Restoring causal signals by analytic continuation: A generalized sampling theorem for causal signals

A band-limited part x0(t) of a non-band-limited causal signal x(t) is used to completely restore x(t) by using analytic continuation. As a consequence, a generalized sampling theorem for causal signals is derived; the total causal signal x(t) can be completely restored by sampling the band-limited part x0(t) with finite sampling frequency.