Fast and Accurate Calculations of Cohen-Class Distributions and Applications.


NUI Fellowship in the sciences


John Healy


The Wigner-Ville distribution (and more generally the Cohen class of time-frequency distributions) is the time-frequency distribution of choice in optical system modelling and its applications. Its adoption in the signal processing community lags behind that of the Spectrogram and the wavelet transform because of assorted difficulties defining a suitable discretisation (fidelity vs mathematical properties, sampling issues, resolution vs large data sets). In this project, we explore how best to numerically approximate the Wigner distribution function (WDF). This project will result in GPU-accelerated software to quickly and accurately numerically approximate the WDF and other Cohen-class distributions using as few samples as necessary. We will apply the resulting software to applications as diverse as processing of digitally-acquired acoustic cardiograms, metrology, and the simulation of systems illuminated by partially coherent light.

Papers (2011-2013):

L. Zhao, J. J. Healy, and J. T. Sheridan, "Unitary discrete linear canonical transform: analysis and application," Appl. Opt. 52, C30-C36 (2013).

D. P. Kelly, J. J. Healy, B. M. Hennelly and J. T. Sheridan "Quantifying the 2.5D imaging performance of digital holographic systems," J. Euro. Opt. Soc. Rap. Public., 6 11034 (2011).

C. Liu, D. Wang, J. J. Healy, B. M. Hennelly, J. T. Sheridan, and M. K. Kim, "Digital computation of the complex linear canonical transform," J. Opt. Soc. Am. A 27(7), 1379-1386 (2011).

J. J. Healy and K. B. Wolf, "Discrete canonical transforms that are Hadamard matrices," J. Phys. A: Math. Theor., 265302(2011).

J. J. Healy and J. T. Sheridan, "The space-bandwidth ratio as a means of choosing between Fresnel and other linear canonical transform algorithms," J. Opt. Soc. Am. A 28, 786-790 (2011).