Campbell Scientific CR3000 Micrologger - Manual (Page 272)

Section 7. Installation
272
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. 273), 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.
The recorded amplitude for this example should be about 1/3 of the
input‐signal amplitude. A program was written with two stored
variables: Accel2 and Accel2RA. The raw measurement was stored in
Accel2, while Accel2RA was the result of performing a running average
on the Accel2 variable. Both values were stored at a rate of 500 Hz.
Figure Running‐Average Signal Attenuation
(p. 273)
show the two values
plotted in a single graph to illustrate the attenuation (the running‐
average value has the lower amplitude).
The resultant delay (delay in time) = (Scan rate)(N‐1)/2 = 2 ms (10‐1)/2 =
9 ms. This is about 1/3 of the input‐signal period.