
than IIR types. Design of a digital
filter involves five steps [6] which
can be summarized as follows:
1-Specification of the filter
requirement:
Requirement specifications include
specifying signal characteristics, the
characteristics of the filter (desired
amplitude and /or phase response),
the manner of implementation (as
high level language routine or DSP
processor-based system), and the
cost.
1-Coefficients calculation:
There are many methods to calculate
the values of the coefficients ak or bk
for IIR filter, such that the filter
characteristics are satisfied. Impulse
invariant method and bilinear
transformation as well as poles –
zeros placement can be used to
calculate the IIR coefficients [7].
3-Representation of a filter by
suitable structure (realization)
Realization involves converting a
given transfer function into a
suitable structure block. Flow
diagrams are often used to depict
filter structure and they show the
computational
procedure
for
implementation of the filter.
4- Implementation calculated the
filter coefficients, chosen a suitable
structure, and verifying that the filter
is stable, the difference equation can
be implemented as software routine
or in hardware. Whatever the
method of implementation, the
output of the filter must be
computed. To implement a filter the
following basic building blocks are
needed:
(i)Memory for storing filter
coefficients (ROM).
(ii)Memory (RAM) for storing the
present and past inputs and output.
(iii)Hardware or software multiplier.
(iv)Adder arithmetic logic units.
(v)Registers (to represent the delay
elements).
2.1 POLE- ZERO PLACEMENT
Frequency response of discrete time
system can be obtained from Ztransform using several methods [8].
Geometric evaluation of frequency
response method is based on its
pole-zero diagram. If the transfer
function is given by[7] :
n
H ( z) 

 (z  p )
H ( e jT ) 
Or :
k (e jT  z1 )(e jT  z 2 )
(e jT  p1 )(e jT  p2 )
H(e jT ) 
kU11U 2  2
(4)
V11V2  2
Where U1 and U2 represent the
amplitude of the vectors from the
zeros to the point Z= ejT and V1 and
V2 represent the amplitude of the
vectors from the poles to the same
point as shown in Fig.1. Thus the
magnitude and the phase response
for the system are:
H(e jT ) 
 H (e
k ( z  zi )
i 1
m
Fig.1. In this case the frequency
response is given by:
jT
U1 U 2
V1 V2
with k=1 (5)
)  1   2  ( 1   2 ) (6)
(3)
i
i 1
The frequency response is obtained
by substitution with z=ejT in
equation (3), where T is the
sampling time. A geometric
interpretation of Eq. (3) with only
two zeros and two poles is shown in
The complete frequency response is
obtained by evaluating H(ejT ) as the
point p moves from zero to z=-1. It
is evident that as the point p moves
closer to pole p1, the length of the
vector V1 decreases and so the
magnitude response, H(ejT ) ,
increases. On the other hand, as the
point p moves closer to the zero z1,
the zero vector U1 decrease and so
the magnitude response, H(ejT ) ,
decreases. Thus at the pole the
magnitude response exhibits a peak
whereas, at the zero, the magnitude
response falls to zero. The design of
the proposed filter is based on this
principle.
signal is recorded in the presence of
noise at wall resonance frequency.
The filter is implemented using the
software and the signal is fed to the
computer with loading the digital
filter to reject the noise. The output
of the filter is recorded. The
recorded signal is replayed again.
3. EXPERMINTS
4. RESULTS AND DISCUSSION
The measurements were carried out
at the Building Research Center at
Dokki (Giza, Egypt) using Bruel &
Kajer instrumentation. The sound
source type 4205 genrates a steady
noise which is filtered in octave
band. A rotating microphone boom
type 3923 is used t sweep the
microphone around a circular path.
The sound pressure detected by the
microphone is integrated over an
approperiated length of time by the
bulding acoustic analyzer 4417. The
sound insulation of the walls of the
studio is measured. From the sound
transmission
loss
curve,
the
resonance frequency of the studio
wall is deduced. The coincidence
phenomena is observed from the
same curve. After determining the
filter specification, it is designed.
Measurements were carried out to
test the system. The noise source is
located outside the studio, speech
The problem is to reject the
component of noise at the resonance
of the studio walls. So the resonance
frequency of the walls must be
calculated. Also the frequency at
which the coincidence occurred must
be calculated. These frequencies can
be observed by investigating the
sound insulation of the walls of the
studio. The sound reduction
(transmission loss) can be calculated
from the relation [4,9]:
S
R  L1  L 2  10 log 10 ( ) dB
A
(7)
Where
L1 : average sound pressure level
outside the studio.
L2 : average sound pressure level in
the studio.
S : area of the separated partition.
A : equivalent absorption area in the
studio.
The sound absorption area in the
studio can be determined from the
relation:
A
0.161V
T
(8)
transfer function can be calculated
and is given by:
H1 ( z ) 
z 2  1.9292 z  0.9999
z 2  1.9098 z  0.9798
(9)
V : volume of the studio.
T : reverberation time in the studio.
Fig.2 illustrates the measured values
of the apparent air-borne sound
insulation of the studio. The
resonance frequency is observed
from the curve which is 315Hz. To
reject the component at 315Hz, a
pair of complex zeros are placed on
the unit circle corresponding to 315
Hz, that is at angle of 360*315/7400,
1= + 14.175, 2= -14.175. The
sampling frequency is taken to be
7.4 kHZ. To achieve a sharp notch
filter and improved amplitude
response on either side of the notch
frequency, a pair of complex
conjugate poles are placed at a
radius r1. The width of the notch is
determined by the location of poles
at angles of +14.175 and -14.175.
The poles –zero placement technique
is used to calculate the poles and
zeros. Substituting with the zeros
and poles in equation (3), the
This is the transfer function of the
filter to reject the noise at the
frequency of 315 Hz which is the
resonance of the wall of the studio.
From the sound transmission loss
measurements given in Fig.2, it is
observed that the coincidence
occurred at frequency of 2500 Hz.
To reject the noise at this frequency
a pair of complex zeros are placed at
an angle of 360*2500/7400,
1=121.32, 2=- 121.32. To
achieve a sharp notch filter and
improved amplitude response on
either side of notch filter, a pair of
complex conjugate poles are placed
at radius of r1. The radius r of the
pole is determined by the desired
bandwidth.
An
approximated
relationship between the radius, r,
(For r> 0.9) and the bandwidth,
(BW), is given in[6], [10] where:
r= 1-(BW)/f) 
(10)
Where f is the frequency. ‘r’ in this
work is taken to be .99 of the unit
circle. ‘r’ is taken .99 to locate the
poles near the unit circle so that the
amplitude of the frequency response
is minimum.
To eliminate the effect of
coincidence phenomena at 2500Hz,
the transfer function of the digital
filter is calculated and it has the
form:
z 2  1.0398 z  0.9998
H 2 ( z)  2
z  1.0294 z  0.9806
(11)
This filter rejects the noise at the
coincidence frequency. Finally the
two filters are implemented together
and the total transfer function is
given by:
H ( z)  H1 ( z) * H 2 ( z)
(12)
The transfer function of the filter is
factored and expressed as the
product of second order sections and
is given by:
H ( z) 
(1  1.929 z 1  0.999 z 2 )(1  1.0398 z 1  0.9998 z 2 )
(1  1.9098 z 1  0.979 z 2 )(1  1.029 z 1  0.9806 z 2 )
(13)
The difference equation of the filter
is given by:
w1 (n)  x(n)  1.9098w1 (n  1)  0.979w1 (n  2)
y1 (n)  w1 (n)  1.929w1 (n  1)  0.999w1 (n  2)
y1 (n)  w1 (n)  1.9292w1 (n  1)  0.999w1 (n  2)
y(n)  w2 (n)  1.0398w2 (n  1)  0.9806w2 (n  2)
w2 (n)  y (n)  1.029w2 (n  1)  0.9806w2 (n  2)
Canonic structure can be used to
realize the filter to save the delayed
elements.
Fig. 3 shows the block diagram
representation of the filter. The
frequency response of the filter is
given in Fig.4. It is clear that the
filter rejects the noisy speech at 315
and 2500 Hz. After implementing
the filter, the filter performance is
analyzed to ensure its performance.
Fig.5 shows poles and zeros of the
filter. It is clear from zooming of
Fig.5 that the poles are inside the
unit circle while the zeroes are on
the unit circle. Fig.6 illustrates that
the zeros are on the unite circle
while the poles are inside the unite
circle. When the filter order is higher
than three, direct realization of the
filter is very sensitive to the finite
wold length effects [11-14]. The
effect of using a finite number of bits
is to degrade the performance of the
filter and in some cases, it makes the
filter unstable. The designer must
analyze these effects and choose
suitable word lengths for the filter
coefficients. The main sources of
performance degradation in digital
filter are input/output quantization,
coefficient quantization, arithmetic
round off errors and overflow which
occurs when the result of an
operation exceeds permissible wordlength. The primary effect of
quantizing the filter coefficients into
a finite number of bits is to alter the
positions of the poles and zeros of
H(z) in the z-plan. The poles will be
close to the unit circle so that any
significant deviation in them could
make the filter unstable. Table 1
illustrates the filter coefficients after
quantization. The fewer the number
of bits used to represent the
coefficient the more will be the
deviation in the poles and zeros
positions. Large-scale overflow
occurs at the output of the adders
and may be prevented by scaling the
input to the adders in such a way that
the outputs are kept low. Table 1
shows that the first the poles and
zeros have an overflow.
Normalization is required to solve
this problem overflow. Principle of
scaling is applied to avoid the
occurrence of overflow errors[13].
The quantized coefficients are
calculated and normalized to avoid
the overflows. Table 2 shows the
filter coefficients after
normalization. The word-length is
found to be 16 bits for the bit word
length while 15 bits for the bit
fraction length, while summing node
is found to be 32 bits for wold and
30 bits for fraction word length.
After designing the filter, the system
is tested experimentally. The noise
source is located outside the studio.
The speech signal is recorded with
the presence of filter and without it.
Fig.7 and Fig.8 show the spectrum
of each signal. The quantized
coefficients are calculated and
normalized to avoid overflows. The
word length is found to 16 bits for
the bit word length while 15 bits for
fraction length, while for summing
node it is found to be 32 bits for the
bit word length while 30 bits for
fraction length.
5. CONCLUSION
An economic technique is
introduced and applied successfully
to eliminate the effects of wall
resonance and coincidence
phenomena on the sound insulation.
The proposed technique is designed,
simulated, and tested. The
experiments show that this method
can be applied in the case of
recording noisy speech in studio
especially after building the studio
instead of acoustical treatment.
REFRENCES
[1] Mingsian R. Yujeng Lin and Jiana
Dawu ”Analysis and DSP
Implementation of a Broadband
Duct ANC System Using Spatially
Feed forward Structure” Journal
of Vibration and Acoustics, April
2001, Vol. 123., 2001
[2] S. J. Elliott and P. A. Nelson “Active
Noise Control” IEEE signal
Processing Mag. 10, No. 4, pp. 1235, 1993.
[3] S. M. Kuo and D.J. Morgan, “Active
Noise Control Systems: Algorithms
and DSP Implementation”, Wiley ,
New York, 1995.
[4] K. B. Ginn, ” Architectural
Acoustics” Bruel & Kjaer, 1978,
Denemark, Copenhagen.
[5] I. W. Selesnick and C.S. Burrus
“Generalized Digital Filter Design”
Proceeding of the IEEE Int. Conf.
Acoustics, speech , Signal
processing , Vol.3, May 1996.
[6] Emmanuel C. Ifeacher and Barrie
W. Jarvis “ Digital Signal
Processing ;A practical Approach”
ADDISON WESLEY PUBLISHING
COMPANY, New YORK 1993.
[7] J.G. Proakis and D.G. Manolakis
”Digital signal processing:
Principles, Algorithms, and
Applications” Englewood Cliffs,
NJ: Prentice Hall,1996.
[8] L. B. Jackson, “Digital Filter and
Signal Processing” Third Ed.,
Boston Kluwer Academic
Publishers, 1989.
[9] ISO 140 , 1978 "Measurement of
sound insulation in building ",
Bruel & Kjaer, Denmark
[10] T. W. Parks and C. S. Burrus,
“Digital Filter Design”, Newyork;
John Wiley & Sons 1987.
[11] Andreas Antonious,” Digital
Filters”, Second Edition, McGrawHill, Inc, 1994.
[12] P. Lapsley, A. Shoham and E. A.
Lee, “ DSP Processor
Fundamental”, IEEE Press, 1997.
[13] S. K. Mitra ,” Digital Signal
Processing: A Computer – Based
Approach”, McGraw-Hill, Inc
1998.
[14] C. Moler, “Floating Points: IEEE
Standard unifies arithmetic model”
Cleve’s Corner, The Mathwoks,
Inc, 1996.
Table 1. The filter coefficients after quantization
Numerator:
Reference Coefficients
0.999969482421875
-.889404296875000
-.0060119628906250
-.889499999999960
.999786376953125
(1)
(2)
(3)
(4)
(5)
Denominator:
Reference Coefficients
(1)
.999969482421875
(2)
-.880004882812500
(3)
-.006011962890625
(4)
-.859985351562500
(5)
. 959991455078125
Quantized Coefficients
1.000000000000
-.88939999999999970
-.006000000000000
-.889495849609375
.9998000000000000
Quantized Coefficients
1.0000000000000000
-.88000000000000000
-.0060000000000000
-.8599999999999999
.95999999999999960
Table 2. The filter coefficients after normalization‫ه‬
Numerator:
Reference Coefficients
(1) .999969482421875
(2) -.889373779296875
(3) -.006011962890625
(4) -.889465332031250
(5) .9997558593750000
Denominator:
Reference Coefficients
(1) .999969482421875
(2) -.879974365234375
(3) -.006011962890625
(4) -.859985351562500
(5) .959960937500000
Quantized Coefficients
.9996948242187000
-.889372857666015590
- .005999816894531250
-.889472854614257740
.999769488525390600
Quantized Coefficients
.999969482421875000
-.879973144531249970
-.005999816894531250
-.859973754882812470
.959970703124999990
V1
p1
p
U1
U2
z2
z1
V2
p2
Fig.1. Geometric evaluation of the frequency response from the
pole–zero diagram
Y1(n)
1.9
Z-1
-1.929
-1.029
-0.979
Z-1
0.999
0.999
-0.98
-1.929
Y(n)
W2(n)
Z-1
Z-1
1.039
w1(n)
0.999
x(n)
Fig.3. Block diagram representation of the proposed filter
‫ه‬
Fig.4. The frequency response of the digital filter
.
Fig.5. Location of poles and zeros of the filter
Fig.7. The recorded speech signal without using the filter
Fig.8. The recorded speech signal with the filter
Fig.6-a. Location of the first pole and zero after normalization
Fig.6-b. Location of the second pole and zero after normalization