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Each of the Frequency Analysis VIs supports averaging. The averaging parameters control in the Frequency Analysis VIs defines how the averaged spectrum is computed, as shown in the following front panel.

averaging mode, weighting mode, number of averages, and linear mode each control a particular feature of the averaging process.

Special Considerations for Averaged Measurements

When you perform averaged frequency measurements, place one of the Frequency Analysis VIs in a For Loop or a While Loop and wire a new block of time data to the VI. The Frequency Analysis VIs return the averaged results based on all the data sent since the first call to the VIs or since the averaging process was restarted.

The following are some conditions in which you can perform averaged measurements with the Baseband FFT VIs and the Baseband Subset VIs:

• You can use either contiguous or overlapping blocks of time data.
• The number of samples in each block of time data determines the FFT block size.
• The averaging automatically restarts if the size of the block of time data changes.

Averaging Mode

You can choose from the following averaging modes when performing frequency analysis with the Frequency Analysis VIs:

• No averaging
• RMS averaging
• Vector averaging
• Peak hold

Note  Not all of the Frequency Analysis VIs support all of the averaging modes listed above.

No Averaging

No averaging is the default setting of the averaging parameters control and does not apply any averaging to the measurement. You can use the No averaging setting for quick computations or when the signal-to-noise ratio is high.

RMS Averaging

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

RMS averaged measurements are computed according to the following equations:

FFT spectrum

power spectrum

<X* ?X>

cross spectrum

<X* ?Y>

frequency response

coherence

coherent output power

COP = y2(Y*Y)

where

X is the complex FFT of the stimulus signal x

Y is the complex FFT of the response signal y

X* is the complex conjugate of X

Y* is the complex conjugate of Y

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

Vector Averaging

Vector averaging, also called coherent averaging or time synchronous averaging, reduces the amount of noise in synchronous signals. Vector averaging computes the average of complex quantities directly. The real and imaginary parts are averaged separately, which preserves phase information. However, for single-channel measurements, using vector averaging without a triggered acquisition can cause strong spectral components to be eliminated in the averaged spectrum.

Vector averaged measurements are computed according to the following equations:

FFT spectrum

<X>

power spectrum

<X*> ?<X>

cross spectrum

<X*> ?<Y>

frequency response

where

X is the complex FFT of the stimulus signal x

Y is the complex FFT of the response signal y

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

<Y> is the average of Y, real and imaginary parts being averaged separately.

RMS versus Vector Averaging

The following example compares the effect of RMS averaging and vector averaging on a typical signal. The input signal is a two-tone signal. The dominant tone is a 10 kHz sine wave with an amplitude of 1 Vp. The smaller component is a 15 kHz sine wave with an amplitude of 0.01 V_p. In addition to the tones, noise is present in the signal. The signal is sampled at 51.2 kHz in blocks of 1,000 samples. A Hanning window is applied to reduce leakage. The VI completes 100 averages. The following front panel shows the results of averaging.

The No Averaging plot identifies only the dominant tone.

The RMS Averaging plot does not reduce the noise floor. However, RMS averaging does smooth the noise out enough to unmask the tone at 15 kHz.

The Vector Averaging, Untriggered Acquisition plot underestimates the energy present at 10 kHz. Also, the tone at 15 kHz is indistinguishable from the noise.

The Vector Averaging, Triggered Acquisition plot accurately computes the energy of the tones, reduces the noise floor by 20 dB, and reveals the tone at 15 kHz. The 20 dB reduction in the noise floor corresponds to a factor of?0, or , where 100 is the number of averages completed.

Peak Hold

A peak hold averaging measurement is performed at each individual frequency line and retains the RMS peak levels of the averaged quantities from one FFT record to the next record. Peak-hold averaging is most useful when configuring a measurement system or when applying limit or upper limit testing to a frequency spectrum.

Peak-hold averaged measurements are computed according to the following equations:

FFT spectrum

power spectrum

MAX(X* ?X)

where

X is the complex FFT of the stimulus signal x.

X* is the complex conjugate of X.

Note  Dual-channel, stimulus-response measurements do not support peak-hold averaging.

Weighting Mode

Linear weighting weights each individual spectrum by the same amount in the averaged spectrum. Linear weighting is most often used for analysis.

Exponential weighting weights the most recent spectrum more than previous spectra. Weighting the most recent spectrum more than previous spectra makes the averaged spectrum more responsive to changes in the input signal. This responsiveness makes exponential weighting ideal for the configuration phase of a measurement. Exponential weighting also is useful for monitoring applications because the averaged spectrum responds to a singular event. A linearly averaged spectrum might not respond noticeably to a singular event, especially with a large number of averages.

Weighting is applied according to the following equation:

where

X_i is the result of the analysis performed on the i^th block.

Y_i is the result of the averaging process from X₁ to X_i.

N = i for linear weighting.

N is a constant for exponential weighting with N = 1 for i = 1.