Capacity Theorem for Finite Duration Symbols

The proof of capacity theorem assumed that the symbols are of infinite time duration. Since the infinite time symbols are not meaningful and is not used in the existing technology, in this paper we decided to prove it over finite time interval. The result shows that the new capacity of a band limited channel explicitly depends on the sample rate. This new approach helps us to show that all shift keying methods do not meet the Shannonpsilas model and therefore cannot achieve the basic capacity limits. We also show that the function modulation method can be engineered to achieve the new extended limits. To establish our theory we use the well known mathematical concept of infinite dimensionality of function space. The new capacity result is stated in a theorem.