Exact and approximate time-shift operators
John E. Piper · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2009
A novel fractional time-shift operator is presented in this paper. It is based on performing a phase shift in the frequency domain, which, of course, corresponds to the desired time shift in the time domain. The operations of transforming to the frequency domain, multiplying by the phase shift, and transforming back to the time domain can be accomplished efficiently using one matrix. This matrix is Toeplitz with terms away from the shift number near zero. By approximating the near zero terms as zero, a banded or truncated Toeplitz matrix results. This reduces the computational load and allows an FIR filter realization for the fractional time shift.