Beamforming: a spatial de-noising approach for civil structural health monitoring

Advances in Bridge Engineering

Table 1 Optimum linear filter corresponding to the three sensors

Frequency bin (Hz)	Real part of ω₁	Real part of ω₂	Real part of ω₃	Image part of ω₁	Image part of ω₂	Image part of ω₃
[0.4 Hz,1.3 Hz]
0.391	0.1361	0.3160	-0.0193	0.2856	-0.0726	0.3589
0.469	0.1407	0.3147	0.0639	0.2968	0.0078	0.3508
0.547	-0.3145	0.0969	0.0653	-0.0340	-0.2906	0.3714
0.625	-0.1184	-0.2336	0.2568	0.2785	0.2178	-0.2772
0.703	0.2805	0.1052	-0.2511	-0.1699	0.2966	0.2540
0.781	0.3011	0.1748	-0.1877	-0.1192	0.3002	0.2697
0.859	0.1976	-0.0109	0.3364	0.2501	0.3214	0.1269
0.937	0.2899	0.2488	-0.3092	-0.1377	0.2259	0.1481
1.016	0.2638	0.1549	-0.2486	-0.2040	0.2933	0.2239
1.094	-0.2686	0.2578	-0.0134	0.1479	-0.2275	0.3490
1.172	0.2992	-0.3216	0.3231	-0.0670	-0.0296	0.1810
1.250	0.2867	-0.0237	0.1295	-0.1543	0.2979	0.3523
[1.9 Hz,2.7 Hz]
1.953	0.1224	0.0529	0.3366	0.2846	0.3483	0.0272
2.031	0.3252	0.2053	-0.2667	0.0105	0.2534	0.2242
2.109	0.2460	0.0923	-0.1447	-0.1998	0.3010	0.3385
2.187	0.0302	-0.1618	0.2897	-0.2927	0.3010	0.3385
2.265	-0.0390	0.0909	0.1469	0.2797	0.3527	-0.3212
2.344	0.1833	0.0557	-0.0028	0.2569	0.3384	-0.3413
2.422	0.0104	0.1366	0.3581	0.3488	0.2520	0.0663
2.500	-0.1206	0.0794	0.4035	0.3355	0.2262	0.0092
2.578	0.1558	-0.0386	0.3535	0.2966	0.2951	0.0990
2.656	-0.1322	0.1337	0.3405	0.3073	0.2758	-0.1130