A Note on the Capacity of the Band-Limited Gaussian Channel

In his 1974 Shannon Lecture, 2 D. Slepian introduced still another way of resolving the well-known paradoxes that arise when bandlimited signals are studied in a physical "real world" context. One such paradox results from the fact that a mathematically bandlimited function is determined for all time by its values in an arbitrarily small temporal interval--a highly nonphysical situation. An essential element in Slepian's resolution of these paradoxes is the recognition of the role of measurement accuracy in the determination of signals. To incorporate this into his mathematical model, he introduces the following concept. Two signals Si(0, s2 (t), -- w.