Efficient gamma-ray signal decomposition analysis based on orthonormal transformation and fixed poles

Gamma-ray energy tracking is a new technique for the detection of gamma radiation. In such scheme, the individual interactions of the gamma rays with the germanium detectors are described by the energy, position and interaction time. Signal decomposition is the name of the procedure used to estimate the three-dimensional positions of the interactions based on pulse-shape analysis of the signals on the two-dimensional segments deposited on the faces of the detector. The present signal decomposition algorithm is computational intensive. For GRETINA, a detector being built based on this concept and that covers just a quarter of a sphere, 140 quad-processors are required to decompose 20,000 gamma interactions per second. In order to reduce the computational cost, we have conceptualized that the segments waveforms are generated by amplitude modulated discrete-time unit impulse. Projection of these waveforms into a more suitable basis reduces the computation costs while optimizing the same cost function. In this article we describe the framework for such projection, and we provide an example. For the present example, the computational cost was reduced by a factor of 5 times.