Quadrature approximation properties of the spiral-phase quadrature transform

Aragonda, Haricharan and Seelamantula, Chandra Sekhar (2011) Quadrature approximation properties of the spiral-phase quadrature transform. In: 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 22-27 May 2011, Prague, Czech Republic.

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Abstract

The notion of the 1-D analytic signal is well understood and has found many applications. At the heart of the analytic signal concept is the Hilbert transform. The problem in extending the concept of analytic signal to higher dimensions is that there is no unique multidimensional definition of the Hilbert transform. Also, the notion of analyticity is not so well under stood in higher dimensions. Of the several 2-D extensions of the Hilbert transform, the spiral-phase quadrature transform or the Riesz transform seems to be the natural extension and has attracted a lot of attention mainly due to its isotropic properties. From the Riesz transform, Larkin et al. constructed a vortex operator, which approximates the quadratures based on asymptotic stationary-phase analysis. In this paper, we show an alternative proof for the quadrature approximation property by invoking the quasi-eigenfunction property of linear, shift-invariant systems. We show that the vortex operator comes up as a natural consequence of applying this property. We also characterize the quadrature approximation error in terms of its energy as well as the peak spatial-domain error. Such results are available for 1-D signals, but their counter part for 2-D signals have not been provided. We also provide simulation results to supplement the analytical calculations.

Item Type:	Conference Proceedings
Publisher:	IEEE
Additional Information:	Copyright of this article belongs to IEEE.
Keywords:	Cauchy-Schwarz Inequality; Parseval Theorem; Riesz Transform; Analytic Signall Quadrature Model; Spiral-Phase Quadrature Transform
Department/Centre:	Division of Electrical Sciences > Electrical Engineering
Date Deposited:	18 Apr 2013 07:08
Last Modified:	18 Apr 2013 07:08
URI:	http://eprints.iisc.ac.in/id/eprint/46224

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