Special non-linear filter and extension to Shannon's channel capacity

The well-known Shannon's channel capacity defines the maximum transmission rate of communications in band-limited AWGN channels. An extended channel capacity equation is proved under the assumption of the different signal and noise bandwidth. Then a special filter named as the geometric feature filter (GFF) and satisfied with this assumption is found. Results indicate that Shannon's channel capacity equation is just a special example of this extension in the case of the same signal and noise bandwidth, but in different signal and noise bandwidth, capacity bounds should be calculated by this extension, which is a very important supplement to information theory.