Theory and design of broadband sensor arrays with frequency invariant far eld beam patterns

The theory and design of a broadband array of sensors with a frequency invariant far eld beam pattern over an arbitrarily wide design bandwidth is presented The frequency invariant beam pattern property is de ned in terms of a continuously distributed sensor and the problem of designing a practical sensor array is then treated as an approximation to this continuous sensor using a discrete set of ltered broadband omni directional array elements The design methodology is suitable for one two and three dimensional sensor arrays it imposes no restrictions on the desired aperture distribution beam shape and can cope with arbitrarily wide bandwidths An important consequence of our results is that the frequency response of the lter applied to the output of each sensor can be factored into two components one component is related to a slice of the desired aperture distribution and the other is sensor independent The results also indicate that the locations of the sensors are not a crucial design consideration although we show that nonuniform spacings simultaneously avoid spatial aliasing and minimize the number of sensors An example design which covers a frequency range which is suitable for speech acquisition using a microphone array illustrates the utility of our method Finally the theory is generalized to cover a parameterized class of arrays in which the frequency dependence of the beam pattern can be controlled in a continuous manner from a classical single frequency design to a frequency invariant design