A generalized Fourier domain: Signal processing framework and applications

In this paper, a signal processing framework in a generalized Fourier domain (GFD) is introduced. In this newly proposed domain, a parametric form of control on the periodic repetitions that occur due to sampling in the reciprocal domain is possible, without the need to increase the sampling rate. This characteristic and the connections of the generalized Fourier transform to analyticity and to the z-transform are investigated. Core properties of the generalized discrete Fourier transform (GDFT) such as a weighted circular correlation property and Parseval’s relation are derived. We show the benefits of using the novel framework in a spatial-audio application, specifically the simulation of room impulse responses for auralization purposes in e.g. virtual reality systems. & 2012 Elsevier B.V. All rights reserved.