Interpolation and the chirp transform: DSP meets optics

This paper considers the problem of interpolating a signal from one uniformly-spaced grid to another, where the grid spacings may be related by an arbitrary, irrational factor. Noting that interpolation is the digital equivalent of magnification, we begin by reviewing optical systems for magnification and “computation” of the chirp Fourier transform. This route suggests several analog schemes for magnification, which can be discretized to produce algorithms for interpolation. We then derive one of these algorithms from first principles, using a digital-signal-processing perspective. The result is an important, but forgotten, algorithm for interpolation first suggested as an application of the chirp-z transform by Rabiner, Schafer, and Rader. Unlike the earlier derivation, our approach is direct – we do not make use of Bluestein’s trick of completing the square. In addition, our approach identifies parameters under user control that can be optimized for best performance.