Chapter 13 Frequency Analysis

Averaging to Improve the Measurement

Averaging successive measurements usually improves measurement accuracy. Averaging is usually performed on measurement results or on individual spectra, but not directly on the time record.

Common averaging modes include the following:

•RMS averaging

•Vector averaging

•Peak hold

RMS averaging reduces signal fluctuations but not the noise floor. The noise floor is not reduced because RMS averaging averages the energy, or power, of the signal. RMS averaging also causes averaged RMS quantities of single-channel measurements to have zero phase. RMS averaging for dual-channel measurements preserves important phase information.

Vector averaging eliminates noise from synchronous signals. Vector averaging computes the average of complex quantities directly. The real part is averaged separately from the imaginary part. This can reduce the noise floor for random signals, because they 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.

Peak hold averaging retains the peak levels of the averaged quantities. Peak hold is performed at each frequency line separately, retaining peak levels from one FFT record to the next.

Equations for Averaging

Averaged measurements are computed according to the following equations.

RMS Averaging

Chapter 13 Frequency Analysis

Y • Y

--------------- (H2)

Y • X

( H1 + H2) H3 = -------------------------

2 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,

Y* is the complex conjugate of Y, and

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

Vector Averaging

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, and

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

Peak Hold

where X is the complex FFT of signal x (stimulus), and

X* is the complex conjugate of X.