Characteristic basis functions of the energy radiation pattern of a sparse true time delay array

A set of characteristic basis functions of the energy radiation pattern for a true-time-delay array of equi-spaced elements radiating a pulsed/transient wave-field was derived. This set is determined by the array layout and by the set of excitation waveforms that can be used to expand the actual excitation pulse. It is established that the characteristic basis function set spans the mapping of the square amplitudes of the discrete Fourier transform of the excitation coefficients to the energy radiation pattern. This mapping is further used to analyze array performance and re-examine the term array sparsity. Additional use of this set can be found in synthesizing an array radiation pattern to meet prescribed requirements.