Public address and sound reproduction by an active noise control sys- tem in ducted ventilation system

Stéphane Lesoinne 1 Belgian Building Research Institute Rue du Lombard 42, B-1000 Bruxelles, Belgium

ABSTRACT In a ventilation duct, two types of silencers are used: passive (medium and high frequencies) and active (low frequencies). Active silencers have a loudspeaker (control loudspeaker) that generates anti-noise. Usually, this system is placed near the source and far from the vent. But, in short ducts, the system is placed close to a vent and the control speaker can be used as a background speaker to play music, information, alerts (the target signal) ... The active noise control (ANC) system is based on the adaptive feedforward normalized FxLMS which uses a reference and an error microphone to pick up respectively the noise to attenuate and the residual noise after control. The algorithm is mod- ified so that the target signal does not contaminate the reference nor the error signals. The new algorithm is tested in real time in a short duct with different types of noise and different types of sound.

1. INTRODUCTION

Modern buildings and housing requires efficient ventilation systems to maintain an indoor air quality within standard expectations. But noises passing through or emitted by the ventilation system have a major impact on the comfort, well-being, sleep quality, work-related task focus... An objective of the TowardsSmartVentilation research project is to reduce the noise emitted by centralized system as well as its perceived annoyance in mid-size building using passive as well as active techniques.

On one hand, some mid-size buildings use public-address system (PA systems) for information and/or music diffusion through loudspeakers. Others use masking system to reduce noise annoyance by emitting pleasant sound that will mask/hide the unpleasant noise. For example, the annoyance caused by road traffic noise can be reduced by speakers that play bird songs [1, 2]. On the other hand, active silencers generate secondary sound waves (“anti-noise”) interfering negatively with the pri- mary noise in order to reduce its amplitude in a given region of space [3]. After the silencer, residual noise remains and depending on its sound level, can still be a source of annoyances.

This paper study the feasibility of using the active silencer loudspeaker as a combined source of “anti-noise”, information, music and masking sounds. This will require to set the control loudspeaker close to an air outlet which is seldomly the case for centralized ventilation. But it also can be seen as moving the PA or masking system to the ventilation duct with the extra benefit of ventilation noise reduction by active noise cancelation, with an extra controller, Figure 1.

1 Stephane.lesoinne@bbri.be

Figure 1 Scheme of sound broadcasting through a feedforward active noise control system

The algorithm must be adapted and the modified version will be referred to as PA-ANC (Public Address - Active Noise Control) in the remainder of this document. These modifications will be pre- sented in the next section while the results of the tests in a rectangular-section duct will be presented in section 3. The tests will be performed on the basis of the Leaky Normalized FxLMS feedforward algorithm but the principle developed here can be used with any other algorithms. 2. FEEDFORWARD PA-ANC

In this section, the principle of the feedforward ANC will be presented followed by the modifications needed to turn it into a PA-ANC system.

Figure 2 Feedforward ANC

Noise din) ad Anti-noise Cs = ce (0) = x(n) + u(n) + Cs Wl 7 | e(n) = dfn) + u(n) + Ce Reference Error signal signal Needed: s(n) = x(n) Needed: e(n) = d(n) + u(n) + Ce ansfer path from control loudspeaker to reference microphone Ce: transfer path from controlloudspeaker to error microphone

As illustrated at Figure 2, the noise is measured by a reference microphone and this measurement is used by the controller to generate the anti-noise. The controller continuously adapts the anti-noise generation by changing internal coefficients in order to minimize the residual noise at the error mi- crophone. To efficiently reduce the noise, the controller needs to know both 𝐶𝑒 and 𝐶𝑠 , which are, respectively: - the transfer path between the towards-loudspeaker output and the error signal input and - the transfer path between the towards-loudspeaker output and the reference signal input. In the controller, 𝐶𝑒 is required at the adaptation stage and 𝐶𝑠 is needed to reconstruct the reference signal. Indeed, when the control loudspeaker emits the anti-noise 𝑢(𝑛) , the signal measured at the reference microphone becomes

𝑠(𝑛) = 𝑥(𝑛) + 𝑢(𝑛) ∗𝐶𝑠 , ( 1 )

which contains the noise and the anti-noise. In practice, as 𝐶𝑒 and 𝐶𝑠 are not known, the approxima- tions 𝐶𝑒 ෢ and 𝐶𝑠 ෢(𝑛) will be used instead. The reconstructed reference signal is thus:

𝑥(𝑛) = 𝑠(𝑛) −𝑢(𝑛) ∗𝐶𝑠 ෢ , ( 2 )

The quality of these approximations is of higher importance as it has a major impact on the stability and the noise attenuation performance.

Figure 3 PA feedforward ANC

Now, as illustrated at Figure 3, in the PA-ANC system, the signal send to the loudspeaker is made of the anti-noise 𝑢(𝑛) and the information signal 𝑦(𝑛) . Thus, the signal measured at the reference microphone becomes:

Noise d(n) alo) Anti-noise Cs(z) s(n) = x(n) + (ae(n) + y(n) # Cs ul en) = a(n) + (u(n) + y(n) # Ce ula) + vio) Reference wea Ercor signal Needed: s(n) = x(n) Needed: e(n) = d(n) + un) Ce

𝑠′(𝑛) = 𝑥(𝑛) + (𝑢(𝑛) + 𝑦(𝑛)) ∗𝐶𝑠 , ( 3 )

and the signal measured at the error microphone becomes:

𝑒′(𝑛) = 𝑑(𝑛) + (𝑢(𝑛) + 𝑦(𝑛)) ∗𝐶𝑒 , ( 4 )

The reference signal can be estimated by:

𝑥(𝑛) = 𝑠 ′ (𝑛) −(𝑢(𝑛) + 𝑦(𝑛)) ∗𝐶𝑠 , ( 5 )

And so is the error signal

𝑒(𝑛) = 𝑒 ′ (𝑛) −𝑦(𝑛) ∗𝐶𝑒 , ( 6 )

As can be seen at Equations ( 5 ) and ( 6 ), the PA-ANC requires one more convolution (by 𝐶𝑒 ) and one addition ( 𝑢(𝑛) + 𝑦(𝑛) ). The error signal is now dependent on the error on the estimation of 𝐶𝑒 . Regarding the reference signal, the dependence to the estimation error of 𝐶𝑠 already existed but now potentially with a higher impact as the energy of the signal send through the control loudspeaker will be higher. Thus, the importance of a good transfer path model.

The active noise control algorithm can be anyone found in the abundant bibliography on the sub- ject [3]. 3. FIRST EXPERIMENTAL RESULTS AND DISCUSSION

The PA-ANC system has been tested at the output of a semi-open rectangular duct (1m x 0.26m x 0.12m) with a 5W control loudspeaker facing the opening, Figure 4. The noise source is a Bluetooth loudspeaker located at the opposite side. The reference microphone is at 65 cm from the control loudspeaker and the error microphone is near the duct opening. The 5W loudspeaker is closed on its back but with a very small volume and a cut-off frequency around 250 Hz. Even if the low frequency control is limited, the general conclusions should be valid for other setups.

Figure 4 Short semi-open rectangular duct with control loudspeaker and error microphone

The controller has been implemented on a DSP board (SHARC Audio Module) with one stereo in/out and one SPDIF connection to receive the PA signals. This board provides a framework to simplify inputs and outputs management but at the cost of higher latencies due to buffering. To achieve sufficiently short round trip delay, the ADAC sampling frequency is set to 96 kHz and bloc sizes are set to 16. Then, the analog as well as the SPDIF signals are subsampled by a factor 8 for an internal sampling frequency of 12 kHz. After the signals have been processed, the output is sampled back to 96 kHz. Thus, the bandwidth of the PA signal will be limited to 6 kHz at most, which should be sufficient for voice and bird singing but can fall short of music reproduction quality expectations.

The ANC algorithm used for the tests is the Leaky Normalized FxLMS [3] which is standard and features a variable step size as well as a “leaky-term” to prevent instabilities due to error accumula- tion. Transfer path are modeled by FIR filters determined at initialization (offline model, see [3]). The models are kept constant during the whole control and the filters lengths are chosen so the control shows no instability. As the duct is quite reverberant, the model filters have 600 coefficients and the control signal filter has 1000 coefficients.

The noise reduction performance of the PA-ANC has been compared to the standard one by meas- uring the noise attenuation on the same primary noise for both system while the control filter adapta- tion was being stopped after the same convergence time on the same learning noise with the same convergence parameter. Three noise types have been tested: a pink noise bandpass-filtered between [250 Hz ; 1500 Hz], a road traffic noise and a fan noise. Each noise has had its lower frequencies (< 250Hz) filtered out to prevent saturation of the control loudspeaker at those frequencies. The PA system has been tested with guitar music, pop songs and bird chirping sounds.

For each tests, the controller exhibits the same noise reduction performance with and without ac- tivation of the PA system. Moreover, the controller remained stable while the primary noise source was active but some instabilities arose with bird songs when no noise was emitted. The source of these instabilities are still unclear and further analysis should be conducted. Suspected causes are fast transient in chirping, saturation of the loudspeaker, insufficient rejection of the anti-aliases and re- construction filters at the under-and-oversampling stage.

A remark must be made about the FIR filters. This type of filter has been chosen for its intrinsic stability compared to IIR filters but in longer ducts, IIR filters must be considered as the transfer path will be become longer resulting in much more coefficients for FIR filters.

4. CONCLUSION

This paper describes the conjoint use of active noise control and a public address system into a ducted ventilation system with the control loudspeaker located close to an air outlet. This should allow the active noise control system to be integrated into a sound-masking or into a public address system in mid-size building. The system has been implemented on a DSP and evaluated in a short semi-open rectangular duct. The first results have shown a good performance and stability of the PA system when primary noise is present. Of course, the instability observed with the bird song when no primary noise is played raises concern which must be further analysed, ideally with a system whose control loud- speaker is more robust. More tests must take place on a real ventilation duct when the test bench will be set in our test facilities. This will probably force the switch to IIR filters before allowing us to extend the research to ventilation sound masking. 5. ACKNOWLEDGEMENTS

The author gratefully acknowledge the Flemish Region for the financial support of the research presented here, as part of the TowardsSmartVentilation project.

6. REFERENCES

1. Coensel, B.D, Vanwetswinkel, S. & Botteldooren, D. Effects of natural sounds on the perception

of road traffic noise, The Journal of the Acoustical Society of America , 148-153 (2011). 2. Hao Y., Kang J., Wörtche H. Assessment of the masking effects of birdsong on the road traffic

noise environment. The Journal of the Acoustical Society of America, 140(2), 978-987 (2016). 3. Hansen, C., Snyder, S., Qiu, X., Brooks, L., & Moreau, D. Active Control of Noise and Vibration ,

2nd Edition, CRC Press, 2012.