10 Signal Processing for Particle Detectors
465
10.6.2 Uncorrelated Sampling and Digital Filtering
Sampled data digital signal processing has become prevalent in detector systems for
gamma-ray and x-ray spectroscopy, for time projection chambers and in various
forms in particle physics. One of the advantages is that it provides flexibility
in the realization of mathematically optimal weighting functions. Optimal signal
processing cannot be achieved without some analogue functions. An anti-aliasing
filter is an essential part of the system. Its function is to limit the bandwidth prior
to sampling so as to satisfy the Nyquist-Shannon sampling criterion: the bandwidth
at the output of this filter must be no more than one half of the sampling frequency
(the “Nyquist limit”). If this is not satisfied, the noise at frequencies higher than
the Nyquist limit is shifted in frequency, i.e., (“aliased”) by undersampling, to the
frequencies below this limit. The resulting loss in S/N due to aliasing cannot be
recovered by any subsequent processing. The role of digital filtering is to create
optimized weighting functions in spectroscopic systems, and to enable an optimal
particle track measurement in tracking systems. In spite of the power of digital
processing, it is most efficient to cancel any long tails in the detector-preamplifier
response by analogue means. If the tail cancellation is performed digitally, much
larger numbers of samples have to be processed (deconvolved) for each event. For
asynchronous (uncorrelated) sampling in semiconductor detectors for gamma-ray
and x-ray spectroscopy see Refs. [37, 38]. In such systems optimum weighting
functions are of trapezoidal form as in Fig. 10.19, where the flat top allows uniform
weighting for a variable charge collection time.
10.6.3 Correlated Sampling
Correlated double sampling (CDS) is being used with many detectors in various
implementations and under different names. One of these is known as “baseline
subtraction”—taking a sample prior to the arrival of the usually unipolar signal (a
delayed signal or with the arrival time known). This case is illustrated in Fig. 10.16,
and it results in a bipolar weighting function, which defines quantitatively the effect
of CDS on the noise, as discussed in Sects. 10.4.2 and 10.4.3. Correlated double
sampling is an essential part of CCD signal processing in astronomy.
Signal processing by multiple correlated (synchronous) sampling has been used
for noble liquid calorimeters, such as the liquid argon electromagnetic calorimeter
in the ATLAS experiment, Refs. [39, 40].
465
10.6.2 Uncorrelated Sampling and Digital Filtering
Sampled data digital signal processing has become prevalent in detector systems for
gamma-ray and x-ray spectroscopy, for time projection chambers and in various
forms in particle physics. One of the advantages is that it provides flexibility
in the realization of mathematically optimal weighting functions. Optimal signal
processing cannot be achieved without some analogue functions. An anti-aliasing
filter is an essential part of the system. Its function is to limit the bandwidth prior
to sampling so as to satisfy the Nyquist-Shannon sampling criterion: the bandwidth
at the output of this filter must be no more than one half of the sampling frequency
(the “Nyquist limit”). If this is not satisfied, the noise at frequencies higher than
the Nyquist limit is shifted in frequency, i.e., (“aliased”) by undersampling, to the
frequencies below this limit. The resulting loss in S/N due to aliasing cannot be
recovered by any subsequent processing. The role of digital filtering is to create
optimized weighting functions in spectroscopic systems, and to enable an optimal
particle track measurement in tracking systems. In spite of the power of digital
processing, it is most efficient to cancel any long tails in the detector-preamplifier
response by analogue means. If the tail cancellation is performed digitally, much
larger numbers of samples have to be processed (deconvolved) for each event. For
asynchronous (uncorrelated) sampling in semiconductor detectors for gamma-ray
and x-ray spectroscopy see Refs. [37, 38]. In such systems optimum weighting
functions are of trapezoidal form as in Fig. 10.19, where the flat top allows uniform
weighting for a variable charge collection time.
10.6.3 Correlated Sampling
Correlated double sampling (CDS) is being used with many detectors in various
implementations and under different names. One of these is known as “baseline
subtraction”—taking a sample prior to the arrival of the usually unipolar signal (a
delayed signal or with the arrival time known). This case is illustrated in Fig. 10.16,
and it results in a bipolar weighting function, which defines quantitatively the effect
of CDS on the noise, as discussed in Sects. 10.4.2 and 10.4.3. Correlated double
sampling is an essential part of CCD signal processing in astronomy.
Signal processing by multiple correlated (synchronous) sampling has been used
for noble liquid calorimeters, such as the liquid argon electromagnetic calorimeter
in the ATLAS experiment, Refs. [39, 40].