Common Signal Analysis

1 Abstract A common signal is defined for any two signals which have non-zero correlation. A mathematical method is provided to extract the best obtainable common signal between the two signals. This analysis is extended to extracting common signal among three signals. When two signals have non-zero correlation [1], it is commonly believed that these two signals have similarity between them. However, so far there is no clear definition about what the similarity actually means. This paper defines the similarity as common signal between the two signals, and provides a mathematical way to extract it. Let  be a constant. Let  2 (), Cov() and () be variance, covariance and correlation functions. Assume A, B 1 , and B 2 are three mutually independent random variables. Define) () (2 1 2 2 1 A B     and) () () () (2 2 2 2 2 2 2 2 2 A B A B