chap 2. signals and spectra: correlation, correlation function

correlation

• in probability theory and statistics, correlation (ofter measured as a correlation coefficient) indicates the strength and direction of a linear relationship between two random variables. that is in contrast with the usage of the term in colloquial speech, denoting any relationship, not necessarily linear.^[각주:1]

correlation function

• correlation functions contain information about the distribution of points or events, or things across some space/time.^[각주:2]
• a normalized correlation function for functions of time can be defined as,

.

when

 and

 represent the same function, this definition geves the auto-correlation, whereas when the represent separate functions, the cross correlation is determined.^[각주:3]

• auto-correlation function

different definitions of auto-correlation are in use depending on the field of study.^[각주:4]

auto-correlation,

, can be defined as

^[각주:5]

• cross-correlation function

• for binary sequences, it turns out that
  
   can be determined relatively simply by noting that the variable
  
   is the number of bits or digits by which the second sequence is shifted with respect to the first. then by comparing the two sequences bit by bit, the normalized correlation function is determined from

auto-correlation function에 대한 위와 같은 간략한 정리는 PN code에 적용되어 유용하게 사용될 수 있다.
좀더 mathematical derivation 을 원한다면, digital and analog communication system, p373을 볼 것.

1. source: http://en.wikipedia.org/wiki/Correlation [본문으로]
2. source: http://en.wikipedia.org/wiki/Correlation_function [본문으로]
3. source: http://worthatry.tistory.com/346 [본문으로]
4. source: http://en.wikipedia.org/wiki/Auto_correlation [본문으로]
5. source: http://en.wikipedia.org/wiki/Auto_correlation [본문으로]