One of the main issues limiting the range resolution of linear frequency-modulated continuous-wave(FMCW) radars is nonlinearity of frequency sweep, which results in degradation of contrast andrange resolution, especially at long ranges. Two novel, slightly different, methods to correct fornonlinearities in the frequency sweep by digital post-processing of the deramped signal wereintroduced independently by Burgos-Garcia et al. (Burgos-Garcia, Castillo et al. 2003) and Meta et al.

(Meta, Hoogeboom et al. 2006). In these publications, however, no formal proof of the techniqueswas given, and no limitations were described. In this thesis, we prove that the algorithm of Meta isexact for temporally infinite chirps, and remains valid for finite chirps with large time-bandwidthproducts provided the maximum frequency component of the phase error function is sufficientlylow. It is also shown that the algorithm of Meta reduces to that of Burgos-Garcia in this limit. Adigital implementation of the method is described. We also propose a novel method to measure thesystematic phase errors which are required as input to the compensation algorithm. The applicabilityof this technique to the field of optical frequency domain reflectometry (OFDR) is noted.