An alternate projections technique is applied to efficiently generate sparse frequency waveforms with constraints on the frequency band suppression levels as well as on range sidelobes. With a complexity of only O(N log N), the algorithm could rapidly generate constant power noise-like sparse frequency waveforms that are very suitable for low probability of intercept radars. It has also proven its ability to generate waveforms having ideal periodic autocorrelation function comparable to well known ideal codes.