A simple approach to the design of one-dimensional sparse arrays

In ultrasound scanners, a two-way radiation pattern is generated by a transmit array and a receive array. The design of such arrays is simplified by treating the problem as the design of an effective aperture function w_eff(n) which is given by the convolution of the transmit aperture function w_T(n) and the receive aperture function w_R(n). In this paper we consider the design of one-dimensional sparse transmit and receive arrays with a uniform effective aperture function. The design approach is based on the factorization of a polynomial representation of the effective aperture function.