Active Suppression of Narrowband Noise by Multiple Secondary Sources

This study presents theoretical and experimental investigation on the active suppression of narrowband noise with C1, C1.5, and C2 components by using multichannel secondary sources in a duct. The quality manipulation in the duct was controlled by changing quality factors which were incorporated into a multichannel FxLMS algorithm.The algorithm is extensively investigated in both theory and real-time control experiment. After analysing the primary and secondary paths of the duct system, an acoustic narrowband signal was chosen as a primary noise and the impulse responses were implemented as the secondary path models. Control results show that the quality factors in the algorithm that was implemented in a dSPACE 1104 provide a stable and excellent response compared to before control. It is obvious that the lower quality factor cancels the more primary noise as defined in the theory although the attenuation levels are not exactly and inversely proportional to the quality factor. The results in this study can be used for practical active sound quality control systems.


Introduction
The active noise control (ANC) systems seek usually to maximize the attenuation of a primary noise by cancelling the unwanted noise based on the principle of superposition [1,2].It takes advantage of the biologically inspired adaptive feedforward learning algorithms such as the filteredreference least mean square (FxLMS) to compensate for the effect of the secondary path in order to ensure convergence [1,2].This ANC has been widely applied successfully to many applications such as airplanes, cars, headsets, mobile devices, and other consumer electronics.
However, in contrast to an ANC system, in some applications it is necessary to retain residual noise with a specified target profile over frequency [3,4] because some intentional residual noise could provide better natural feeling rather than simply minimizing the residual noise.This approach is known as an active sound quality control (ASQC) and it can be implemented by incorporating some factors in its algorithm.A typical ASQC system, therefore, needs to have a capability of attenuating unwanted noise to a certain level and, at the same time, of enhancing wanted noise to a predefined target level.An adaptive noise equalization (ANE) is one of the concepts and has been extending to control narrowband and broadband noises [5][6][7][8].Although a narrowband ANC system can reduce narrowband noise components at maximum, a narrowband ANE system can be independently manipulated.
The duct systems are widely applied to a number of different buildings, factories, and facilities.In some applications, such as clean rooms for precise manufacturing, they need to keep a comfortable noise level for workers and this leads to product quality.Also excessive reduction of noise can cause uncomfortable awkward silence.Thus the quality factor allows operating the noise reduction level with the ANC systems.
In this study, thus, an active sound quality control (ASQC) system using this ANE algorithm based the FxLMS is investigated in depth in order to control narrowband noise, which are dominant in a duct, separately or altogether in terms of sound quality control.For the selective quality control, a quality factor or parameter which is predetermined is applied in the real-time FxLMS adaptive algorithm.

Noise
Sinewave generator Error mic.
− ∑ e  y 1 (n) Figure 1: Active sound quality control for narrowband noise using a factor  in a duct.
The rest of the paper is organized as follows.In Section 2, theoretical considerations are described to derive proper equations for sound quality control based on the multichannel FxLMS algorithm with a quality factor matrix in a duct.Section 3 presents the experimental arrangement including the test duct and control board for the real-time control.In the same section, the primary and secondary paths are discussed and the modeling of the secondary path to implement in the control algorithm is included.Intensive analysis and discussions from the measured results from the real-time sound quality control in terms of time and frequency domain are written in Section 4. Finally, conclusions are summarized in Section 5.

Multichannel Active Sound Quality Control for Narrowband
Noise.An ANC system with an adaptive feedforward approach is known as an effective method to suppress unwanted noise [1,2].As shown in Figure 1, a duct with a noise source (primary source), a secondary source, and an error microphone are considered to suppress the primary noise as much as necessary.A real-time algorithm which is embedded in a digital signal processor is applied for sound quality control as illustrated schematically in Figure 1 as well.The summation of the primary noise () and the secondary noise () at the error microphone is the error signal () as () = () − ().
Assuming that there are  reference signals,  secondary loudspeakers, and  error microphones, the practical form of the multichannel FxLMS update equation based on the steepest descent algorithm in the time domain without the sound quality factor can be given as [1,2] w +1 = w  −  X () e () , where w is the vector of filter coefficient,  is a convergence coefficient, and e() is the error signal vector.
X() is the filtered-reference signal matrix which can be expressed as where the filtered-reference signal vector can be written by In (1), the practical update quantity in the multichannel system is given as /w, where  is the cost function and is identical to the gradient of the instantaneous sum of squared outputs of the error signals with respect to the filter weights.Thus it can be presented as follows [1,2]: In this control system, sound quality can be controlled using a digital equalizer [2].The quality factor matrix Β, which consists of each quality factor   to each secondary loudspeaker as presented in Figure 1, can be considered in the multichannel FxLMS algorithm and can allow actively controlling sound quality in a duct system.The output vector u() from the adaptive filter matrix W is designed to separate and to multiply with I−Β for the actual secondary path matrix S in one branch and Β for the modelled one Ŝ in the other branch.This makes the error signal vector capable of being written by (5) This error signal vector now indicates that the residual noise after control can be kept by the quality factor matrix Β [5].Thus, the practical update equation of the multichannel FxLMS algorithm for ASQC with the quality factor matrix Β is given by The new update equation in ( 6) operates automatically to minimize the signal vector e  ().So if the disturbance signal vector d() ≈ ∑ −1 =1 S  u( − ), then ( 5) can be expressed as Equation ( 7) represents the quality factor matrix governing the residual noise level at the error microphones positions in the duct.The separation of the signal   introduces four different cases of results as follows: (1) if   = 0, it acts as a normal ANC system which is on (this is equivalent to (1)) and makes   () ≈ 0, (2) if   = 1, it acts as the ANC system which is off and makes   () ≈   (), (3) if 0 <   < 1, it acts to control the noise to a certain level dependent upon the value  i and makes   () ≈     (), and (4) if   > 1, it acts to enhance the noise level and makes   () >   ().

Experimental Set-Up and Primary
Path.The experimental set-up for the real-time narrowband active sound quality control consists of an acrylic duct (length = 1800 mm), a primary loudspeaker at the left end, two secondary sources (control loudspeakers), an error microphone (1/2  PCB 377B0E) at the right end, a power amplifier (B&K 2716C), a PCB signal conditioner, and low-pass filters.In addition, it involves the real-time control unit of a dSPACE 1104 for the implementation of control algorithm.So there are 1 reference signal ( = 1), 2 secondary loudspeakers ( = 2), and 1 error microphone ( = 1) in this control system.
The sampling frequency was   = 6.000 kHz and the cut-off frequencies of the antialiasing low-pass filters before the two ADCs (for the reference signal and the error signal) and the reconstruction low-pass filter after the DAC (for the control signal) were both 500 Hz.The control signal vector u(), which was generated in the control algorithm, was transferred to the control loudspeakers through the DAC.The physical acoustic path lengths between the secondary sources and the error microphone are 1140 mm for the source 1 and 600 mm for source 2, respectively.In a duct system, fan noise is the most dominant one in general.Thus a narrowband signal is highly likely as the input.Other different signals pure tones or broadband signals can be the input.Control against pure tones is very easy but the usefulness in practical applications is very low.Control against broadband signals is useful but the signals require very long control filters for successful control.However, many practical applications such as fan, motors, engines, and other rotating devices generate nonstationary narrowband signals.
The narrowband control based on the adaptive notch filter needs two filter coefficients per order, and this allows less control filter lengths.By the way, this study investigates the narrowband signal which consists of three different orders.
Thus, a narrowband signal with three components of C1 (mode 1), C1.5 (mode 2), and C2 (mode 3) is considered for the primary disturbance noise as shown in Figure 2(a).
The spectrogram of the disturbance signal in Figure 2(a) indicates that three components are involved as described previously and it stays stationarily for the first and the last 2 seconds, respectively, but sweeps nonstationarily for 5 seconds between the two stationary signals.

Secondary Path Modelling.
The plants of the active control system which is known as secondary paths between each control loudspeaker, LS1 or LS2, and the error microphone were measured with the dSPACE 1104 as plotted in Figure 1.Both the plant models Ŝ1 () and Ŝ2 () were obtained using the offline identification method from the measured data.As it can be seen from Figure 3, the frequency response function (FRF) and the impulse response functions (IRF) are plotted.
The FIR filters ŝ1 () and ŝ2 () were implemented for the plant models in the control algorithm as shown in Figure 2(b).The lengths of the FIR filters were 50 samples, respectively, although the IRFs in Figure 3 show 200 samples.The length of ŝ1 () depends upon the performance of the control processor for the real-time control and the complexity of the algorithm used.
The lengths of the secondary path models in FIR filters were chosen after analyzing the mean square of the error signal which is the difference of the outputs between the actual secondary path and the secondary path model.The analysis showed that the length of 50 samples is reasonable to choose as it offers nice control performance in terms of the   MSE (mean square error) and real-time computation time.The longer filter length gives the further reduction in control but it requires further real-time processing capability.

Results and Discussions
In this experiment, either LS1 or LS2 or both (LS1 + LS2) the two secondary loudspeakers were used for the control.Also the control results present without ( = 0) and with the quality factor (0 ≤  ≤ 1).

Active Control
Results without the Quality Factor ( = 0).When the quality factor was not applied ( = 0) to the control implementation, the real-time control experiment results show the full performance with the largest attenuations as shown in Figure 4. Figures 4(a where the subscripts after and before represent "after control" and "before control," respectively, and   () is the disturbance spectrum.
When only LS1 is used, the spectrogram of the error signals after control, compared with Figure 2(a), shows that three sweeping components (C1, C1.5, and C2) are attenuated very well.The average attenuation level over the frequency range of 100-400 Hz in this case is about 25.62 dB as summarized in Table 1.
Figures 4(b), 4(e), and 4(h) show that the average attenuation level of the error signals over the same frequency range is about 24.09 dB as only LS2 is used.Also Figures 4(c), 4(f), and 4(i) demonstrate that the average attenuation level is about 29.74 dB when both LS1 and LS2 are used.
It is noted that the case with both LS1 and LS2 shows the best performance compared with the other two cases.It is eminent from the results in Figure 4 that the frequency region especially around 320 Hz (C3) is not controlled effectively.This is caused by the fact that the eigenvalue spread is inherently wider than other regions in this duct control system.
The less controlled peak around 300 Hz in Figure 4 is caused by the sudden phase change in the secondary path around that frequency as plotted in Figure 3(a), which is determined by the physical dimension of the duct and the physical and electrical properties between the secondary loudspeakers and the error microphone.In active control, the sudden phase change at a certain frequency especially limits the convergence coefficient value in order to maintain the stability of the control system.So the sudden phase change determines the control performance.Once the convergence coefficient value increases, the peak around that frequency can be increased abruptly and threatens the stability.Thus even if the duct dimension cannot be redesigned, one can reduce the amount of the phase change at a certain frequency by modifying the physical and electrical properties of the secondary paths.Then the change can lead to better control performance.
From Table 1, the result differences between LS1 only and LS2 are observed although they are not big.This is mainly caused by the differences in terms of the physical and electrical properties between the two secondary paths.The convergence coefficient values are different slightly in the two paths and bring about the result difference.
In addition, although it might look so natural this justifies the fact that the use of more control loudspeakers can introduce better attenuation in active noise control provided that the complexity of the algorithm is not beyond the computation power of the real-time processor and the control is stable.

Active Control Results for Each Component without the
Quality Factor ( = 0).Again if the quality factor was not applied ( = 0) to the narrowband control implementation, the spectrograms of the error signals after control on each component by using either LS1 only or LS2 only are plotted in Figure 5. Figures 5(a), 5(b), and 5(c) show that C1, C1.5, and C2 components are cancelled out by using LS1 only.The noise at about 320 Hz in C2 is still not suppressed even if the control is dedicated only to one component (C2) by LS1.The average attenuation levels in this case are summarized in Table 1.
In Figures 5(d), 5(e), and 5(f), the spectrograms of the error signals after control are quite similar to Figures 5(a), 5(b), and 5(c).It is noted that the average attenuation at C1.5 with LS2 is a bit better than LS1 from Figures 5(b) and 5(e), although the average attenuation level in Table 1 shows differently.Because the C1.5 which extends from 150 Hz to 300 Hz overlaps with C1 at 150-200 Hz and C2 at 200-300 Hz, the average attenuation levels for C1.5 cannot represent actual results in this case.

Active Control
Results with the Quality Factor (0 ≤  ≤ 1).In this section, three different quality factors of  = 0,  = 0.2, and  = 0.5 were applied to the actual control implementation; the real-time control experiment results in terms of their attenuations when both LS1 and LS2 are used are shown in Figure 6.As Figures 6(a During the sweep, C1, C1.5, and C2 order signals vary from 100 Hz to 200 Hz, 150 Hz to 300 Hz, and 200 Hz to 400 Hz, respectively.In Figure 2(b), the block diagram of the multichannel narrowband FxLMS which was implemented in dSPACE 1104 is displayed.The block diagram shows adaptive notch filters to cancel actively the narrowband disturbances.The block diagram in Figure 2(b) is the extended version of Figure 1 to generate proper control signals to operate the two secondary loudspeakers.Each dashed rectangle in Figure 2(b) represents an adaptive notch filter against one of the three orders to drive one of the two loudspeakers.

Figure 2 :Figure 3 :
Figure 2: Disturbance and the control algorithm.(a) Spectrogram of the disturbance signal.(b) Implementation of the multichannel FxLMS algorithm for narrowband noise control.

Table 1 :
Average attenuation in dB of the error signals without/with the quality factor.