Signal Reconstruction
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In signal processing, reconstruction usually means the determination of an original continuous signal from a sequence of equally spaced samples. This article takes a generalized abstract mathematical approach to signal sampling and reconstruction. For a more practical approach based on band-limited signals, see Whittaker Shannon interpolation formula. Let F be any sampling method, i.e. a linear map from the Hilbert space of square-integrable functions L2 to complex sp...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In signal processing, reconstruction usually means the determination of an original continuous signal from a sequence of equally spaced samples. This article takes a generalized abstract mathematical approach to signal sampling and reconstruction. For a more practical approach based on band-limited signals, see Whittaker Shannon interpolation formula. Let F be any sampling method, i.e. a linear map from the Hilbert space of square-integrable functions L2 to complex space Bbb C^n. In our example, the vector space of sampled signals Bbb C^n is n-dimensional complex space. Any proposed inverse R of F (reconstruction formula, in the lingo) would have to map Bbb C^n to some subset of L2. We could choose this subset arbitrarily, but if we''re going to want a reconstruction formula R that is also a linear map, then we have to choose an n-dimensional linear subspace of L2. This fact that the dimensions have to agree is related to the Nyquist Shannon sampling theorem.
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