Transmitted signals are modified to facilitate the emulation of circular convolution in non-contiguous transmission environments. These modified signals may be derived from well-known signature sequences. In an exemplary method, a tail portion of a final segment of a base signal is prefixed to an initial segment of the base signal, to form a first transmit segment. One or more additional transmit segments are formed by prefixing, to each of the one or more segments of the base signal other than the initial segment, a tail portion of the immediately preceding segment of the base signal. The transmit segments so formed are transmitted in respective ones of the plurality of non-contiguous transmit-time intervals. Corresponding methods for receiving the transmitted segments and reconstructing the base signal are also described, as are corresponding transmitting and receiving apparatuses.