Vector Averaging

Vector averaging eliminates noise from synchronous signals and computes the average of complex quantities directly.

In vector averaging, the real part is averaged separately from the imaginary part. Averaging the real part separately from the imaginary part can reduce the noise floor for random signals because random signals are not phase coherent from one time record to the next. The real and imaginary parts are averaged separately, reducing noise but usually requiring a trigger.

Vector-averaged measurements are computed according to the following equations:

Table 7. Equations for Calculating Vector-Averaged Measurements
Measurement Equation
FFT spectrum
〈 X 〉
Power spectrum
〈 X * 〉 ⋅ 〈 X 〉
Cross spectrum
〈 X * 〉 ⋅ 〈 Y 〉
Frequency response
( Y ) ( X )

where

X is the complex FFT of signal x (stimulus)

Y is the complex FFT of signal y (response)

X* is the complex conjugate of X

(X) is the average of X, real and imaginary parts being averaged separately