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Ch 17 GK
Linear and Logical Pulse
Instruments Standard
Application Specific Integrated Circuits
Summary of Pulse Processing Units
Components common to many applications.
Pulse Counting Systems
Pulse Height Analysis
Digital Pulse Processing
 A. Analog-to-Digital Converters
 B Digital Shaping or Filtering
C. Pulse Shape Analysis
D. Digital Baseline Restoration
E. Deconvolution of Piled-Up Pulses
 System Involving Pulse Timing
a) Time Pick off methods
b) Measurements of Timing Properties
 c) Modular Instruments for Timing Measurements
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Pulse shape discrimination
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8-9:
Figure 17.33a shows the architecture of a module that carries out
one stage of the process described above.
At each clock cycle, the input voltage is momentarily held by a track-hold
(T /H) circuit.
A flash ADC carries out a digitization to n bits (n = 3 in the example
above), and that value serves as the digital output of the stage.
 That same value is supplied to a digital-to-analog converter (DAC) and
subtracted from the input voltage. The analog difference is sent through an
amplifier with gain of G corresponding to the magnification factor (G = 8 in
the example above), and the amplified analog voltage is passed on to the next
stage.
 A number of such modules can now be combined in a "multipass" or
"pipelined" arrangement illustrated in Fig. 17.33b, with all stages
synchronized by a common clock.
 The digital outputs of all the modules are combined in a logic block that
typically includes functions of bit alignment, error correction, and selfcalibration to form the overall digital result.
Because of the serial operation of the individual stages, the final result is
produced a number of clock cycles following the appearance of the
corresponding analog input.
 This "latency time" is the same for all samples and introduces some delay.
between input and output, but it does not affect the frequency of the
conversions.
Examples of some representative commercially available multipass or 17
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1. LINEAR TIME-INVARIANT FILTERS-8-10
The processes of shaping the signal pulse from a radiation detector can be
thought of as a filtering operation. For example, we have seen that the CR
differentiator is equivalent to a high-pass filter in the frequency domain. Most
(If the puIs" shxping op.-!ra'ions involve what are known as "linear timeinvariant filters." Their definition incorporates the restriction that the
properties of the filter are fixed and do not change with time. A "transversal
filter“ or "finite impulse response" filter is, by definition, limited to using input
data over the restricted time range L < t < 0, where L is the length of the
filter. This time range reaches backward from the present time simply because
only data that have already occurred can contribute. to the output at a
specific instant. The mathematical expression of the filtering
process then takes the form of the convolution integral
Set) = It vet') H(t - t') dt' (17.26)
t - L
where H(t) is called the impulse response function of the system. This function
reflects the operations carried out by the analog shaping networks in
conventional linear amplifiers.
The definitions given above apply to cases in which the input data appear as an
analog or smoothly varying function. That would be the case if we were dealing
with the standard analog voltage output produced by a radiation detector.
However, the fast digital converters described in the previous section Can be
applied to convert
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voltage into a series of digital samples. Once this conversion to digital data it
8-11: For the digital case, we start by assuming that the input signal has
been sampled series of values Veil that starts at i = O. The time period
between each sequential i simply represents the sampling period of the ADC.
For the filtering process, the lent of the impulse response function now
becomes a discrete set of weighting
H(O) ., . H(L). We will assume that this filter is of finite length L so that
the values of
are 0 for values of i < 0 or i > L. The convolution process equivalent to Eq.
(17.26)
then can be written
i=j
S(j) = 2: V(i)H(j - i) (17.21
i=j-L
where S(j) now represents the discrete series of output values produced by
the digital fiiltering process. To give a more graphic picture of this filtering
process, let us choose an examaple,,‘ which the filter consists of four
weighting factors, H(O) ... H(3), so the length of the filter' .
is equal to 3. Values of H{i) are by definition 0 outside this range. The input
consists of .'~.'.'.'
digital samples Veil, where we assume that the data begin at i = O.
Evaluating the sum giv ,.
in Eq. (17.27) for this example then gives, starting with the first nonzerO
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output value (j = tJ <04. The process continues producing output values for
8-12:
This convolution process is illustrated graphically in Fig. 17.34. For the
example shoWll the weighting factors are written along the upper line in
sequence from right to left.
[]Qfl H(2) I H(I) I H(O) I
I V(O) I V(I) I V(2) I V(3) I V(4) I V(S) I
S(O) ., V(O)H(O)
I H(3) I H(2) I H(I) I H(O) I
I V(O) I V(I) I V(2) I V(3) I V(4) I V(S) I
5(1) ., V(O)H(l) + V(l)H(O)
I H(3) I H(2) I H(I) I H(O) I
I V(O) I V(l) I V(2) I V(3) I V(4) I V(S) I
S(2) = V(O)H(2) + V(I)H(l) + V(2)H(0)
Figure 17.34 An illustration of a digital transversal filter. The filter element
are shown
(right to left) along the top line of each step, with the digitized data along
the lower line.
The output is formed by multiplying factors that are aligned and summing.
Directly below, the sampled input values are written starting at V(O). The
output is then given by multiplying each of these input voltages by the
weighting factor shown directly
above it and summing over the length of the filter. The first nonzero value
o
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the output
2. ADAPTIVE FILTERING-8-13
Digital pulse-processing systems, since they are controlled through
software, easily
allow the filter weighting functions to be customized to suit the
circumstances of the
measurement. In our previous discussion of pulse shaping, it was
illustrated that each
particular shaping choice results in a somewhat different theoretical
signal-to-noise
ratio (see Fig. 17.15). The choice of the optimum shaping method
depends on the magnitude
and nature of the noise that is present with the signal. Systems have
been
designed48- 51 that sample the detailed character of the noise
present with the signal and
then choose a weighting function that is optimal for the measured
results. This is one
. . r xp . .
adjust the shaping parameters.
Another example of adaptive filtering is applied to systems in which the
counting rate
changes substantially during a measurement. In many cases, one would 24
like to use shaping
I, Pulse Shape Analysis 8-14
Once the input waveform from the detector has been digitized,
measurements of its
detailed shape also become straightforward. We have seen many examples
of detectors in
which the detailed time profile of the current pulse reveals additional
information about
the nature of the event in the detector. Examples are in distinguishing
one type of radiation
from another, measuring the spatial position of an event, or distinguishing
pulses that
arise from multiple gamma-ray interactions from those that are due to a
single interaction
only. Sophisticated algorithms can be used to inspect the string of digital
data representing
each individual pulse so that rather subtle differences among them can be
distinguished. As
these operations become more complex, however, it is increasingly
difficult to carry them
out entirely in real time at high counting rates because of the limited time
available
between signal pulses. In such cases, the digital data can be sent to 25
D. Digital Baseline Restoration-8-15
In digital pUlse-processing systems, the baseline restoration process
described on
be accomplished by digitally sampling the baseline between pulses and
then
appropriate value from the measured pulse amplitude.52 Independent
baseline
can be obtained for each pulse that is processed or, alternatively, a
common
applied to a series of pulses between more widely spaced samples of
the baseline.
one would like multiple digital measurements of the baseline to be
taken for a
sample to enhance its accuracy, requiring a relatively long time interval
between
Long intervals occur less frequently than short ones, so there must be
a trade-off
the accuracy of the baseline measurement and the frequency with
which they can be
Digital filters that can be applied to these baseline samples to optimize
the lllt:aSllrem
accuracy are described in Ref. 53.
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E. Deconvolution of Piled-Up Pulses
8-16: Figure 17.35 Demonstration of the deconvolution of piled-Up pulses from
output of a
scintillation counter. The sampled data from the ADC operating at 100 MHz are
shown as
the series of points in both plots. In the bottom plot, an analytic fit to these da
using the
assumption that a single pulse shape should suffice results in a poor fit. In the t
plot, an
iterative procedure was used to fit two pulse components that allow the separati
of both
from the piled-up recorded data. (From Komar and Mak.54)
Chapter 17 Systems Involving Pulse TIming 659
carried by the two separated pulses can be obtained. Although the utility of this
type of
pile-up deconvolution has been demonstrated in off-line systems,54.55 the requi
processing
times are still sufficiently long that it is not yet routine in standard spectroscop
systems
in which the pulse analysis is carried out in real time.
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