%FSJWJOHESJWJOHTJHOBMTPGMPVETQFBLFST y x z r0 rref Φ φs P(rref , φ, 0, ω) = 1 P(rref , φ, 0, ω) = 0 Bright zone Circular loudspeaker array Reference circle Dark Zone <latexit sha1_base64="WeZsnZwk5UGw+Dx58344ySFZpfU=">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</latexit> cn,l(rref ) = 1 2⇡ Z 2⇡ 0 Hl(rref , )e jn d ' 1 M M X m=1 Hl(rref , m)e jn m <latexit sha1_base64="w77DHJ0cpBVEi7ri+sh27w+FFVo=">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</latexit> Hl(rref , m) <latexit sha1_base64="ENxoC8BAov895nidMWiG1Mvap1E=">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</latexit> ˆ d = C(r ref )HC(r ref ) + I 1 C(r ref )Ha(r ref ) <latexit sha1_base64="pudrKLQmB8dnxmsYuHL5YGr2ceg=">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</latexit> C(rref ) = 2 6 4 c N,1(rref ) · · · c N,L(rref ) . . . ... . . . cN,1(rref ) . . . cN,L(rref ) 3 7 5 <latexit sha1_base64="u25XTEhOVbL/8OuvkFUjAmPUrGs=">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</latexit> an,rect( , S) = sinc ✓ n 2⇡ ◆ e jn s <latexit sha1_base64="DB31CbEgzeBbvhJ6gGtkWpP5wRY=">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</latexit> an,hann( , S) = ⇢ sinc ✓ 1 2 + n 2⇡ ◆ + sinc ✓ 1 2 n 2⇡ ◆ 2 e jn s ۣܗ૭ )BOO૭