For a signal composed of the linear superposition of randomly-arriving pulses, as the product of count rate and pulse width becomes large with respect to unity, the amplitude distri­bution of the signal approaches a normal distribution; also, the average number of times per

(2-22)

where fg is the frequency of the upper half-power point of the power spectral density of the signal.

For the system considered in this section, the pulse width is of the order of r^, . and the counting rate is of the order of 1/T^; so the product is т^/Т^, and this product is much greater than unity. Also, a single pulse is described approximately by.

(2-23)

so the upper cutoff frequency is, approximately,

The false trip rate is obtained by combining Equation (2-22) with Equation (2-24): .

rT. MO e-(sT-s)2/(2«s2) (2_.

. . rk.

Values of S and Og, for use in this equation, can be obtained by plotting S and <jg’ versus k, using Equations (2-15), (2-17), and (2-19), and then transforming the linear к scale of the plot to a logarithmic count-rate scale. Note that for this purpose the values of A and V do not have to be known, for they divide out in the exponent.