Applying Analytics

Related Lists and 1-Dimensional Data Sets 145

φ

ψ

- 

Zero Offset Positive Offset Negative Offset

FIGURE 6.11

Illustration of the periodicity used to calculate the cross-correlation function.

In this diagram, φ and ψ have been given arbitrary shapes. To calculate the

cross-correlation function, each element in ψ is multiplied by the element in φ

directly above it; elements of φ that don’t have corresponding elements of ψ

located directly below don’t contribute to X. The horizontal arrows show the

direction and amplitude of the shift. The vertical line marks the discontinuity

that can result when periodicity is assumed. Note how strange the function

by which ...