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Bandwidth of a digital communication channel is a valuable natural resource. Therefore it is important that the usage of this resource is minimized by carefully designing the digital modems. In this paper a new modulation scheme, called function modulation, is discussed that satisfies the Shannon's model and therefore can help to save bandwidth by creating a green modem. It is also shown that all existing modulation methods based on sinusoidal functions do not meet the requirements of Shannon's model and therefore have lower capacity for a given bandwidth. In addition, the paper shows that Shannon's capacity is also not the limit.
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