The interpolation operator interpolates a signal by an integer factor using bandlimited interpolation. For frequency-domain signals , , we may write spectral interpolation as follows:
Since is initially only defined over the roots of unity in the plane, while is defined over roots of unity, we define for by ideal bandlimited interpolation (specifically time-limited spectral interpolation in this case).
For time-domain signals , exact interpolation is similarly bandlimited interpolation, as derived in Appendix D.