Campbell Scientific CR800 and CR850 Measurement and Control Systems - Manual (Page 265)

Section 7. Installation
265
Figure Running-Average Frequency Response
(p. 266)
is a graph of signal
attenuation plotted against signal frequency normalized to 1/(running average
duration). The signal is attenuated by a synchronizing filter with an order of 1
(simple averaging): Sin(πX) / (πX), where X is the ratio of the input signal
frequency to the running-average frequency (running-average frequency = 1 /
time length of the running average).
Example:
Scan period = 1 ms,
N value = 4 (number of points to average),
Running‐average duration = 4 ms
Running‐average frequency = 1 / (running‐average duration = 250 Hz)
Input‐signal frequency = 100 Hz
Input frequency to running average (normalized frequency) = 100 / 250
= 0.4
Sin(0.4π) / (0.4π) = 0.757 (or read from figure Running‐Average
Frequency Response
(p. 266), where the X axis is 0.4)
For a 100‐Hz input signal with an Amplitude of 10‐V peak to peak, a
running average outputs a 100‐Hz signal with an amplitude of 7.57‐V
peak to peak.
There is also a phase shift, or delay, in the AvgRun() output. The formula for
calculating the delay, in number of samples, is:
Delay in samples = (N‐1)/2
Note N = Number of points in running average)
To calculate the delay in time, multiply the result from the above equation by the
period at which the running average is executed (usually the scan period):
Delay in time = (scan period) (N ‐ 1) / 2
For the example above, the delay is:
Delay in time = (1 ms) (4 ‐ 1) / 2 = 1.5 ms
Example:
Actual test using an accelerometer mounted on a beam whose resonant
frequency is about 36 Hz. The measurement period was 2 ms. The
running average duration was 20 ms (frequency of 50 Hz), so the
normalized resonant frequency is,
36/50 = 0.72, SIN(0.72π) / (0.72π) = 0.34.