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.
© 2009 Optical Society of America
Fourier Optics and Signal Processing
Original Manuscript: August 28, 2008
Manuscript Accepted: December 8, 2008
Published: February 12, 2009
Kurt Bernardo Wolf, "Mode analysis and signal restoration with Kravchuk functions," J. Opt. Soc. Am. A 26, 509-516 (2009)