Một mảng thường xuyên sẽ có một mô hình lặp đi lặp lại tại một khoảng thời gian là 1,5 trong u, và điều này được thể hiện bởi các phản ứng rải rác. Mảng bất thường "lặp đi lặp lại" được nhìn thấy để làm suy giảm nhanh chóng, nhưng mô hình mà vấn đề là nằm trong khoảng [-1, 1] u | Array Beamforming 163 oo g u E a x exp 2pix sin OH dx The integral is over the whole domain of x though with a finite aperture a x will be zero outside this finite region. If we define the aperture positions in units of the wavelength of operation 10 then we replace x Ả0 with x and also if we define u sin O as in Section then becomes g u E a x exp 2pixu dx and we see that g is formally the inverse Fourier transform of the aperture distribution a and correspondingly the distribution a is the Fourier transform of the pattern g. However we must treat this with some caution because although defines values for g u when u 1 these u values do not correspond to real directions. If we wanted to determine the aperture distribution for a given pattern and the pattern is defined only for the real angles p 2 O p 2 then we only have the information for the integration over this finite interval for u 1 u 1 . However if g can be defined as the required function in this range of u but the function extends outside this range then we can integrate over the whole u domain knowing that the resultant aperture distribution a will give the required pattern over the basic interval. An example is the case of a uniform aperture distribution a x rect x X where the aperture is given by X 2 x X 2 and the distribution is uniform over this interval. This has the transform g u X sinc Xu a sinc function response with first zeros at 1 X. This response is curtailed for the pattern over real angles at p 2 rad . for u 1 . However if we were given that the required pattern over the real angles 1 u 1 is sinc Xu by integrating sinc Xu over the whole range of u - u o we obtain the rect function for the aperture distribution which gives the wanted pattern in the real angle region. In the case of an array of identical elements with their patterns aligned in parallel we can partition or factorize the array response into an array factor which would be given by using omnidirectional .
