## 5 Experimental Verification  
Once the control algorithm used in the multichannel ANC system was verified by simulations, we performed 1:1:1 ANC experiments in a wooden duct to validate it. The aim of this experiment was to show how the inclusion of the automatic scaling factor reduces the time required to develop real-time practical ANC applications since the manual setting of this factor is very time consuming. In addition, the proposed automatic adjustment of the scaling factor allows an easy adaptation of the control algorithm when abrupt changes in the reference signal occur. As a consequence, real-time analysis can be performed. The length and width of the duct are 1.21 m and 0.09 m, respectively, as shown in Figure 5.  
In addition, the experimental set-up involves analogue low-pass filters, microphones, speakers, an audio power amplifier and a DSK board TMSC3206713, as shown in Figure 6. In general, we use analog low-pass filters to eliminate signals with high frequencies obtained from the microphones (#1 and #2). Here, the error microphone (#1) and reference microphone (#2) were employed to measure the residual error signal and reference signal, respectively. On the other hand, the noise source loudspeaker (#1) and the cancelling loudspeaker (#2) were used to generate a primary disturbance signal and anti-noise signal, respectively. Here, we used an audio power amplifier along with a loudspeaker (#2) to generate the anti-noise signal. The control algorithm was implemented in the DSK TM320C6713 from Texas Instruments (TI). In general terms, the error signal was measured by means of a microphone (#1), and then filtered by a low-pass filter. The resulting analog signal was converted to a digital signal to be processed by the DSK TM320C6713 board. Once the control algorithm generated the anti-noise signal, the DSK TM320C6713 board sent the analog signal to the power amplifier to ensure the acoustic cancellation via loudspeaker (#2). Figure 5: Acoustic duct used in ANC experiments. In this experiment, the transfer function of the secondary path was estimated offline using an LMS algorithm with 128 coefficients. Using this strategy, we can easily obtain the acoustic characteristics between the microphone (#1) and loudspeaker (#2). On the other hand, we considered two types of reference signal, a single-tonal input of 500 Hz and a multi-tonal input of 600, 750 and 900 Hz, in order to evaluate the ANC system in the acoustic duct. In addition, the variance of the noise and SNR were obtained by means of acoustic sensors. Case 1: Single-tone as a reference signal  
Figure 7 shows a comparison between the FXECAP-L algorithm, the FXAPL-I algorithm and the proposed algorithm in terms of the power spectrum of the error signal at the microphone (#1). In all algorithms, the projection order was \(L=5\) and the error was encoded with \(b=10\) bits. As can be observed from Figure 7, all algorithms can effectively attenuate noise. However, the automatic adjustment of the scaling factor has allowed the ANC system to be rapidly developed. In addition, the average number of updates performed by the proposed algorithm and the conventional FXECAP-L algorithm were 52,164 (48.07%) and 78,131 (72%), respectively. For simplicity, Figure 8 shows only how the projection order changes over time to reduce the computational complexity of the proposed algorithm. Here, the proposed algorithm and the conventional FXECAP-L algorithm exhibit similar behavior. Case 2: Multi-tone as a reference signal  
In this case, we compared the FXECAP-L algorithm, the FXAPL-I algorithm and the proposed algorithm. Figure 9 shows how the proposed algorithm performs the noise cancellation of a multi-tone signal. All of the algorithms effectively cancel multi-tone signals. However, the proposed algorithm and the conventional FXECAP-L algorithm require 51.18% (95,302) and 81% (150,829) fewer updates when compared with the FXAPL-I algorithm. As in the previous case, Figure 10 shows only the dynamic adjustment of the projection order of the proposed algorithm.