Degrees of freedom of band limited signals measured over space
In this paper, we provide the degrees of freedom of a band limited signal observed over a finite spatial window at a given time instant. The limit is based on Claude E. Shannon's sampling theorem which is also known as Whittaker-Nyquist-Kotelnikov-Shannon sampling theorem. The result is derived by using a series expansion of the solution to the Helmholtz wave equation. The expanded terms of wave equation are then bounded exponentially to zero beyond a threshold. The derived result is more...[Show more]
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