Methods and apparatus are described for interference cancellation of interference components of a time domain signal in the frequency domain. A communications device receives a time domain sequence and generates overlapping time domain segments from the time domain sequence. The overlapping time domain segments are then converted to the frequency domain to generate frequency domain representations of the overlapping time domain segments. The frequency domain representations are stored in a residual memory, and interference components are directly removed from the frequency domain representations stored in the residual memory in the frequency domain.