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Cases where the linear canonical transform of a signal has compact support or is band-limited

2008-02-01, Healy, John J., Sheridan, John T.

A signal may have compact support, be band-limited (i.e., its Fourier transform has compact support), or neither (“unbounded”). We determine conditions for the linear canonical transform of a signal having these properties. We examine the significance of these conditions for special cases of the linear canonical transform and consider the physical significance of our results

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Reevaluation of the direct method of calculating Fresnel and other linear canonical transforms

2010-04-01, Healy, John J., Sheridan, John T.

The linear canonical transform may be used to simulate the effect of paraxial optical systems on wave fields. Using a recent definition of the discrete linear canonical transform, phase space diagram analyses of the sampling requirements of the direct method of calculating the Fresnel and other linear canonical transforms are more favorable than previously thought. Thus the direct method of calculating these Transforms may be used with fewer samples than previously reported simply by making use of an appropriate reconstruction filter on the samples output by the algorithm.

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Cross terms of the Wigner distribution function and aliasing in numerical simulations of paraxial optical systems

2010-04-15, Healy, John J., Rhodes, William T., Sheridan, John T.

Sampling a function periodically replicates its spectrum. As a bilinear function of the signal, the associated Wigner distribution function contains cross terms between the replicas. Often neglected, these cross terms affect numerical simulations of paraxial optical systems. We develop expressions for these cross terms and show their effect on an example calculation

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Wigner cross-terms in sampled and other periodic signals

2009-10-11, Rhodes, William T., Healy, John J., Sheridan, John T.

If we sample a scalar wave field, it becomes periodic in frequency. We examine the cross-terms which occur between these periodic replicas in the Wigner-Ville distribution function of such a signal. We present analytic results for Gaussian signals. The results also have implications for physical systems which contain periodic gratings.