Frequency stepping is one of the known techniques employed by modern radars to attain high range resolution.
One of the main advantages of this approach is that it allows to achieve wideband pulse compression through
narrowband processing. It is also known that the traditional linear stepped-frequency waveform suffers from
relatively high range sidelobes and grating lobes that appear due to periodicities in the Discrete Fourier Transform
(DFT). An amplitude weighting (applied prior to the DFT) is typically used to reduce the near-in sidelobes.
This results in undesirable losses in sensitivity. In this paper, we propose a new approach that may be used
to derive families of nonlinear stepped-frequency waveforms that would have desired characteristics such as
suppressed grating lobes and built-in low range sidelobes. Our approach is based on new analytical properties
of stepped-frequency waveforms presented in the paper. We give examples of nonlinear waveforms generated by
this approach and show that they exhibit improved performance when compared with traditional waveforms.