Mode analysis and signal restoration with Kravchuk functions.

When a continuous-signal field is sampled at a finite number N of equidistant sensor points, the N resulting data values can yield information on at most N oscillator mode components, whose coefficients should in turn restore the sampled signal. We compare the fidelity of the mode analysis and synthesis in the orthonormal basis of N-point Kravchuk functions with those in the basis of sampled Hermite-Gauss functions. The scale between the two bases is calibrated on the ground state of the field. We conclude that mode analysis is better approximated in the nonorthogonal sampled Hermite-Gauss basis, while signal restoration in the Kravchuk basis is exact.