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.