In this paper, we propose a new algorithm for the detection of howling signal employing LMS adaptive notch filter and digital phase locked loop. The main ...
A NEW ALGORITHM FOR HOWLING DETECTION Jianqiang Wei, Limin Du, Zhe Chen, Fuliang Yin Institute of Acoustics Chinese Academy of Sciences Beijing 100080, China
ABSTRACT In this paper, we propose a new algorithm for the detection of howling signal employing LMS adaptive notch filter and digital phase locked loop. The main advantages of the proposed algorithm are that it has very low computational complexity and has a short detection delay. Computer simulations are given to demonstrate the performance of this method.
1. INTRODUCTION In many acoustic equipments such as hand-free telephone and videoconference, the channel, i.e. acoustic couple path, forms a closed loop. The basic structure of acoustic couple path in acoustic equipments is shown in Figure 1, which includes acoustic equipment, loudspeaker and microphone. High volume level output at the loudspeaker can cause the loop to get into an oscillatory mode, usually referred to as howling. It not only disturbs normal communication, but also damages power amplifier for overload. This is undesirable and this problem can be combated by reducing the total loop gain with the insertion of an attenuation unit if howling is detected. Hence, it is crucial to detect howling signal in these cases.
howling condition, both near-end signals and received signals consist of a strong (unwanted) sinusoid waveform at the oscillation frequency, along with noisekpeech. That is to say, when being howling, the frequency of signals in location A, B, C and D shown in Figure 1 are same, but their phase are different. Moreover, the phase difference changes slowly and the change rate is about second-level.
3. HOWLING DETECTION BASED ON LMS ADAPTIVE NOTCH FILTER Howling detection can be considered as the detection of narrowband (sinusoid) noise from the broadband speech signal and can be achieved by using an adaptive notch filter [SI. Several .forms of the adaptive notch filter can be found in previous papers [4][5]. In this paper, we consider a LMS adaptive notch filter with only two adaptive parameters. The structure of howling detection based on LMS adaptive notch filter is shown in Figure 2, where the howling detector is composed of LMS adaptive filter and 90' phase shifter.
Traditional algorithms for the detection of howling signal are usually designed using adaptive notch filter. A recent paper on howling control by S. M. Kou and J. Chen [4] generalizes the conventional methods. Their approach is based on the LMS algorithm and IIR adaptive notch filter. In this paper, we propose a novel algorithm for the detection of howling signal based on LMS adaptive notch filter and digital phase locked loop. The proposed algorithm has not only very low computational complexity but also a short detection delay. Intensive computer simulations illustrate that it really works well.
I
I
M algorithm Figure 2. Howling detection based on LMS adaptive notch filter. One input of the adaptive filter is x, (n), and after undergoing 90' phase shift giving another input x,(n) . The output of the adaptive filter is given by
Figure 1. The basic structure of acoustic couple path in acoustic equipment.
A n ) = w,(n)x,( n )+ w, Consequently, the error signal
2. HOWLING Howling phenomenon can be explained as signal feedback inphase at a particular frequency that is further amplified until it can be perceived by the listeners. It is evident that, under the
0-7803-7761-3/03/$17.0002003 IEEE
(n)
(1)
e(n) is given by
e@) = 0 ) -Y b )
(2)
The value of w,(n) and w,(n) are chosen using the LMS algorithm, so that the mean squared error E [ e ' ( n ) ] is
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minimized [ 1][2]. Thus, the update equation for weights w,(n) and w,(n) can be written as
w,(n + 1) = w,(n)+ 2 p e ( n ) x ,(n)
(3)
w,(n + 1) = w2(n)+ 2 p e ( n ) x 2 ( n )
(4)
where p is the step size. Based on howling signal property mentioned above, we know that, under the howling condition, the frequency of signal in location A, B, C and D shown in Figure 1 are same, however, their phase are different. Consequently, let A COS(~ , + tp a ) be the signal in location A, then the signal in location B is B COS( m , t + p h ). The reference input x ( n ) of Figure 2 is assumed to be the signal in location A shown in Figure 1, i.e.
x ( n ) = Acos(w,t
+ p#)
x , ( n ) = Asin(w,t
+ pu)
(5)
(6)
(8)
According to the triangle equations, B COS( ~ , + tp h ) which is included in d(n) can be entirely cancelled under the condition
B
that W,(n)=-cos(p, A
Figure 3. The math model of analog phase locked loop. It is easy to realize a digital phase locked loop based on this math model. The details of digital phase locked loop are as follows: Phase detector (PD) can be realized by a simple multiplier, i.e.
(7)
The primary input d(n) of Figure 2 is assumed to be the signal in location B shown in Figure 1, i.e.
d(n)= Bcos(w,t + p,,)
v CO
LPP
Then a Hilbert transform (90' phase shifter) is introduced to give the signal x 2( n ) which has 90' phase difference with X , ( n ) ,i.e.
x , ( n ) = Acos(w,t+pa)
An analog phase locked loop includes three parts [3]: phase detector (PD), loop low pass filter (LPF) and voltage controlled oscillator (VCO). The principle of analog phase locked loop is that: the reference input signal and the output signal of voltage controlled oscillator (VCO) is compared in phase detector (PD), in turn, the phase detector (PD) feeds back an error voltage signal in proportion to the phase difference. Then loop low pass filter (LPF) selects the voltage element which changes slowly, uses it to control voltage controlled oscillator (VCO), and makes its output frequency is as same as the reference input signal's. The math model of an analog phase locked loop is shown in Figure 3.
B . -pa) and w,(n)=--sin(pb -9") A
In conclusion, when being howling, the howling signal will come about in both location A and B shown in Figure 1. After a period of adapting, the output e(n) of LMS adaptive notch filter depicted in Figure 2 will become very little, that is to say, the energy of e(n) is far less than that of d ( n ) . In contrast, when no howling presents, the energy of e(n) is almost equal to that
pd(n) = ref(n)cos[2~p(n)]
where ref(n) is the reference input signal at time n , pd(n) is the input signal of loop low pass filter at time n and p(n) is the phase of VCO output signal at time n . Loop low pass filter (LPF) can be realized by a digital low pass filter which is designed properly, i.e.
lpf(n) = (1 -a)lpf(n -1)+apd(n)
n and a is the parameter that can decide the frequency property of loop low pass filter ( 0 < a < 1 ). It is little difficult to realize the integral section of voltage controlled oscillator (VCO). As depicted in Figure 3, this section has the property of low pass filtering. Consequently, it can be realized using a low pass filter, i.e.
o ( n + 1) = bo(n) +
4. HOWLING DETECTION BASED ON
In Figure 2, a 90' phase shifter can be realized by using a FIR filter which is designed by a few methods [6]. In these cases, the excellent phase shifting effect can only be achieved under the condition that the order of corresponding filter designed is high enough, but its computation cost is too much to bear. In order to reduce computation complexity, digital phase locked loop is introduced to realize the 90' phase shifter in this work.
(10)
where lpf(n) is the output signal of loop low pass filter at time
of d ( n ) . Hence, the howling signal can be effectively detected as long as a proper threshold is set.
LMS ADAPTIVE NOTCH FILTER AND DIGITAL PHASE LOCKED LOOP
(9)
f,,
f"C0
(n)+ k lpf(n)
f,
(n+ 1) = (1 - P ) f " C O (n)+ PIpf(n)
(1 1)
(12)
where f,, ( n ) is the frequency of VCO at time n , k is the parameter that can decide the change rate of VCO, f, is the sampling frequency and p is the parameter that can decide the frequency property of integral section of VCO ( o < p < 1 ). As shown in equation (9), when p ( n ) = 114 (i.e. the phase difference between the reference input signal and the output signal of voltage controlled oscillator is 90°), the input signal pd(n) of loop low pass filter at time n is minimized, that is to
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say, digital phase locked loop is locked. Hence, digital phase locked loop can be used to realize the 90’ phase shifter. The signal flow graph of digital phase locked loop is depicted in Figure 4.
[5] Widrow B., et al. “Adaptive noise canceling: principles and applications”. Proc. ZEEE, pp. 1692-13 16, December 1975. [6] Oppenheim A. V., Schafer R. W.and Buck J. R. Discretetime signal processing (2ed.). Prentice-Hall, 1999.
Figure 4. The signal flow graph of digital phase locked loop. (a). Howing signal and detect results.
5. SIMULATION RESULTS To verify the effectiveness of the proposed algorithm, we acquire some howling signals by computer sound card, where sample rate f,= 8 kHz and A/D conversion is 16 bits. For the LMS adaptive notch filter, we choose initial weights W ,(0) = 0.0 , ~ ~ ( =00.0) and step size p = 0.25 . While for digital phase
locked loop, we use a = 2.‘’ and p = k = 2.’ . After about 20 samples, the adaptive notch filter shown in Figure 2 converges. Detect results are depicted in Figure 5, where the transversal axis represents sampling number of input data and the vertical axis represents amplitude of input data. The rectangular direct line indicates detect results (the higher level shows the existence of howling signal). Figure 5(b) is the first 200 samples zoomed from that of Figure 5(a). The float-point computation cost of the proposed algorithm is about 0.4 MIPS. The detect delay is about 0.2 s and it is acceptable to most of practical applications.
50
100 150 S a m p h g number
200
(b). The first 200 samples of Figure 5(a).
Figure 5. Detect results of the proposed algorithm.
6. CONCLUSIONS In acoustic equipments and communication systems, it gradually becomes one of the basic performance demands to detect the existence of howling signal quickly and exactly with very low computation cost. To detect howling signals, a new algorithm based on LMS adaptive notch filter and digital phase locked loop is presented. Computer simulations illustrate that this method is very effective in detecting howling signal and has the advantage of low computational complexity.
7. REFERENCES Haykin S . Adaptivejlter theory. Prentice-Hall, 1993. Widrow B. and Steams S . D. Adaptive signal processing. Prentice-Hall, 1985. Hardy J. K., et al. High frequency circuit design. Reston Publishing Co., 1979. Kou S . M. and Chen J. “New adaptive IIR notch filter and its application to howling control in speakerphone system”. Electronics Letters, vol. 28, no. 8, pp. 764-166, April 1992.
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