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Digital Gamma-Ray Spectrometer User’s Manual 794380D / 0914
6
Figure 2. Typical Trapezoidal Weighting Function
(right) Arising from Detector Preamplifier Output
Signal (left).
Figure 3. Example of Weighting Function Output
Resulting from the Positive Slope Due to Low-
Frequency Noise (shown as a sine wave).
step signal is obtained by averaging the
digitized samples of the signal before and
after the step. M samples immediately after
the event are first ignored, to allow for a
maximum rise time of M times the sample
interval. N samples of the baseline prior to
the step pulse are averaged and then sub-
tracted from the average of N samples
taken after the step pulse. This simple
procedure produces a trapezoidal weight-
ing function with a rise time of N sample
intervals and a flattop of M sample intervals. The maximum value of the trapezoid output, occur-
ring at the end of the flattop, is the best estimate of the step height and therefore the gamma-ray
energy. With a proper selection of M and N, this filter is very nearly the optimum filter for a
system with noise arising only from the detector leakage (parallel noise) and the FET current
(series noise).
The trapezoidal filter is essentially inde-
pendent of dc offsets, since the averaging
and subtracting removes the dc component
of the signal. Unfortunately, it is just as sen-
sitive as analog filters to slowly varying
signals such as those produced in micro-
phonic noise. Figure 2 shows the output of
the trapezoidal filter is equal to the slope
of the baseline signal multiplied by the
full width at half maximum (FWHM) of
the trapezoid. If a step pulse were to be
measured on such a base-line, the filter
output value would be too great by an
error equal to the difference between the
average values A1 and A2. Since the
microphonic noise component in a signal
is approximately a sine wave, as illus-
trated in Fig. 3, the error induced can be
positive, negative, or zero. This error
signal adds to the width of the spectral
lines, appearing as degraded resolution
performance from the detector, and can
in many cases be a dominant noise
source, especially at lower energies.