and
n
f = 1000 x 1010 for Third Octave filters
m
(5.9)
where n = ± 1, ± 2, ± 3, etc..
n
(ASA standards say f = 1010 where n is a positive or negative whole number equal to
the band number.)
Upper and lower filter band frequencies fu and fl follow from the effective bandwidth of
the filter, B, and the relationships:
fm u
m u I
B = fu — fl
5.2. RMS MEASUREMENT AND STATISTICAL ACCURACY
(5.1 0)
(5.6)
The Band Pass Filter Type 1618 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:
liM 1 /1
= X` dt
TA —).00 TA
0
where TA is the averaging time
x(t) is a time varying signal
rG is the RMS value of x over an averaging time TA
(5.11)
It can be seen from equation (5.1 1) 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 (5.11) it can also be shown that the observed level of RMS fluctuations
will increase if the averaging time is held constant while the measuring bandwidth is
decreased. That is, the level of the 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.
25
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