A new method of aperture analysis and synthesis via Gaussian beam expansion

An arbitary function f(x), defined In the finite interval [-l,l], may be expressed in terms of a series of modulated Gaussian functions. This kind of series representation has several advantages. First of all unlike the ordinary Fourier series representation, it is no longer a periodic function. Secondly, FFT method can be applied to evaluate the expansion coefficients. Finally, intesrals connected to f(x) and mostly invloved in aperture analysis and synthesis problems can be performed in closed form. The numerical results show that this kind of function expansion is really promising in the aperture analysis and synthesis applications.