Gabor representation of optical signals using a truncated von Neumann lattice and its practical implementation

The Gabor expansion of an arbitrary optical signal in terms of Gaussian sig nals that form an N x M truncated von Neumann lattice in the time-frequency plane is studied. The accuracy of the expansion for various values of (N,M ) and various widths of the Gaussians is examined. The accuracy of the meth od is also demonstrated by comparing and contrasting the Wigner function fo r both the original and reconstructed signals. Practical implementation of the method through "Gabor analyzers" that directly measure the Gabor coeffi cients of optical signals is also discussed. (C) 2000 Society of Photo-Opti cal Instrumentation Engineers. [S0091-3286(00)02507-1].