Performance of Digital Signal Processors for Gamma Spectrometry

Introduction

With current analog spectrometer systems the detector signal is processed, shaped and filtered by a shaping amplifier and digitized by an analog-to-digital converter (ADC) at the very end of the analog signal processing chain. In digital signal processing (DSP) systems, the detector signal is digitized immediately after the preamplifier with only some minor signal conditioning added before digitization. The digitized data is then filtered and optimized using digital processing algorithms, and finally transferred to the MCA for storage, view and analysis.

DSP allows implementation of signal filtering functions that are not possible through traditional analog signal processing. Potential benefits include higher throughput, reduced sensitivity to ballistic deficit, adaptive processing, improved resolution and improved temperature stability for repeatable performance. After much theoretical study and computer simulation we and others have come to realize that throughput performance will be the most notable improvement. At low count rates the resolution is limited by the detector and will only improve marginally. However, since DSP filter algorithms require considerably less overall processing time, the resolution is expected to remain fairly constant over a large range of count rates whereas the resolution of analog systems typically degrades rather rapidly as the count rate increases.

Improved system stability is another potential benefit of DSP techniques. The detector signal is digitized much earlier in the signal processing chain and that minimizes the drift and instability normally associated with analog signal processing. However, the DSP spectrometers are not entirely digital. An analog preamp is required to convert the detector charge to a voltage signal and some additional analog front end conditioning is required to match the preamp output signal to the input of the digitizing ADC. Thus, the stability and integrity of the analog front end electronics continues to be important in achieving good system performance.

Theory

With digital signal processing, the input signal is sampled, multiplied and summed, using specific weighted values for each sample, to achieve the desired signal filtering.

If the sampled and processed signals are plotted as a function of time, they would appear to produce a specific shape such as Gaussian, triangular or trapezoidal. However, it is only necessary for the DSP processing algorithm to transfer the maximum calculated value to the MCA. When discussing DSP processing, references to weighting functions are used in place of the traditional shaping times to describe the filter and pulse shape behavior.

Triangular and trapezoidal weighting functions are commonly used in DSP spectrometers in use today. They are the best understood and easiest to implement. Triangular weighting functions are used for very small detectors. Trapezoidal weighting functions include a flat top and are employed for large detectors with long charge collection times or ballistic deficit effects.

Triangular/Trapezoidal filter implementations are a very close approximation of the optimal (cusp) filter but with a much shorter processing time. When compared to Gaussian shaping, triangular/trapezoidal weighting functions require approximately half the processing time to achieve comparable resolution performance. As a result, triangular/trapezoidal processing will provide a much higher throughput without significant resolution degradation.

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