# Directional Active Noise Control with a Local Minimax Error Criterion
## 4 Experimental Setup  
In this section, the experimental setup is explicitly introduced. The geometric configuration of the experiment can be seen in Figure 3.  
The setup involved an actuator (a 44-mm resonant speaker), an array of loudspeakers (Swans, monitor-level active speaker, China), microphones (Bruel&Kjae, 4189-A-021, Denmark), a thin wooden board (1 m \(\times\) 0.6 \(\times\) 0.004 m), a digital signal processing (DSP) development board (TI, TMS320C6678, USA), a power amplifier, an analogue-to-digital (A/D) converter (Maxim, max11049, USA), and a digital-to-analogue (D/A) converter (TI, dac764, USA). The actuator was directly attached to the center of the board and excited the board, producing harmonic noise at 100 Hz. Four speakers were used as secondary sources and were arranged 60 cm in front of the board. Eleven microphones, serving as the desired, monitor, or error points, surrounded the primary and secondary sources.  
Directional noise reduction experiments were carried out in two areas. Microphones No. 2, No. 4, and No. 6 constituted the desired Area 1, where we wanted higher reductions. Microphones No. 3 and No. 5 were the monitor points in Area 1. Microphones No. 1, No. 8, No. 10, and No. 11 were other error points where we also expected reductions. Desired Area 2 consisted of Microphones No. 6, No. 8, and No. 10, where Microphones No. 7 and No. 9 were the corresponding monitor points and  
Figure 2: An iteration in the Nelder–Mead algorithm.  
Microphones No. 1, No. 2, No. 4, and No. 11 were the remaining error points. Detailed distance and angle parameters can be found in Figure 3.  
Considering the amount of calculation required in a practical application, the fixed controller was embedded in the DSP development board. The experiment was conducted with the following steps, as shown in Figure 4.  
Step 1. Computation of the frequency domain transfer functions \(\mathbf{G}(jw)\) and recording of the primary noise field \(\mathbf{P}(jw)\). The DSP development board generated a harmonic signal \(x(n)\) and passed the signal to the power amplifier through the D/A converter. The actuator received the amplified signal \(x(t)\) and excited the board. The microphones obtained the primary noise field \(\mathbf{p}(t)\) at error points and passed it to the DSP development board through the A/D converter. Then, \(x(n)\) and \(\mathbf{p}(n)\) were sent to the personal computer (PC). Therefore, the frequency-domain transfer functions can be calculated:  
\[\mathbf{G}(jw)=\frac{\mathbf{P}(jw)}{X(jw)} \tag{8}\]  
Figure 4: Flow diagram of the experiment.  
Figure 3: Geometric configuration of the experiment.  
Optimal filter coefficients \(\textbf{W}_{opt}\left({{jw}}\right)\) in the frequency domain of the methods, respectively mentioned in Section 2 and Section 3, and \(\textbf{w}_{opt}\left({n}\right)\) in the time domain can be obtained by a discrete inverse Fourier transformation.  
Step 2. ANC. Firstly, the optimal filter coefficients \(\textbf{w}_{opt}\left({n}\right)\) in Step 1 were loaded on the DSP development board from the PC. The amplified harmonic signal from the DSP development board excited the board again. At the same time, the original signal \(x(n)\) was also the reference input of the optimal controller filter on the DSP development board. Finally, the outputs of the controller after the D/A converter were the inputs of the loudspeakers, producing the secondary field, ensuring that the residual noise \(\textbf{E}({jw})\) of the arc discrete control points satisfied the relevant error criterion.