BRUEL & KJAER 1618 - Rms Measurement and Statistical Accuracy

and
n
f m 1000 x 10
10
for Third Octave filters
(4. 9)
where n = ± 1, ± 2, ± 3 , etc ..
3n
(ASA Standards say f = 30 where n is a positive or negative integer equal to the band
number .) 10
Upper and lower filter band frequencies f u and fl follow from the effective bandwidth of
the filter , B, and the relationships :
B = f - f
u I
(4 . 10)
(4 . 6)
4.2. RMS MEASUREMENT AND STATISTICAL ACCURACY
40
The Band Pass Filter Type 1617 is intended primarily for the analysis of signals whose
properties do not change with time. These " stationary" signals are subdivided into two
broad classifications . Deterministic signals, with a time history that can be specified ex-
actly at every point in time , are assumed to consist entirely of discrete sinusoidal compo-
nents at different frequencies . Random signals, where only the statistical properties can
be
specified, have a frequency spectrum that is distributed continuously with frequency .
Briefly , deterministic signals have spectra that contain discrete frequency components,
while random signals have a continuous type spectrum .
In any system for obtaining true RMS values, the accuracy of the data recorded depends
not only upon the accuracy of the system as a whole, but also on the accuracy of the sta-
tistical averaging process employed for stationary signals . To understand these relation-
ships* it will be necessary to examine the RMS value of a stationary signal , which can
be
defined as follows :
l/J = \ / lim
T ~oo
A
where T A is the averaging time
x(t) is a time varying signal
f
T
X
2
(t) dt
o
if; is the RMS value of x over an averaging time T A
(4 .11 )
It can be seen from equation (4 . 11) that to obtain the true RMS value of a stationary sig-
nal, the averaging time would have to be infinitely long. As this condition is impossible
to realise in a practical measuring system , the RMS value of a stationary signal may fluc-
tuate when shown on a meter or some other display or readout device that employs a
more realistic averaging time. The shorter the averaging time used, the greater will be
the fluctuation .
From equation (4.11) it can also be shown that the observed level of RMS fluctuations
will increase if the averaging time is held constant while measuring bandwidth is de-
creased. That is, the level of fluctuation depends on the measuring bandwidth .
* A considerably more detailed discussion of the problems and relationships involved in frequency analysis is
contained in the B & K Handbook on Frequency Analysis by R.B. Randall.