Abstract
A method is introduced for deriving the 'covariance length curve (Cov-L)' from the existing variance length curve. Some critical information hidden in existing variance length curve will be revealed through the Cov-L derived. It includes the correlation between any arbitrary measurement lengths, which is not readily available from the variance length curve but that is critical. Correlation functions of arbitrary measurement lengths are derived directly from the variance length curve given without requiring any further information. Use of the correlation functions has more advantages over the traditional V-L curves. First, they represent a yarn diameter (or mass) profile both in scale (resolution) and frequency (periodicity) rather than in scale only which is the case for V-L curves. Second, periodicities hidden in seemingly irregular signals are easily detected and revealed by the correlation functions. It is also beneficiary that the functions are readily available from a V-L curve without further efforts for measurement and analysis.