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Reconfigurable Computing has been making inroads in the front-end digital signal processing systems deployed at radio telescopes around the world. The National Radio Astronomy Observatory (NRAO) at Green Bank has developed a signal processing system expressly for pulsar search and timing observations. These observations are among the most demanding experiments in terms of real-time computational and data rate requirements. In this paper, we describe the application domain, the challenges in designing a system to meet these demands, and the resulting heterogeneous computing system.