Bounds on generalised integrated sidelobe level in waveforms with stopbands

Bounds on the generalised integrated sidelobe level (GISL) are built for waveforms with stopbands, i.e. sparse frequency waveforms. The bounds predict the best achievable GISL for any average-pass-to-stopband power ratio in sparse frequency waveforms. The optimal condition for the lower bounds also suggests new approaches for designing sparse frequency waveforms with sidelobe constraints.