Correlation Entering New Fields with Real-Time Signal Analysis

Correlation analysis is a convenient technique for deyrtmining the spectral characteristics of a signal or the similarity of two different signals. One point of a correlation function is the long-term average of the product of two functions of time. The complete function is generated when the delay between the two time functions is varied. For example, if one voltage V1(t) and another voltage V2(t ¿ r), where r represents a finite and variable delay, are continuously multiplied together and the product fed into a low-pass filter, then the filter´s output closely approximates the true mathematical correlation function. If V2; is identical to V1; in every respect except for the delay r, the result is the autocorrelation function. If V1; and V2; are totally different functions, then the result is the cross-correlation function. The outputs in both cases are functions of the delay time r. Mathematically for autocorrelation begin{equation*}C_{11}(r) = lim_{Trightarrowinfty}frac{1}{2T}int^T_{-T}V_1(t)V_1(t - r) dtend{equation*} for cross correlation begin{equation*} C_{12}(r) = lim_{Trightarrowinfty}frac{1}{2T}int^T_{-T}V_1(t)V_2(t - r) dt end{equation*} An instrument, therefore, that does this integrating process will show whether correlation exists between two signals and, if so, when maximum correlation takes place. In practice, the averaging process indicated in the above equations is performed only for a time longer than the longest period in signals f1(t) and f2(t). Autocorrelation is useful for the detection of an unknown periodic signal in the presence of noise or to measure some particular band of signal or noise frequencies.