BRUEL & KJAER 1617 - Practical Analysis of Stationary Signals; Averaging Time

A simple measure of the statistical RMS fluctuation for random signals (the possible
range of error in the averaged RMS signal) is given by:
€=
(4.12)
where € is the fluctuation
B is the measuring bandwidth, or signal frequency bandwidth (whichever is the
smaller) in Hertz
T A is the averaging time, or signal duration (wh i chever is the smaller) in se-
conds.
This expression is an approximate
relationship, but carries sufficient accuracy for BT pro-
ducts
greater than 5. It expresses the limits of the signal variation to a confidence level
of approximately 68%, i.e. there is a 68% probability that the result will be within ± € of
the true value.
4.3. PRACTICAL ANALYSIS OF STATIONARY SIGNALS
The following parameters must be considered:
1. Averaging Time
2.
DC or AC recording
3. Recorder
Writing Speed
4 . Recorder Paper Speed
4.3.1 . Averaging Time
Use equation (4 . 12) to obtain a suitable averaging time for random signals, depending
upon the desired accuracy. Table 4 .1 gives a range of standard deviations (in dB) for a
series of averaging times and frequencies. Normally the lowest frequency in the analysis
governs the averaging time selected. However, for each half decade that frequency is in-
creased, the averaging time can be reduced by a factor of v'TO (normal steps on B & K
Measuring Amplifiers). The Type 1617 contains a program for controlling the averaging
time of Measuring Amplifiers, see section 4.4.
The SINE program is not shown in the table as it does not fulfil the requirement B.T A ~ 5 .
It is suitable for measurement only on deterministic signals having one sinewave per
measuring band.
As the bandwidth of octave-band filters is three times greater than that of third octaves,
averaging
times for them should be reduced by a factor of 3 from the values given in
Table 4 .1.
The
major requirement for deterministic signals is that the ripple be reduced to an ac-
ceptable level. Where only a single sinusoidal component is included in the bandwidth
the ripple wi II be reduced to less than ± 1/ 4 dB for :
(4 . 13)
where f is the frequency of the single component.
41