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The University of Southampton

Research project: Generalized sampling theorem with Sperhical Harmonics

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The generalized sampling expansion introduced by Papoulis allows the reconstruction of a band limited function sampled at a frequency lower than the Nyquist frequency using the outputs of several linear time-invariant systems. The work carried out in the framework of this project includes the formulation of the generalized sampling expansion for functions defined on the sphere, using spherical harmonics decomposition, thus facilitating sub-Nyquist sampling without aliasing error. An analysis of spherical convolution and the aliasing phenomenon in the spherical harmonic domain is undertaken, and examples are studied to of performance and limitations of the method. The project aims at the application of this technique to engineering problems such as the DSP for spherical microphone arrays.

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