Digital techniques for real-time pulse shaping in radiation measurements

Recursive algorithms for real-time digital pulse shaping in pulse height measurements have been developed. The differentiated signal from the preamplifier (exponential pulse) is amplified and then digitized . Digital data are deconvolved so that the response of the high-pass network is eliminated. The deconvolved pulse is processed by a time-invariant digital filter which allows trapezoidal/ triangular or cusp-like shapes to be synthesized . A prototype of a digital trapezoidal processor was built which is capable of sampling and processing digital data in real time at clock rates up to 50 MHz. In our previous work [1] we described recursive algorithms for real time pulse processing in high resolution spectroscopy . In that paper we also proposed a hardware configuration for a trapezoidal/ triangular pulse shaper . Although we presented some initial results obtained using a quasi-real time system, our further work has now resulted in the assembly and testing of a prototype that operates in true real time . In the discussion that follows, it is assumed that an exponential pulse is digitized. This signal can be obtained by CR differentiation of the signal from a reset type charge sensitive preamplifier or by differentiation with a pole-zero cancellation network of the signal from a resistive feedback preamplifier . This approach allows elimination of the do offset of the preamplifier signal and sufficient amplification of the short exponential pulses so that maximum utilization of the resolution of the sampling ADC can be achieved . We also include processing algorithms assuming a digitized step input signal . This situations holds when the output of a reset type preamplifier is directly digitized . In this case, the digital resolution of the processor depends on the noise characteristics of the signal and the number of samples per convolution window [2] . The practical realization of digital processors depends on the complexity of the algorithms they implement. Because of their suitability for real-time implementation, our initial efforts have concentrated on the use of two digital shaping algorithms [1]. The first allows symmetrical trapezoidal/triangular pulse shapes to be synthesized. The * Corresponding author. a AmptekInc., 6 DeAngelo Dr., Bedford, MA 01730, USA b The Uniuerstty ofMichigan, Department ofNuclearEngineering, Ann Arbor, MI 48109, USA 0168-9002/94/$07.00 C 1994 Elsevier Science B.V. All rights reserved SSDI0168-9002(94)00868-X second algorithm transforms an exponential or step pulse to a symmetrical pulse shape with the leading edge proportional to t2+ t. We call this shape "cusp-like ." 2. Trapezoidal digital pulse-shaper The recursive algorithm [1] that converts a digitized exponential pulse v(n) into a symmetrical trapezoidal pulse s(n) is given as d"t(n) = v(n) v(n -k) v(n l) + v(n -k1), (1) where vi(n), p(n), and s(n) are equal to zero for n < 0. The parameter M depends only on the decay time constant T of the exponential pulse and the sampling period Tctk of the digitizer, and is given by Mexp(Tctk/T) 1 For values of T/Tctk > 5, Eq . (5) can be approximated as MT/Tctk 0.5 . Eq. (1) can be expressed as a consequence of two The unit that implements the algorithm of Eq . (6) or Eq . (7) is depicted in Fig. 1 . We call this building block a III. INFORMATION PROCESSING identical procedures given by the set of equations dk(n) = v(n) v(n k), (6) dk,r(n) =dk(n) dk(n 1) . (7) p(n) =p(n 1) + dk.l (n), n >0, (2) r(n) =p(n) +Mdk,l(n), (3) s(n) = s(n 1) + r(n), n >0, (4)