Techniques for arbitrary sampling in two-dimensional Fourier transforms

Optical implementations of two-dimensional fractional fourier transforms and linear canonical transforms with arbitrary parameters.

We provide a general treatment of optical two-dimensional fractional Fourier transforming systems. We not only allow the fractional Fourier transform orders to be specified independently for the two dimensions but also allow the input and output scale parameters and the residual spherical phase factors to be controlled. We further discuss systems that do not allow all these parameters to be con...

Two-dimensional Hilbert Transforms'

DISTRIBUTED TWO - DIMENSIONAL FOURIER TRANSFORMS ON DSPs : WITH AN APPLICATIONS FOR PHASE RETRIEVAL

Title of Document: DISTRIBUTED TWO-DIMENSIONAL FOURIER TRANSFORMS ON DSPs: WITH APPLICATIONS FOR PHASE RETRIEVAL Jeffrey Scott Smith, Master of Science, 2006 Directed By: Professor Bruce Jacob Department of Electrical Engineering Many applications of two-dimensional Fourier Transforms require fixed timing as defined by system specifications. One example is image-based wavefront sensing. The ima...

An FPT algorithm with a modularized structure for computing two-dimensional discrete Fourier transforms

With the change of variables U = U*q, substitution into (21) results in UCU*q = Ud. Consequently, the solution vector U of (20) can be obtained from the solution vector q of (22) or q can be obtained from U. Note that if a system of real equations is Toeplitz-plus-Hankel (T + H) , where T i s symmetric Toeplitz and H i s skew-centrosym-metric Hankel, then the equations may be transformed into H...

Two-dimensional transforms for device color calibration

Color device calibration is traditionally performed using one-dimensional per-channel tone-response corrections (TRCs). While one-dimensional TRCs are attractive in view of their low implementation complexity and efficient real-time processing of color images, their use severely restricts the degree of control that can be exercised along various device axes. A typical example is that 1-D TRCs i...